v12 XSPEC software User's Guide
Below you will find brief information for software v12 XSPEC. The v12 XSPEC software is a command-driven interactive X-ray spectral-fitting program. It has been used to analyze data from a variety of X-ray observatories, including HEAO-1 A2, Einstein Observatory, EXOSAT, Ginga, ROSAT, BBXRT, ASCA, CGRO, IUE, RXTE, Chandra, XMM-Newton, Integral/SPI, Swift and Suzaku. The program is detector independent and can be used for any spectrometer.
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An X-Ray Spectral Fitting Package
User's Guide for version 12.8.1
Keith Arnaud, Ben Dorman, and Craig Gordon
HEASARC
Astrophysics Science Division
NASA/GSFC
Greenbelt, MD 20771
Aug 2013
ii
1.
1.1
1.2
How to find out more information .....................................................3
1.3
1.4
Acknowledgements ............................................................................4
1.5
2.
Spectral Fitting and XSPEC.....................................................................5
2.1
2.2
The Basics of Spectral Fitting ...........................................................5
2.3
The XSPEC implementation...............................................................6
2.4
A more abstract and generalized approach .....................................9
2.5
XSPEC Data Analysis .......................................................................10
2.5.1
2.5.2
INTEGRAL/SPI Data............................................................................... 11
2.6
3.
XSPEC Overview and Helpful Hints......................................................14
3.1
3.2
How to return to the XSPEC> prompt .............................................14
3.3
3.4
Commands ........................................................................................14
3.5
Issuing Commands...........................................................................15
3.6
Control Commands...........................................................................15
3.6.1
Query, chatter and shutting XSPEC up (somewhat) .......................... 16
3.6.2
Scripts and the Save command ........................................................... 16
3.6.3
3.7
Data Commands ...............................................................................17
3.7.1
Reading data and modifying calibration and auxiliary files .............. 17
3.7.2
Controlling channels being fitted ........................................................ 17
3.7.3
3.7.4
3.8
Model Commands .............................................................................18
3.8.1
Models with multiple responses and background models................ 19
3.9
Fitting Commands ............................................................................19
iii
3.9.1
What to do when you have Poisson data ............................................ 20
3.9.2
Binning and Grouping data .................................................................. 20
3.10
Plotting Commands ..........................................................................20
3.11
Setting Commands ...........................................................................21
3.12
Breaking With Ctrl-C.........................................................................22
3.13
Customizing XSPEC .........................................................................22
3.13.1
Customizing system-wide .................................................................... 25
4.
Walks through XSPEC ...........................................................................26
4.1
4.1.1
Brief Discussion of XSPEC Files ......................................................... 26
4.2
Fitting Models to Data: An Old Example from EXOSAT ................26
4.3
Simultaneous Fitting ........................................................................45
4.4
Multiple Models: a Background Modeling Example.......................49
4.5
Using XSPEC to Simulate Data: an Example for Chandra ............51
4.6
Producing Plots: Modifying the Defaults........................................54
4.7
INTEGRAL/SPI...................................................................................59
4.7.1
A Walk Through Example ..................................................................... 59
4.7.2
INTEGRAL Specific Command Line Scripts ....................................... 64
5.
XSPEC commands .................................................................................67
5.1
Summary of Commands...................................................................67
5.2
Description of Syntax .......................................................................72
5.3
Control Commands...........................................................................72
5.3.1
autosave: set frequency of saving commands................................... 72
5.3.2
chatter: set verboseness level ............................................................. 73
5.3.3
5.3.4
help: display manual or help for a specific command/theoretical
model component.................................................................................. 73
5.3.5
log: log the session output................................................................... 74
5.3.6
parallel: enable parallel processing for particular tasks in XSPEC. . 75
5.3.7
query: set a default answer for prompts in scripts ............................ 76
5.3.8
save: save the current session commands ........................................ 76
5.3.9
script: write commands to a script file ................................................ 77
5.3.10
show: output current program state.................................................... 77
5.3.11
syscall: execute a shell command....................................................... 78
5.3.12
tclout: create tcl variables from current state .................................... 80
5.3.13
tcloutr: tclout with return value............................................................ 85
5.3.14
time: print execution time..................................................................... 86
5.3.15
undo: undo the previous command .................................................... 86
5.3.16
version: print the version string .......................................................... 86
5.4
Data Commands ...............................................................................87
iv
5.4.1
arf: change the efficiency file for a given response ........................... 87
5.4.2
backgrnd: change the background file for a given spectrum ........... 87
5.4.3
corfile: change the correction file for a given spectrum ................... 88
5.4.4
cornorm: change the normalization of the correction file ................. 89
5.4.5
data: read data, background, and responses ..................................... 90
5.4.6
diagrsp: set a ‘perfect’ response for a spectrum ............................... 94
5.4.7
fakeit: simulate observations of theoretical models .......................... 94
5.4.8
ignore: ignore detector channels......................................................... 98
5.4.9
notice: notice data channels ................................................................ 99
5.4.10
response: change the detector response for a spectrum ............... 101
5.5
Fit Commands .................................................................................102
5.5.1
bayes: set up for Bayesian inference ................................................ 102
5.5.2
chain: run a Monte Carlo Markov Chain. ........................................... 103
5.5.3
error, uncertain: determine confidence intervals of a fit ................. 107
5.5.4
5.5.5
freeze: set parameters as fixed .......................................................... 110
5.5.6
ftest: calculate the F-statistic from two chi-square values ............. 110
5.5.7
goodness: perform a goodness of fit Monte-Carlo simulation ....... 111
5.5.8
margin: MCMC probability distribution. ............................................ 111
5.5.9
renorm: renormalize model to minimize statistic with current
5.5.10
steppar: generate the statistic “surface” for 1 or more parameters
5.5.11
thaw: allow fixed parameters to vary................................................. 113
5.5.12
weight: change weighting used in computing statistic ................... 114
5.6
Model Commands ...........................................................................114
5.6.1
addcomp: add component to a model............................................... 115
5.6.2
addline: add spectral lines to a model .............................................. 117
5.6.3
delcomp: delete a model component ................................................ 117
5.6.4
dummyrsp: create and assign dummy response ............................. 118
5.6.5
editmod: edit a model component ..................................................... 120
5.6.6
energies: specify new energy binning for model fluxes.................. 120
5.6.7
eqwidth: determine equivalent width ................................................ 122
5.6.8
5.6.9
gain: modify a response file gain....................................................... 124
5.6.10
identify: identify spectral lines........................................................... 127
5.6.11
initpackage: initialize a package of local models ............................. 128
5.6.12
lmod, localmodel: load a package of local models .......................... 129
5.6.13
lumin: calculate luminosities ............................................................. 129
5.6.14
mdefine: Define a simple model using an arithmetic expression... 130
5.6.15
model: define a theoretical model ..................................................... 132
5.6.16
modid: write out possible IDs for lines in the model. ...................... 137
5.6.17
newpar: change parameter values..................................................... 137
5.6.18
systematic: add a model-dependent systematic term to the variance
5.6.19
untie: unlink previously linked parameters ...................................... 140
5.7
Plot Commands ..............................................................................140
5.7.1
cpd: set current plotting device ......................................................... 140
v
5.7.2
5.7.3
iplot: make a plot, and leave XSPEC in interactive plotting mode.. 142
5.7.4
5.7.5
setplot: modify plotting parameters .................................................. 146
5.8
Setting Commands .........................................................................152
5.8.1
abund: set the Solar abundances ...................................................... 152
5.8.2
cosmo: set the cosmology ................................................................. 154
5.8.3
method: change the fitting method ................................................... 155
5.8.4
statistic: change the objective function (statistic) for the fit .......... 156
5.8.5
xsect: set the photoionization cross-sections ................................. 157
5.8.6
xset: set variables for XSPEC models. .............................................. 158
5.9
5.9.1
lrt: likelihood ratio test between two models.................................... 161
5.9.2
multifake: perform multiple fakeit iterations and save to file.......... 161
5.9.3
rescalecov: rescale the covariance matrix. ...................................... 162
5.9.4
simftest: estimate the F-test probability for adding a component.. 162
5.9.5
writefits: write information about the current fit and errors to a FITS
6.
XSPEC V12 Models ..............................................................................164
6.1
Alphabetical Summary of Models .................................................164
6.2
Additive Model Components (Sources) ........................................170
6.2.1
apec, vapec, vvapec: APEC emission spectrum ............................. 170
6.2.2
atable: tabulated additive model....................................................... 172
6.2.3
bapec, bvapec, bvvapec: velocity broadened APEC thermal plasma
6.2.4
bbody, zbbody: blackbody ................................................................ 175
6.2.5
bbodyrad: blackbody spectrum, area normalized............................ 176
6.2.6
bexrav: reflected e-folded broken power law, neutral medium....... 176
6.2.7
bexriv: reflected e-folded broken power law, ionized medium ....... 177
6.2.8
bknpower: broken power law ............................................................ 178
6.2.9
bkn2pow: broken power law, 2 break energies ................................ 178
6.2.10
bmc: Comptonization by relativistic matter ...................................... 179
6.2.11
bremss, vbremss, zbremss: thermal bremsstrahlung ..................... 180
6.2.12
c6mekl, c6vmekl, c6pmekl, c6pvmkl: differential emission measure
using Chebyshev representations with multi-temperature mekal .. 181
6.2.13
cemekl, cevmkl: plasma emission, multi-temperature using mekal
6.2.14
6.2.15
compbb: Comptonization, black body ............................................. 184
6.2.16
compLS: Comptonization, Lamb & Sanford .................................... 184
6.2.17
compmag: Thermal and bulk Comptonization for cylindrical
accretion onto the polar cap of a magnetized neutron star ............ 185
6.2.18
compPS: Comptonization, Poutanen & Svenson ............................. 185
6.2.19
compST: Comptonization, Sunyaev & Titarchuk ............................ 188
6.2.20
comptb: Thermal and bulk Comptonization of a seed blackbody-like
6.2.21
compTT: Comptonization, Titarchuk ................................................ 190
vi
6.2.22
cplinear: a non-physical piecewise-linear model for low count
background spectra. ........................................................................... 191
6.2.23
cutoffpl: power law, high energy exponential cutoff ....................... 193
6.2.24
disk: accretion disk, black body ........................................................ 193
6.2.25
diskbb: accretion disk, multi-black body components................... 193
6.2.26
Diskir: Irradiated inner and outer disk............................................... 194
6.2.27
diskline: accretion disk line emission, relativistic ........................... 195
6.2.28
diskm: accretion disk with gas pressure viscosity.......................... 195
6.2.29
disko: accretion disk, inner, radiation pressure viscosity .............. 195
6.2.30
diskpbb: accretion disk, power-law dependence for T(r) ............... 196
6.2.31
diskpn: accretion disk, black hole, black body ................................ 196
6.2.32
eplogpar: log-parabolic blazar model with
6.2.33
Eqpair, eqtherm, compth: Paolo Coppi's hybrid (thermal/non-
thermal) hot plasma emission models. ............................................. 197
6.2.34
equil, vequil: collisional plasma, ionization equilibrium.................. 199
6.2.35
expdec: exponential decay................................................................. 200
6.2.36
ezdiskbb: multiple blackbody disk model with zero-torque inner
6.2.37
gadem, vgadem: plasma emission, multi-temperature with gaussian
distribution of emission measure. ..................................................... 201
6.2.38
gauss, zgauss: gaussian line profile ................................................ 202
6.2.39
gnei, vgnei: collisional plasma, non-equilibrium, temperature
6.2.40
grad: accretion disk, Schwarzschild black hole ............................... 204
6.2.41
grbm: gamma-ray burst continuum ................................................... 205
6.2.42
kerrbb: multi-temperature blackbody model for thin accretion disk
around a Kerr black hole .................................................................... 205
6.2.43
kerrd: optically thick accretion disk around a Kerr black hole ....... 206
6.2.44
kerrdisk: accretion disk line emission with BH spin as free
6.2.45
laor: accretion disk, black hole emission line .................................. 207
6.2.46
laor2: accretion disk with broken-power law emissivity profile, black
6.2.47
logpar: log-parabolic blazar model ................................................... 208
6.2.48
lorentz: lorentz line profile.................................................................. 209
6.2.49
meka, vmeka: emission, hot diffuse gas (Mewe-Gronenschild) ..... 209
6.2.50
mekal, vmekal: emission, hot diffuse gas (Mewe-Kaastra-Liedahl)
6.2.51
mkcflow, vmcflow: cooling flow, mekal ........................................... 212
6.2.52
nei, vnei: collisional plasma, non-equilibrium, constant temperature
6.2.53
npshock, vnpshock: shocked plasma, plane parallel, separate ion,
electron temperatures......................................................................... 215
6.2.54
nsa: neutron star atmosphere ............................................................ 216
6.2.55
nsagrav: NS H atmosphere model for different g............................ 217
6.2.56
nsatmos: NS Hydrogen Atmosphere model with electron
conduction and self-irradiation .......................................................... 218
6.2.57
nsmax: Neutron Star Magnetic Atmosphere..................................... 219
6.2.58
nteea: non-thermal pair plasma ......................................................... 220
6.2.59
Nthcomp: Thermally comptonized continuum ................................. 221
vii
6.2.60
Optxagnf, optxagn: Colour temperature corrected disc and
energetically coupled Comptonisation model for AGN. .................. 222
6.2.61
pegpwrlw: power law, pegged normalization ................................... 224
6.2.62
pexmon: neutral Compton reflection with self-consistent Fe and Ni
6.2.63
pexrav: reflected powerlaw, neutral medium................................... 225
6.2.64
pexriv: reflected powerlaw, ionized medium ................................... 226
6.2.65
plcabs: powerlaw observed through dense, cold matter ............... 227
6.2.66
posm: positronium continuum.......................................................... 228
6.2.67
powerlaw, zpowerlw: power law photon spectrum ......................... 228
6.2.68
pshock, vpshock: plane-parallel shocked plasma, constant
6.2.69
raymond, vraymond: emission, hot diffuse gas, Raymond-Smith 230
6.2.70
redge: emission, recombination edge ............................................... 231
6.2.71
refsch: reflected power law from ionized accretion disk................. 232
6.2.72
sedov, vsedov: sedov model, separate ion/electron temperature.. 233
6.2.73
sirf: self-irradiated funnel .................................................................. 234
6.2.74
smaug: optically-thin, spherically-symmetric thermal plasma. ...... 235
6.2.75
srcut: synchrotron spectrum, cutoff power law ............................... 237
6.2.76
sresc: synchrotron spectrum, cut off by particle escape................ 238
6.2.77
step: step function convolved with gaussian ................................... 238
6.3
Multiplicative Model Components .................................................239
6.3.1
absori: ionized absorber..................................................................... 239
6.3.2
acisabs: Chandra ACIS q.e. decay..................................................... 239
6.3.3
cabs: Optically-thin Compton scattering. ......................................... 240
6.3.4
constant: energy-independent factor ............................................... 240
6.3.5
cyclabs: absorption line, cyclotron ................................................... 240
6.3.6
dust: dust scattering .......................................................................... 241
6.3.7
edge, zedge: absorption edge ........................................................... 241
6.3.8
etable: exponential tabular model ..................................................... 242
6.3.9
expabs: exponential roll-off at low E ................................................ 242
6.3.10
expfac: exponential modification....................................................... 242
6.3.11
gabs: gaussian absorption line.......................................................... 243
6.3.12
heilin: Voigt absorption profiles for He I series................................ 243
6.3.13
highecut, zhighect: high-energy cutoff ............................................. 243
6.3.14
hrefl: reflection model......................................................................... 244
6.3.15
lyman: Voigt absorption profiles for H I or He II Lyman series ....... 245
6.3.16
mtable: multiplicative tabular model ................................................. 245
6.3.17
notch: absorption line, notch ............................................................ 246
6.3.18
pcfabs, zpcfabs: partial covering fraction absorption .................... 246
6.3.19
phabs, vphabs, zphabs, zvphabs: photoelectric absorption ......... 247
6.3.20
plabs: power law absorption .............................................................. 247
6.3.21
pwab: power-law distribution of neutral absorbers ......................... 248
6.3.22
recorn: change correction norm for a spectrum .............................. 248
6.3.23
redden: interstellar extinction ............................................................ 248
6.3.24
smedge: smeared edge...................................................................... 249
6.3.25
spexpcut: super-exponential cutoff absorption .............................. 249
6.3.26
spline: spline modification ................................................................. 249
6.3.27
SSS ice: Einstein SSS ice absorption ............................................... 250
viii
6.3.28
swind1: absorption by partially ionized material with large velocity
6.3.29
tbabs, ztbabs, tbgrain, tbvarabs: ISM grain absorption................... 250
6.3.30
uvred: interstellar extinction, Seaton Law ........................................ 252
6.3.31
varabs, zvarabs: photoelectric absorption ....................................... 252
6.3.32
wabs, zwabs: photoelectric absorption, Wisconsin cross-sections
6.3.33
wndabs, zwndabs: photo-electric absorption, warm absorber....... 253
6.3.34
xion: reflected spectrum of photo-ionized accretion disk/ring ....... 254
6.3.35
zbabs: EUV ISM attenuation ............................................................... 256
6.3.36
zdust: extinction by dust grains ....................................................... 256
6.3.37
zigm: UV/Optical attenuation by the intergalactic medium. ............ 256
6.3.38
zredden: redshifted version of redden .............................................. 257
6.3.39
zsmdust: extinction by dust grains in starburst galaxies .............. 257
6.3.40
zvfeabs: photoelectric absorption with free Fe edge energy .......... 258
6.3.41
zxipcf: partial covering absorption by partially ionized material.... 258
6.4
Convolution Model Components...................................................258
6.4.1
6.4.2
cpflux: calculate photon flux.............................................................. 260
6.4.3
gsmooth: gaussian smoothing .......................................................... 260
6.4.4
ireflect: reflection from ionized material ........................................... 261
6.4.5
kdblur: convolve with the laor model shape..................................... 262
6.4.6
kdblur2: convolve with the laor2 model shape................................. 262
6.4.7
kerrconv: accretion disk line shape with BH spin as free parameter
6.4.8
lsmooth: lorentzian smoothing .......................................................... 263
6.4.9
partcov: partial covering..................................................................... 263
6.4.10
rdblur: convolve with the diskline model shape .............................. 264
6.4.11
reflect: reflection from neutral material............................................. 264
6.4.12
simpl: comptonization of a seed spectrum....................................... 265
6.4.13
Zashift: Redshift an additive model. .................................................. 265
6.4.14
Zmshift: Redshift a multiplicative model. ......................................... 266
6.5
Pile-Up Model Components ...........................................................266
6.5.1
pileup: CCD pile-up model for Chandra ............................................ 266
6.6
Mixing Model Components ............................................................267
6.6.1
ascac: ASCA surface brightness model ........................................... 267
6.6.2
projct: project 3-D ellipsoidal shells onto 2-D elliptical annuli ....... 268
6.6.3
suzpsf: suzaku surface brightness model ........................................ 269
6.6.4
xmmpsf: xmm surface brightness model ......................................... 270
Appendix A
The User Interface..............................................................272
Appendix B
Statistics in XSPEC............................................................281
Appendix C
Adding models to XSPEC..................................................290
Appendix D
Overview of PLT ...........................................................6.6-297
Appendix E
Associated programs.........................................................301
ix
Appendix F
Using The XSPEC Models Library In Other Programs ....303
Appendix G
Adding a Custom Chain Proposal Algorithm ..................306
Appendix H
Changes between v11 and v12 .........................................310
Appendix I
Older Release Notes............................................................313
Updates to the manual
Aug 2013 (v12.8.1 release)
New models: cpflux, heilin, lyman, zbabs.
New ‘pstat’ option for statistics, and new ‘#’ option for ‘whittle’ statistic.
‘setplot delete’ now has additional ‘all’ and range options.
‘fakeit’ has new ‘nowrite’ option.
‘parallel’ has new ‘steppar’ option.
Updates to ‘tclout’ command’s ‘chain’, ‘stat’, and ‘statmethod’ options.
The ‘improve’ command has been removed. It is no longer supported by the new Minuit library that is contained within v12.8.1.
New ATOMDB_VERSION Xspec.init setting mentioned in ‘apec’ and
‘bapec’ model docs.
New ‘DGNFLT’ and ‘DGFILT’ routines added to Appendix F.
Updates and revisions to ‘lrt’ and ‘simftest’ Tcl script commands.
Updated the default values for the ‘cosmo’ command.
Correction to gamma equation in lstat description of Appendix B.
Correction to par2, par9, and par10 description in ‘optxagn’ model.
In ‘chain’ command, Goodman-Weare is now the default.
Dec 2012 (v12.8.0 release)
Major rewrite and expansion of the ‘Walkthrough’ section, including examples with features that are new for v12.8.0.
New ‘parallel’ command.
New models compmag and comptb.
New ‘test’ option for the ‘statistic’ command, and new choices for statistics.
Enhanced the ‘Poisson data’ subsection of the ‘Overview’.
New <critical beta> option for ‘method’ and ‘fit’ commands.
New options for the ‘chain’ command: ‘type’ and ‘walkers’.
Added several sections in Appendix B for new statistics.
Added ‘plot goodness’ and ‘thin’ option to ‘plot chain’.
Note on grouped spectra added to fakeit.
xi
Note on uniform binning added to gsmooth model.
Updated description for simpl convolution model.
New tclout options: ‘tclout ignore’ and ‘tclout goodness sims’. Also added units to ‘tclout lumin’ description.
Added to ‘ftest’ a warning against using on a multiplicative component.
Added clarification on trace element abundances when using ‘apec’ and ‘vapec’ models.
Feb 2012 (v12.7.1 release)
Compps, eqpair, and nteea models descriptions modified for change in handling Compton reflection.
Corrections made to the model strings table for the ‘xset’ command.
Added RFLABD Fortran wrapper to the Appendix F table.
For ‘rmodel ‘ command, the ‘none’ option now also resets responses to their initial state.
Initpackage and lmod are now supported on Cygwin. The
“static_initpackage” workaround has been removed.
New ‘tclout’ options: nullhyp and rerror. Tclout eqwidth, flux, and lumin now also have an ‘errsims’ option for returning error values array.
New additive models: eplogpar, gadem, vgadem, logpar, optxagn, optxagnf, pexmon.
Correction to parameter description in kerrconv model.
Minor rewording in cflux model description to improve clarity.
For apec and bapec models, replaced ATOMDB 2.0 with version
2.0.1.
Correction to description of par3 in gabs model.
1
1. XSPEC
XSPEC is a command-driven, interactive, X-ray spectral-fitting program, designed to be completely detector-independent so that it can be used for any spectrometer. XSPEC has been used to analyze data from HEAO-1 A2, Einstein
Observatory, EXOSAT, Ginga, ROSAT, BBXRT, ASCA, CGRO, IUE, RXTE, Chandra,
XMM-Newton, Integral/SPI, Swift and Suzaku. There now over 1000 papers listed on
ADS which cite the Arnaud 1996 XSPEC reference.
This manual describes XSPEC v12, which is available on Linux (gcc 3.2.2 and later), MacOSX/Darwin (gcc 3.3 and later) , Solaris (2.6-9; WS6.0 and later). New users are advised to read
Chapter 2
, which introduces spectral fitting and the XSPEC approach,
Chapter 3
, which gives an overview of the program commands, and
Chapter
4
, which contains walkthroughs of XSPEC sessions. They should then experiment with
XSPEC and, if necessary, look up individual commands in
Chapter 5
, or descriptions of the spectral models in use, in
Chapter 6
.
The User Interface for XSPEC, which employs a
tcl
scripting shell and the
XSPEC parser are described in
Appendix A
. Users possessing X-ray spectra with small numbers of counts per bin are referred to
Appendix B
, which describes the C-statistic option. Users interested in adding their own models can read how to do so in
Appendix
C
.
Appendix D
describes the
PLT
plotting package which XSPEC currently uses for graphical output. Some of the tools (FTOOLS, fortran programs, scripts) that can operate on XSPEC files are listed in
Appendix E
. The XSPEC model library can be linked into other programs following the instructions in
Appendix F
.
Appendix G
describes how to use your own proposal distribution for Markov Chain Monte Carlo. Finally,
Appendix H
includes some notes on the changes between XSPEC v11 and v12.
1.1 New in v12.8.1
New features:
New models:
cpflux - a variant of cflux for photon flux.
heilin - Voigt absorption profiles for the HeI series
lyman - Voigt absorption profiles for the HI or HeII series
zbabs - EUV ISM attenuation
A new statistic, pgstat, has been added for the case of Poisson-distributed data with a Gaussian-distributed background. The whittle statistic can now be used when fitting averaged power density functions by appending an integer (so eg whittle5 is the statistic to use when fitting a pdf constructed by averaging those from 5 observations).
The old CERN Minuit library, which is used for the migrad, minim, monte, and simplex fitting methods and the improve command, has been replaced by the new version. The minim and monte methods are no longer supported and the new version does not include an improve command. The output from the migrad and simplex fitting methods now looks the same as that from the leven method.
Note however that the rules for when to write intermediate fit results are not
2
directly comparable so do not provide a measure of the relative speed of the methods.
Fakeit now has a 'nowrite' option to generate fake spectra without producing output files. This is also now available in the multifake.tcl script command.
Parallel processing capability has been added to the steppar command and can be invoked using the parallel command.
Markov Chain Monte Carlo (the chain command) now uses the Goodman-Weare algorithm by default. Previously the default was Metropolis-Hastings.
After a chain run, the best-fit parameters and statistic are now displayed with
"chain info", and are available through the "tclout chain" option.
The default atom_db version used in apec models may now be modified with the
ATOMDB_VERSION keyword in the user's Xspec.init file.
Steppar now has a 'delta' option for performing grids centered on the best-fit parameters.
The 'setplot delete' option has been enhanced to allow removal of all or a range of commands.
For external programs calling XSPEC, new wrapper functions have been added for retrieving XFLT keywords from data files.
Norm parameters are now set with a default 'soft' upper limit below their 'hard' upper limit.
In PyXspec, the Fit.statMethod and statTest attributes can now be set for individual spectra.
Enhancements previously released as patches to 12.8.0:
AtomDB has been upgraded to version 2.0.2.
The tclout 'stat' and 'statmethod' options can now retrieve the test statistic as well as the fit statistic.
The simftest Tcl script command now takes an optional filename argument for output.
Attributes added to PyXspec classes: Xset.parallel, Fit.statTest.
All bug fixes to v12.8.0 released as patches are included in v12.8.1. In addition the following problems have been corrected:
The command history file xspec.hty (in the user's ~/.xspec directory) is now updated when exiting XSPEC with the 'quit' command. Previously it was only updated when exiting with 'exit'.
The 'chain' command can now read/write files in ASCII format when running in the default Goodman-Weare mode. Previously this feature was only available for Metropolis-Hastings chains.
Fix to an array access error in the nthcomp model.
PyXspec fix removes error messages generated when accessing response parameters in Python versions 2.6.x.
3
1.2 How to find out more information
XSPEC is distributed and maintained under the aegis of the GSFC High Energy
Astrophysics Science Archival Research Center (HEASARC). It can be downloaded as part of HEAsoft
http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/download.html
XSPEC is available either as binaries or source. We recommend downloading the source and compiling locally to avoid potential system library conflicts and allow installation of any patches we release. If you have any problems compiling or running XSPEC please email us at
The XSPEC Web page comprises links to the anonymous ftp site, a Web version of the manual, and several useful documents, including a list of known bugs. The Web address is
http://xspec.gsfc.nasa.gov/
with the list of issues and available patches at
http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/bugs.html
and additional models which can be added at
http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/newmodels.html
Further useful information can be found on the XSPEC Wiki at
https://astrophysics.gsfc.nasa.gov/XSPECwiki/XSPECPage
and the xspector blog at
http://xspector.blogspot.com/
1.3 History
The first version of XSPEC was written in 1983 at the Institute of Astronomy,
Cambridge, under VAX/VMS by Rick Shafer. It was written to perform spectral analysis of data from the ESA EXOSAT X-ray observatory, which was launched that year.
XSPEC is a descendant of a series of spectral-fitting programs written at NASA/Goddard
Space Flight Center for the OSO-8, HEAO-1 and EO missions. The initial design was the fruit of many discussions between Rick Shafer and Andy Szymkowiak. Rick Shafer subsequently joined the EXOSAT group, where he enhanced the VAX/VMS version in collaboration with Frank Haberl. Meanwhile, Keith Arnaud ported XSPEC to a
Sun/UNIX operating system. The two implementations of XSPEC diverged for several years until a determined and coordinated effort was made to recover a single version. The results of that effort was XSPECv6, described in the first edition of this manual.
Subsequent editions have covered later versions of the program. In recent years XSPEC has become the de facto standard for X-ray spectroscopic analysis for the ROSAT mission and the de jure standard for the BBXRT, ASCA, and RXTE missions. It is now in extensive use for all current X-ray and gamma-ray missions. An extensive reengineering effort was started in the fall of 1998 to improve long-term maintainability,
4
allow significant new features to be added, and support the analysis of spectra from coded-mask instruments.
1.4 Acknowledgements
This project would not have been possible without ignoring the advice of far more people than can be mentioned here. We would like to thank all our colleagues for their suggestions, bug reports, and (especially) source code. The GSFC X-ray astronomy group are particularly thanked for their patience exhibited while functioning as the beta test site for new releases. The initial development of XSPEC was funded by a Royal Society grant to Prof. Andy Fabian and subsequent development was partially funded by the European
Space Agency's EXOSAT project and is now funded by the HEASARC at NASA/GSFC.
1.5 References
Arnaud, K.A., 1996, Astronomical Data Analysis Software and Systems V, eds. G. Jacoby and J. Barnes,p17, ASP Conf. Series volume 101.
Dorman, B., and Arnaud, K. A. 2001, Astronomical Data Analysis Software and Systems X eds. F.R. Harnden, Jr., F.A. Primini, and H. E. Payne, vol. 238, p. 415
Dorman, B., Arnaud, K. A., and Gordon, C. A. XSPEC12: Object-Oriented X-Ray Data
Analysis, AAS HEAD meeting No. 35, #22.10
5
2. Spectral Fitting and XSPEC
2.1 Introduction
This chapter comprises a brief description of the basics of spectral fitting, their application in XSPEC, and some helpful hints on how to approach particular problems.
We then provide more details on the way XSPEC provides flexibility in its approach to the minimization problem. We also describe the data formats accepted.
2.2 The Basics of Spectral Fitting
Although we use a spectrometer to measure the spectrum of a source, what the spectrometer obtains is not the actual spectrum, but rather photon counts (C) within specific instrument channels, (I). This observed spectrum is related to the actual spectrum of the source (f(E)) by:
0
( ) ( , )
Where R(I,E) is the instrumental response and is proportional to the probability that an incoming photon of energy E will be detected in channel I. Ideally, then, we would like to determine the actual spectrum of a source, f(E), by inverting this equation, thus deriving
f(E) for a given set of C(I). Regrettably, this is not possible in general, as such inversions tend to be non-unique and unstable to small changes in C(I). (For examples of attempts to circumvent these problems see Blissett & Cruise 1979; Kahn & Blissett 1980; Loredo
& Epstein 1989).
The usual alternative is to choose a model spectrum, f(E), that can be described in terms of a few parameters (i.e., f(E,p1,p2,...)), and match, or “fit” it to the data obtained by the spectrometer. For each f(E), a predicted count spectrum (C
p
(I)) is calculated and compared to the observed data (C(I)). Then a “fit statistic'” is computed from the comparison and used to judge whether the model spectrum “fits” the data obtained by the spectrometer.
The model parameters then are varied to find the parameter values that give the most desirable fit statistic. These values are referred to as the best-fit parameters. The model spectrum, f
b
(E), made up of the best-fit parameters is considered to be the best-fit model.
2
, defined The most common fit statistic in use for determining the “best-fit” model is as follows:
2
C I C p
I
2
I
2
where σ(I) is the (generally unknown) error for channel I (e.g., if C(I) are counts then σ(I) is usually estimated by
Once a “best-fit” model is obtained, one must ask two questions:
1. How confident can one be that the observed C(I) can have been produced by the best-fit model f
b
(E)? The answer to this question is known as the “goodness-of-fit”
6
of the model. The
2
statistic provides a well-known-goodness-of-fit criterion for a given number of degrees of freedom (ν, which is calculated as the number of channels minus the number of model parameters) and for a given confidence level.
If
2
exceeds a critical value (tabulated in many statistics texts) one can conclude that f
b
(E) is not an adequate model for C(I). As a general rule, one wants the
“reduced
2
” (
to be approximately equal to one (
. A reduced
2 that is much greater than one indicates a poor fit, while a reduced
2
that is much less than one indicates that the errors on the data have been over-estimated. Even if the best-fit model (f that f
b b
(E)) does pass the “goodness-of-fit” test, one still cannot say
(E) is the only acceptable model. For example, if the data used in the fit are not particularly good, one may be able to find many different models for which adequate fits can be found. In such a case, the choice of the correct model to fit is a matter of scientific judgment.
2. For a given best-fit parameter (p1), what is the range of values within which one can be confident the true value of the parameter lies? The answer to this question is the “confidence interval” for the parameter.
The confidence interval for a given parameter is computed by varying the parameter value until the
2
increases by a particular amount above the minimum, or “bestfit” value. The amount that the critical
2
is allowed to increase (also referred to as the parameters whose confidence space is being calculated. The critical common cases are given in the following table (from Avni, 1976):
Confidence Parameters
2.3 The XSPEC implementation
To summarize the preceding section, the main components of spectral fitting are as follows:
A set of one or more observed spectra measurements B(I) where available
D
with background
The corresponding instrumental responses
R
A set of model spectra
M
7
These components are used in the following manner:
Choose a parameterized model which is thought to represent the actual spectrum of the source.
Choose values for the model parameters.
Based on the parameter values given, predict the count spectrum that would be detected by the spectrometer in a given channel for such a model.
Compare the predicted spectrum to the spectrum actually obtained by the instrument.
Manipulate the values of the parameters of the model until the best fit between the theoretical model and the observed data is found.
Then calculate the “goodness” of the fit to determine how well the model explains the observed data, and calculate the confidence intervals for the model's parameters.
This section describes how XSPEC performs these tasks.
C(I): The Observed Spectrum
To obtain each observed spectrum, , XSPEC uses two files: the data
(spectrum) file, containing D(I), and the background file, containing B(I). The data file tells XSPEC how many total photon counts were detected by the instrument in a given channel. XSPEC then uses the background file to derive the set of backgroundsubtracted spectra C(I) in units of counts per second. The background-subtracted count rate is given by, for each spectrum:
b
-
a t b a t
( )
D
( )
B
where ( ) and
B(I)
are the counts in the data and background files; are the exposure times in the data and background files;
b
D(I)
and
b
B(I)
,
a
D(I)
and
a
B(I)
are the background and area scaling values from the spectrum and background respectively, which together refer the background flux to the same area as the observation as necessary. When this is done, XSPEC has an observed spectrum to which the model spectrum can be fit.
R(I,E): The Instrumental Response
Before XSPEC can take a set of parameter values and predict the spectrum that would be detected by a given instrument, XSPEC must know the specific characteristics of the instrument. This information is known as the detector response. Recall that for each spectrum the response
R(I,E)
is proportional to the probability that an incoming photon of energy E will be detected in channel I. As such, the response is a continuous function of E. This continuous function is converted to a discrete function by the creator of a response matrix who defines the energy ranges
8
R
( , )
D
E
J
( , )
E
J
1
E
J
E
J
1
XSPEC reads both the energy ranges, E , and the response matrix ( , ) a response file in a compressed format that only stores non-zero elements. XSPEC also includes an option to use an auxiliary response file, which contains an array multiplied into R I J as follows:
R
D
( , )
R
D
( , )
A J
D
( )
This array is designed to represent the efficiency of the detector with the response file representing a normalized Redistribution Matrix Function, or RMF. Conventionally, the response is in units of cm
2
.
M(E): The Model Spectrum
The model spectrum, ( ) , is calculated within XSPEC using the energy ranges defined by the response file :
M
( )
D
E
E
J
J
1
and is in units of photons cm
-2 s
-1
. XSPEC allows the construction of composite models consisting of additive components representing X-ray sources (e.g., power-laws, blackbodys, and so forth), multiplicative components, which modify additive components by an energy-dependent factor (e.g., photoelectric absorption, edges, ...). Convolution and mixing models can then perform sophisticated operations on the result. Models are defined in algebraic notation.
For example, the following expression:
phabs (power + phabs (bbody))
defines an absorbed blackbody, phabs(bbody), added to a power-law, power. The result then is modified by another absorption component, phabs. For a list of available models, see
Chapter 6
.
Fits and Confidence Intervals
Once data have been read in and a model defined, XSPEC uses a fitting algorithm to find the best-fit values of the model parameter. The default is a modified Levenberg-
Marquardt algorithm (based on CURFIT from Bevington, 1969). The algorithm used is local rather than global, so be aware that it is possible for the fitting process to get stuck in a local minimum and not find the global best-fit. The process also goes much faster
(and is more likely to find the true minimum) if the initial model parameters are set to sensible values.
The Levenberg-Marquardt algorithm relies on XSPEC calculating the 2 nd derivatives of the fit statistic with respect to the model parameters. By default these are calculated analytically, with the assumption that the 2 nd
derivatives of the model itself
9
may be ignored. This can be changed by setting the
USE_NUMERICAL_DIFFERENTIATION flag to “true” in the Xspec.init initialization file, in which case XSPEC will perform numerical calculations of the derivatives (which are slower).
At the end of a fit, XSPEC will write out the best-fit parameter values, along with estimated confidence intervals. These confidence intervals are one sigma and are calculated from the second derivatives of the fit statistic with respect to the model parameters at the best-fit. These confidence intervals are not reliable and should be used for indicative purposes only.
XSPEC has a separate command (error or uncertain) to derive confidence intervals for one interesting parameter, which it does by fixing the parameter of interest at a particular value and fitting for all the other parameters. New values of the parameter of interest are chosen until the appropriate delta-statistic value is obtained. XSPEC uses a bracketing algorithm followed by an iterative cubic interpolation to find the parameter value at each end of the confidence interval.
To compute confidence regions for several parameters at a time, XSPEC can run a grid on these parameters. XSPEC also will display a contour plot of the confidence regions of any two parameters.
2.4 A more abstract and generalized approach
The sections above provide a simple characterization of the problem. XSPEC actually operates at a more abstract level and considers the following:
Given a set of spectra C(I), each supplied as a function of detector channels, a set
of theoretical models {M(E)
j
} each expressed in terms of a vector of energies together
with a set of functions {R(I,E)
j
} that map channels to energies, minimize an objective
function S of C, {R(I,E)
i
}, {M(E)
j
} using a fitting algorithm, i.e.
)
k k
M R j k j
In the default case, this reduces to the specific expression for single source
2
fitting of a
S
2
i
(
C i
R i
M i
)
2
where
i
runs over all of the channels in all of the spectra being fitted, and using the Levenberg-Marquadt algorithm to perform the fitting.
This differs from the previous formulation in that the operations that control the fitting process make fewer assumptions about how the data are formatted, what function is being minimized, and which algorithm is being employed. At the calculation level,
XSPEC requires spectra, backgrounds, responses and models, but places fewer constraints as to how they are represented on disk and how they are combined to compute
10
the objective function (statistic). This has immediate implications for the extension of
XSPEC analysis to future missions.
New data formats can be implemented independently of the existing code, so that they may be loaded during program execution. The ‘data format’ includes the specification not only of the files on disk but how they combine with models.
Multiple sources may be extracted from a spectrum. For example, it generalizes the fitting problem to minimizing, in the case of the
2
statistic,
2
i
C i
j
R ij
M j
2
and j runs over one or more models. This allows the analysis of coded aperture data where multiple sources may be spatially resolved.
Responses, which abstractly represent a mapping from the theoretical energy space of the model to the detector channel space, may be represented in new ways. For example, the INTEGRAL/SPI responses are implemented as a linear superposition of 3
(fixed) components.
Instead of explicitly combining responses and models through convolution
XSPEC places no prior constraint on how this combination is implemented. For example, analysis of data collected by future large detectors might take advantage of the form of the instrumental response by decomposing the response into components of different frequency.
Other differences of approach are in the selection of the statistic of the techniques used for deriving the solution. Statistics and fitting methods may be added to XSPEC at execution time rather than at installation time, so that the analysis package as a whole may more easily keep apace of new techniques.
2.5 XSPEC Data Analysis
XSPEC is designed to support multiple input data formats. Support for the earlier SF and
Einstein FITS formats are removed. Support for ASCII data is planned, which will allow
XSPEC to analyze spectra from other wavelength regions (optical, radio) transparently to the user.
2.5.1 OGIP Data
The OGIP data format both for single spectrum files (Type I) and multiple spectrum files
(Type II) is fully supported. These files can be created and manipulated with programs described in
Appendix E
and the provided links. The programs are described more fully in
George et al. 1992
.
(the directories below refer to the
HEAsoft
distribution).
Spectral Data: callib/src/gen/rdpha2.f, wtpha3.f
Responses: callib/src/gen rdebd4.f, rdrmf5.f, wtebd4.f, wtrmf5.f. The “rmf” programs read and write the RMF extension, while the “ebd” programs write an extension called EBOUNDS that contains nominal energies for the detector channels.
11
Auxiliary Responses: callib/src/gen rdarf1.f, and wtarf1.f
2.5.2 INTEGRAL/SPI Data
XSPEC also includes an add-in module to read and simulate INTEGRAL/SPI data, which can be loaded by the user on demand. The INTEGRAL/SPI datasets are similar to OGIP
Type II, but contain an additional FITS extension that stores information on the multiple files used to construct the responses.
The Spectrometer (
SPI
) is a coded-mask telescope, with a 19element Germanium detector array. The Spectral resolution is ~500, and the angular resolution is ~3
. Unlike focusing instruments however, the detected photons are not directionally tagged, and a statistical analysis procedure, using for example crosscorrelation techniques, must be employed to reconstruct an image. The description of the
XSPEC analysis approach
which follows assumes that an image reconstruction has
already been performed; see the SPIROS utility within the INTEGRAL offline software analysis package (
OSA
), OR, the positions on the sky of all sources to be analyzed are already known (which is often the case). Those unfamiliar with INTEGRAL data analysis should refer to the
OSA documentation
. Thus, the INTEGRAL/SPI analysis chain must be run up to the event binning level [if the field of view (FoV) source content is known, e.g. from published catalogs, or from IBIS image analysis], or the image reconstruction level. SPIHIST should be run selecting the "PHA" output option, and selecting detectors 0-18. This will produce an OGIP standard
type-II PHA spectral file
, which contains multiple, detector count spectra. In addition, the SPIARF procedure should be run once for each source to be analyzed, plus one additional time to produce a special response for analysis of the instrumental background. If this is done correctly, and in the proper sequence, SPIARF will create a table in the PHA-II spectral file, which will associate each spectrum with the appropriate set of response matrices. The response matrices are then automatically loaded into XSPEC upon execution of the data command in a manner very transparent to the user. You will also need to run SPIRMF (unless you have opted to use the default energy bins of the template SPI RMFs). Finally, you will need to run the FTOOL SPIBKG_INIT. Each of these utilities - SPIHIST, SPIARF,
SPIRMF and SPIBKG_INIT - are documented elsewhere, either in the INTEGRAL or
(for SPIBKG_INIT the HEAsoft) software documentation.
There are several complications regarding the spectral de-convolution of codedaperture data. One already mentioned is the source confusion issue; there may be multiple sources in the FoV, which are lead to different degrees of shadowing on different detectors. Thus, a separate instrumental response must be applied to a spectral model for each possible source, for each detector. This is further compounded by the fact that
INTEGRAL's typical mode of observation is “dithering.” A single observation may
1
This is one of several possible analysis paths. The most commonly used method involves the SPIROS utility in spectral extraction mode, which leads to a effective-area corrected, background subtracted "pseudo-count" spectra. A (single) customized XSPEC RMF is then applied to approximate the photon-to-count redistribution for model fitting.
12
consist of ~10's of individual exposures at raster points separated by ~2
. This further enumerates the number of individual response matrices required for the analysis. If there are multiple sources in the FoV, then additional spectral models can be applied to an additional set of response matrices, enumerated as before over detector and dither pointing. This capability - to model more than one source at a time in a given Chi-Square
(or alternative) minimization procedure - did not exist in previous versions of XSPEC.
For an observation with the INTEGRAL/SPI instrument, where the apparent detector efficiency is sensitive to the position of the source on the sky relative to the axis of the instrument, the
2 statistic is:
2
p d I
D
j E
R j
( , )
j
;
x
s
B I
x
2 where:
run over instrument pointings and detectors;
j
E
enumerates the sources detected in the field at different position indexes the energies in the source model
x s
parameters of the source model, which is combined with the response
x b
parameters of the background model, expressed as a function of detector channel
Examination of this equation reveals one more complication; the term B represents the background, which, unlike for chopping, scanning or imaging experiments, must be solved for simultaneously with the desired source content. The proportion of background-to-source counts for a bright source such as the Crab is ~1%.
Furthermore, the background varies as a function of detector, and time (dither-points), making simple subtraction implausible. Thus, a model of the background is applied to a special response matrix, and included in the de-convolution algorithm.
2.6 References
Arnaud, K.A., George, I.M., Tennant, A.F., 1992. Legacy, 2, 65.
Avni, Y., 1976. ApJ, 210, 642.
Bevington, P.R., 2002, 3 rd
Edition. Data Reduction and Error Analysis for the
Physical Sciences, McGraw-Hill.
Blissett, R.J., Cruise, A.M., 1979. MNRAS, 186, 45.
George, I.M., Arnaud, K.A., Pence, W., Ruamsuwan, L., 1992. Legacy, 2, 51.
Kahn, S.M., Blissett, R.J., 1980. ApJ, 238, 417.
Loredo, T.J., Epstein, R.I., 1989. ApJ, 336, 896.
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992.
Numerical Recipes (2nd edition), p687ff, CUP.
Wheaton, W.A. et.al., 1995. ApJ, 438, 322.
13
14
3. XSPEC Overview and Helpful Hints
3.1 Syntax
XSPEC is a command-driven, interactive program. You will see a prompt
XSPEC12> whenever input is required. Command recall and inline editing are available using the arrow keys. XSPEC uses Tcl as its user interface, providing looping, conditionals, file
I/O and so on. For further details of the Tcl syntax, consult the “Description of Syntax” section, the
User Interface
appendix, and links therein.
3.2 How to return to the XSPEC> prompt
The string /* acts as an emergency escape back to the XSPEC prompt. This string in answer to any question should bounce XSPEC out of whatever it is doing and back to the command prompt.
3.3 Getting Help
Quick help: If you are uncertain about command syntax, typing a command followed by a “?” will print a one-line summary. The
help
command:
XSPEC12> help without arguments will bring up the full XSPEC manual in a PDF document reader (e.g. Adobe
Acrobat Reader), or will open a browser to the XSPEC manual home page either locally or on the HEASARC site. See “Customizing XSPEC” later in this section to see how to select between these options, and how to assign a PDF reader and web browser to XSPEC. Typing
XSPEC12> help <command> will display the manual section corresponding to <command>. Help for individual model components can be displayed by
XSPEC12> help model <modelName> if all else fails you can e-mail your questions to the XSPEC team at
3.4 Commands
XSPEC commands can be divided into 6 categories: Control, Data, Model,
Fitting, Plotting and Setting, as follows:
Control commands include items such as controlling logging, obtaining help, executing scripts, and other miscellaneous items to do with the program control rather than manipulating data or theoretical models.
Data commands load spectral data and calibration data such as backgrounds and responses, and specify channel ranges to be fit.
15
Model commands define and manipulate theoretical models and their parameters, and compute additional information such as fluxes or line identifications.
Fit commands initiate the fitting routines, control the parameter set, perform statistical tests and compute confidence levels.
Plot commands generate about 50 different kinds of 2-dimensional plots
Setting commands change a variety of XSPEC internals which control details of models, statistics, and fitting methods.
These command types are summarized below. For full details see Chapter 5.
3.5 Issuing Commands
In an interactive session, the command interpreter accepts the shortest unambiguous abbreviation for any command. Since the interpreter is built on the Tcl language, some possible XSPEC command abbreviations might coincide with both
XSPEC and Tcl commands. In this case, the interpreter will print the multiple possibilities and stop. Command abbreviations may be specified in a start-up script
($HOME/.xspec/xspec.rc) – see
Appendix A
for details.
Inside a script, command abbreviations are not recognized. This behavior can be overridden but we do not recommended it: however, specific abbreviations can be defined in the custom startup script.
Operating-system commands can be given from within XSPEC simply by typing the command, as at the shell prompt: however, if wild cards are needed (e.g. ls *.pha) the operating system command must be preceded by syscall. Note that an XSPEC abbreviation which corresponds to a system command will run the latter.
3.6 Control Commands
Control commands include those for: controlling parallel operations: parallel writing program information:
log
, (save session to an ASCII file)
script
(record a set of commands),
save
(save commands needed to restore the current program state),
autosave
(automatically run the save command at specified intervals); controlling program output:
chatter
(control the amount of program output),
query
(give an automatic response to prompts),
tclout
and
tcloutr
(create Tcl variables for manipulation in scripts) displaying status information:
show
,
time
, and
version
ending the session:
exit
(or quit) displaying online help
help
and ‘?”. Help can be given either in summary, in specific manual pages, a manual section, or the entire manual.
16
3.6.1 Query, chatter and shutting XSPEC up (somewhat)
The
fit
command will run a certain number of iterations and then query the user whether he or she wants to continue. While useful under most circumstances, the constant questioning can be a pain if one leaves XSPEC running and expects to find it finished when one gets back, or if one habitually runs scripts. One way around this problem is to reset the number of iterations before the question is asked by giving a single argument.
For example,
XSPEC12> fit 100 will run 100 iterations before asking a question.
A more drastic solution is to use the
query
command.
XSPEC12> query yes
This will suppress all questions and assume that their answer is yes, while
XSPEC12> query no will suppress all questions but assume that their answer is no.
The amount of output that XSPEC writes is set by the
chatter
command, which takes two arguments applying to the terminal and to the log file.
3.6.2 Scripts and the Save command
XSPEC commands can be written into a file and then executed by entering
XSPEC12> @filename
Alternatively, from the shell prompt
% xspec - filename & for batch execution (remember to end the script in file filename.xcm with exit if you want the program to terminate after completion!). Note that the default suffix for xspec scripts is .xcm
The
save
command writes the current XSPEC status to a command file, which later can be run to reset XSPEC to the same configuration. XSPEC has a mechanism to save the current status automatically. This is controlled through the
autosave
command.
This command is very useful when reading a large number of data sets and/or fitting complicated models. If autosaving is operating (the default) then the equivalent of
XSPEC12> save all xautosav.xcm
is run after each command, so if a disaster occurs it is possible to recover.
3.6.3 Miscellaneous
Information on the current XSPEC status can be printed out using the
show
command. The
time
command writes out system-timing information, and the version command writes out the version number and the build time and date. Finally, XSPEC can be terminated with the
exit
or
quit
commands.
17
3.7 Data Commands
XSPEC is designed to allow complicated, multi-instrument analysis, so most commands can take arguments specifying more than one data set. Arguments in XSPEC are separated by either blanks or commas. A single argument can define a range. The ranges are delimited by a dash (–). A colon (:) is used to separate ranges (e.g., the phrase
1–2:11–24 refers to channels 11–24 in files 1 and 2).
3.7.1 Reading data and modifying calibration and auxiliary files
XSPEC reads in spectra from spectral files using the
data
command. Several datasets may be specified in one command. Several datasets may be stored in a single file and accessed separately. A particular dataset in use may be replaced by another or dropped entirely. The input data file contains pointers to background, redistribution and auxiliary response files, but these pointers may be overridden by the
backgrnd
,
response
, and
arf
commands. All these commands have the same syntax as
data
. An auxiliary background file, called the correction file (an absolute subtraction with zero variance), also can be included using the
corfile
command. Its use is described in the section on fitting. The current response can be replaced by a diagonal version using
diagrsp
. A dummy response for testing purposes can be defined using
dummyrsp
.
3.7.2 Controlling channels being fitted
PHA channels may be left out of fitting using the
ignore
command and included again using the
notice
command. These commands have a syntax allowing the same channels to be specified for more than one input file. The ignored and noticed ranges can be specified either as channels or as energies. If the command
setplot wave
has been entered, real ranges are interpreted as wavelengths.
3.7.3 Simulations
The
fakeit
command is used to generate simulated data. The current response matrix and model (a model must be defined prior to using the
fakeit
command) are used to create fake data. The user is prompted for various options. To make fake data when only a response matrix is available, give the command
XSPEC12> fakeit none
.
XSPEC will prompt the user for the response and ancillary filenames from which to build the simulated data. It is important to note that a model must be defined prior to issuing this command.
3.7.4 Data groups
The most common use of XSPEC is to fit one or more data sets with responses to a particular model. However, it is often useful to be able to fit simultaneously several data sets with a model whose parameters can be different for each data set. A simple example would be a number of data sets that we expect to have the same model spectrum shape but different normalizations. XSPEC caters to this need through the use of data
18
groups. When files are read in they can be labeled as belonging to a particular data group.
When a model is defined a set of model parameters is allocated for each data group.
These parameters can all vary freely or they can be linked together across data groups as required.
To set up data groups, the
data
command should be given as in the following example :
XSPEC12> data 1:1 file1 1:2 file2 2:3 file3 which sets up two data groups. The first data group comprises data sets from file1 and file2, and the second data group takes the data set from file3. Now when a model is defined, XSPEC will give two sets of model parameters, one for the first datagroup and one for the second.
3.8 Model Commands
XSPEC allows users to fit data with models constructed from individual components. These components may be either additive, multiplicative, mixing, or convolution. Multiplicative components simply multiply the model by an energydependent factor. Convolutions apply a transformation to the model component they operated on whereby the output can be affected by a range of input energies, such as in smoothing operations. Mixing components are two dimensional and designed to transform fluxes between different spatial regions (such as in projection). Multiplicative, and convolution components can act on individual components, on groups of components, or on the entire model, whereas mixing transformations apply to the whole model.
The
model
command defines the model to be used and prompts for the starting values of its parameters. The user also can set the allowed ranges of the parameter.
Parameters can be linked to an algebraic function of the other parameters, and unlinked using the
untie
command. The value of an individual parameter can be changed with the command
newpar
(and the current setting queried with
newpar 0
). Parameters can be fixed at their current value with the
freeze
command and allowed to vary freely with the
thaw
command. Individual components can be added or subtracted from the model using
addcomp
,
delcomp
, and
editmod
. The plasma emission and photoelectric absorption models require an assumption about relative elemental abundances.
The
flux
command calculates the flux from the current model in the given energy range. This energy range must be within that defined by the current response matrix. If a larger energy range is required, then the
energies
command can be given to compute the model over the desired range. The
lumin
command calculates the luminosity for the source redshift given. The
eqwidth
command determines the equivalent width of a model component, usually a line. The user of either of these last two commands should read the help descriptions carefully. The Tcl script
addline
can be used to automatically add lines to a model. These can be identified using
identify
and
modid
.
New model components which can be described by a simple algebraic formula can be set up using
mdefine
and used in the same way as the standard models except they will run slower being interpreted rather than compiled.
19
3.8.1 Models with multiple responses and background models
Multiple models and responses can be assigned to a single spectrum. This generalizes and replaces the ‘/b’ technique of specifying background models in v11. In the FITS file format, a single response file can be associated with a spectrum either through a header keyword or a table column entry. XSPEC always assigns this response to a spectrum’s source number 1. The
model
command by default also creates new models for source number 1. The
response
command in tandem with
model
can be used to create additional sources. For example to add a background model to loaded spectrum 1, first load a 2 nd response:
XSPEC12> response 2:1 resp2.rsp then define a background model to apply to source 2:
XSPEC12> model 2:my_background_model_name wa(po)
This model will now apply to spectrum 1 and any other spectrum that has a response loaded for source 2. To apply a different background model to spectrum 2, load a response for source 3 rather than 2:
XSPEC12> response 3:2 another_response.rsp
XSPEC12> model 3:another_background_model ga
An
arf
can also be assigned to a particular source number and spectrum:
XSPEC12> arf 2:1 arf_file.pha
Source numbers do not need to be entered in consecutive order for a given spectrum, and gaps in numbering are allowed. Please see the individual
model
and
response
entries in the “XSPEC Commands” section for more information and examples.
3.9 Fitting Commands
The basic fit command is called
fit
. This command performs a minimization using the currently selected algorithm (default: Levenberg-Marquardt).
fit
takes arguments that are passed to the fitting method: by default, these are the number of iterations to execute before asking the user whether to continue, and the numerical convergence criterion.
A systematic model uncertainty can be included using the
systematic
command.
The
error
or
uncertain
command calculates error bounds for one interesting parameter for the specified parameters and confidence levels. To produce multi-dimensional errors the
steppar
command is used to generate a fit-statistic grid. Two-dimensional grids may be expressed as contour plots (using
plot contour
). The model normalization can be set using the
renorm
command. The normalization of the correction file background can be set with
cornorm
.
ftest
and the Tcl script
simftest
can be used to calculate F-test probabilities.
Markov Chain Monte Carlo runs can be performed using the
chain
command with a useful Tcl script
rescalecov
to rescale the proposal distribution covariance if the
Metropolis-Hastings algorithm is selected. The results can be analyzed using the
margin
command.
20
3.9.1 What to do when you have Poisson data
The
χ
2 statistic assumes that all the spectral channels are Gaussian distributed and that the estimate for the variance is uncorrelated with the observed counts. If the data are Poisson then these are bad assumptions especially if there are small numbers of counts in a channel. An alternative fit statistic, the C-statistic, should be used in this case.
2
The C-statistic can also provide confidence intervals in exactly the same way as
χ
.
To use, give the command
XSPEC12> statistic cstat and then use the
fit
and
error
commands as usual. An alternative (and deprecated) approach is to continue using the
χ
2 statistic but change the weighting to provide a better estimate of the variance in the small number limit. This can be done using the
weight gehrels
or
weight churazov
commands. The latter is to be preferred.
The goodness-of-fit statistic can be set using the command statistic test. There are a number of options available. They can be interpreted using the
goodness
command, which utilizes Monte Carlo methods.
3.9.2 Binning and Grouping data
Often one does not want to use the full resolution of a spectrum, either because the channels over-sample the spectral resolution or because the S/N is low. XSPEC and the associated programs provide a number of ways of handling this. Firstly, the XSPEC command
setplot rebin
can be used to add channels together in the plot. It is important to realize that this effects only the plot and not the data being fitted.
Two FTOOLS are available to bin and group data for fitting purposes. RBNPHA bins up the data in a non-reversible manner and should only be used to ensure that the number of bins in the spectrum is the same as that in the response. GRPPHA is the tool of choice for grouping the data to get adequate S/N or number of counts in each channel.
GRPPHA does not actually add together channels, but instead sets a flag which is read by
XSPEC and causes XSPEC to sum the appropriate channels. If a data file is read with some grouping then XSPEC will apply the same operation to any background or response files used.
3.10 Plotting Commands
XSPEC plotting is currently performed using the PLT interface. There are two basic commands:
plot
and
iplot
. The
plot
command makes a plot and returns the user to the XSPEC prompt, while the
iplot
command leaves the user in the interactive plotting interface, thus allowing the user to edit the plot. A variety of different quantities may be plotted, including the data and the current model; the integrated counts; the fit residuals; the ratio of data to model; the contributions to the fit statistic; the theoretical model; the unfolded (incident) spectrum; the detector efficiency; the results of the goodness command; and the fit-statistic contours. All data plots can have an x-axis of channels, energy, or wavelength, which are specified with
setplot channel
,
setplot energy
,
setplot wavelength
respectively. A number of different units are available for energy or
21
wavelength. The plotting device to be used is set using
setplot device
or
cpd
. Separate spectra may be added together and channels binned up (for plotting purposes only) using
setplot group
(and ungrouped with
setplot ungroup
) and
setplot rebin
. There is an option to plot individual additive model components on data plots, this option is enabled by
setplot add
and disabled by
setplot noadd
. The effective area can be divided out of data plots using setplot area (which option can be turned off using setplot noarea). Line
IDs can be plotted using
setplot id
and turned off by
setplot noid
. A stack of PLT commands can be created and manipulated with
setplot command
, s
etplot delete
, and
setplot list
. This command stack then is applied to every plot.
PLT is built on top of the PGPLOT package, which comes with a standard set of device drivers. Any machine running X-windows should support /xs and /xw, while xterm windows should support /xt. PGPLOT supports monochrome and color postscript and both landscape and portrait orientation with the drivers /ps, /cps, /vps, and /vcps.
The easiest way to make a hardcopy of an XSPEC plot is to use
XSPEC12> iplot command and then at the PLT prompt to enter
PLT> hard /ps
This will make a file called pgplot.ps which can be printed. Alternatively, the sequence
XSPEC12> cpd <filename>/ps
XSPEC12> … plot commands …
XSPEC12> cpd none will place the plots in a PostScript file <filename>.
3.11 Setting Commands
The fit and goodness-of-fit test statistics are set using the
statistic
command.
Other fit-minimization algorithms are available, and can be selected using the
method
command. The various fit methods require first and in some cases second derivatives of the statistic with respect to the parameters. By default XSPEC calculates these analytically, using an approximation for the second derivatives. This may be changed by setting the USE_NUMERICAL_DIFFERENTIATION flag in the user’s startup
2
Xspec.init file. The weighting algorithm used to calculate
χ
can be altered by the
weight
command.
Other setting commands modify: cosmological parameters used to calculate luminosity (
cosmo
) solar abundances for 18 elements (
abund )
photoionization cross-sections (
xsect )
The
xset
command can be used as an interface for
abund
,
cosmo
,
method
,
statistic
, and
xsect
. Additionally,
xset
may set string expressions that are used by models, for example the path to, and version number of APEC atomic line calculations,
22
or the coordinate system for surface brightness calculations used in the
xmmpsf
mixing model.
3.12 Breaking With Ctrl-C
Ctrl-C can be used to break out of the
data
,
chain
,
error
,
fit
, and
steppar
commands. If a Ctrl-C is entered elsewhere, it will have no effect.
When a break is entered during the fitting commands (
error
,
fit
, and
steppar
), the fit will proceed until the end of the current fit iteration (ie. current lambda value when using Levenberg-Marquardt) before breaking. This is to ensure the program remains in a stable well-defined state. Therefore on slower machines, a user may notice a slight delay before the program actually breaks. Ctrl-C breaking is currently only implemented for the Levenberg-Marquardt fitting method.
Breaking is implemented for the data command primarily for users who load a large number of Type-II spectra with one data command. So if you enter
XSPEC12> data my_data{1-1000} and decide it is taking too long to load, you can break out at any time. However, if you do choose to break, all spectra loaded from that particular data set will be lost. For example, if the command below is entered and a Ctrl-C is sent while the spectra from my_data2 are loading, the 50 spectra from my_data1 will be retained while none will be from my_data2:
XSPEC12> data my_data1{1-50} mydata2{1-50}
3.13 Customizing XSPEC
The XSPEC environment can be customized using two separate files, both of which are searched for in the directory
$HOME/.xspec
The first file,
Xspec.init contains a number of settings that control items in
XSPEC. An abridged version of this file is reproduced below.
################################################
#
# options and commands for displaying helpfiles
#
USE_ONLINE_HELP: true
# Recognized local help formats: html pdf
# This is ignored when using online help
LOCAL_HELP_FORMAT: html
# Recommended command for Adobe Acrobat version 7 and later:
# PDF_COMMAND: acroread -openInNewWindow -tempFileTitle
# Recommended command for Adobe Acrobat prior to version 7:
# PDF_COMMAND: acroread -useFrontEndProgram -tempFileTitle
23
# Recommended command for Mac PDF viewing
PDF_COMMAND: open
# Recommended command for Cygwin PDF viewing
# PDF_COMMAND: xpdf -q
# Recommended command for Mac html
HTML_COMMAND: open
# HTML_COMMAND: firefox
#################################################
#
# setting for GUI mode. The code requires that the GUI setting
# starts with a 't' (case-insensitive) otherwise GUI mode is false
# and the command line mode is used.
#
GUI: false
#
# user-definable setting for the dummy response. Arguments required
# begin-range end-range, number of bins, logarithmic/linear. Defaults
# are {0.1,100,200,log} respectively. Setting for bin type must be
"linear"
# if linear bins are to be created.
#
DUMMY: 0.1 50. 1000 log
#
# Chatter Level: Console chatter level then log chatter level.
Currently (4/2001)
# logging has not been reimplemented.
#
CHAT: 10 10
#
# photo absorption cross section table setting.
# possible values are vern, bcmc, obmc.
XSECT: bcmc
#
# solar abundance table indicator. Hard coded solar abundance vector.
Choices are
# 'feld' Feldman, U., 1992. Physica Scripta, 46, 202.
# 'angr' is from Anders, E. & Grevesse, N., 1989. Geochimica and
Cosmochimica Acta 53, 197.
# 'aneb' is from Anders, E. & Ebihara, 1982. Geochimica and
Cosmochimica Acta 46, 2363.
#
ABUND: angr
#
# fitting method (leven | anneal ...)
#
METHOD: leven
#
# statistic to be minimized (chi | cstat)
#
STATISTIC: chi
#
# weighting technique (standard | gehrels | churazov | model )
#
WEIGHT: standard
#
# If true, fitting algorithm will calculate parameter derivatives
# numerically. If false, a faster analytic expression will be used,
# if applicable to the current fitting statistic.
#
USE_NUMERICAL_DIFFERENTIATION: false
#
# cosmology parameters ( H0, q0, lambda0 )
#
COSMO: 70. .0 .73
#
#
# Default graphics package (PLT is currently the only option).
#
GRAPH: plt
#
# Default plotting device (e.g. for PGPLOT)
#
PLOTDEVICE: /null
#
# Y-axis plotting units when in setplot wave mode (angstrom, hz)
#
WAVE_PLOT_UNITS: angstrom
#
# User scripting directory
#
24
25
USER_SCRIPT_DIRECTORY: $HOME/.xspec
#
# Default setting for parameters' fit delta values.
# Valid options are:
#
# fixed
# proportional <fraction of parameter value>
#
# If set to 'fixed', the default values come from the settings in the
# model.dat model definition file.
#
FIT_DELTAS: proportional .01
A copy of this file is placed in the
$HOME/.xspec directory on XSPEC12’s first start-up or when it is not found. After this users can modify settings such as default cosmology or the energy range for dummy response for their own requirements.
This is also the place where users can select if they want to view PDF help files from the XSPEC distribution or HTML either locally or from the HEASARC site.
Setting USE_ONLINE_HELP to true uses the remote HTML files while false will use either PDF or HTML local files depending on the value of LOCAL_HELP_FORMAT.
The PDF_COMMAND and HTML_COMMAND entries determine which applications are run for the two viewing cases. The HTML_COMMAND value should typically just be the name of a web browser, or “open” for Mac OS X users. The default settings for the PDF_COMMAND entry are what work best for launching Adobe Acrobat
Reader 7.0.x on Linux/Unix systems. For those launching earlier versions, the “openInNewWindow” flag should be replaced with “-useFrontEndProgram”. For Mac users, again we recommend the entire entry simply be replaced with “open”.
The second file that is searched for is the xspec.rc file. This contains users’ own customizations, for example Tcl or XSPEC command abbreviations, packages to be loaded on startup, or Tcl scripts containing procedures that are to be executed as commands. Please consult
Appendix A
and references/links therein for details of Tcl commands and scripting.
3.13.1 Customizing system-wide
When an XSPEC build is intended for many users across a system, it is also possible for the installer (or whoever has write access to the distribution and installation areas) to globally customize XSPEC. This is done through the file global_customize.tcl, located in the …/Xspec/src/scripts directory. (This was done in the xspec.tcl file prior to v12.2.1) Any of the customizations mentioned above for the individual’s own xspec.rc file can also be placed in the global_customize.tcl file. After making the additions, run
“hmake install” out of the …/Xspec/src/scripts directory in order to copy the modified global_customize.tcl file to the installation area. This additional code will be executed for all users upon startup, BEFORE any of their own customizations in their xspec.rc files.
26
4. Walks through XSPEC
4.1 Introduction
This chapter demonstrates the use of XSPEC. The brief discussion of data and response files is followed by fully worked examples using real data that include all the screen input and output with a variety of plots. The topics covered are as follows: defining models, fitting data, determining errors, fitting more than one set of data simultaneously, simulating data, and producing plots.
4.1.1 Brief Discussion of XSPEC Files
At least two files are necessary for use with XSPEC: a data file and a response file. In some cases, a file containing background may also be used, and, in rare cases, a correction file is needed to adjust the background during fitting. If the response is split between an rmf and an arf then an ancillary response file is also required. However, most of the time the user need only specify the data file, as the names and locations of the correct response and background files should be written in the header of the data file by whatever program created the files.
4.2 Fitting Models to Data: An Old Example from EXOSAT
Our first example uses very old data which is much simpler than more modern observations and so can be used to better illustrate the basics of XSPEC analysis. The 6s X-ray pulsar 1E1048.1–
5937 was observed by EXOSAT in June 1985 for 20 ks. In this example, we'll conduct a general investigation of the spectrum from the Medium Energy (ME) instrument, i.e. follow the same sort of steps as the original investigators (Seward, Charles & Smale, 1986). The ME spectrum and corresponding response matrix were obtained from the HEASARC On-line service. Once installed,
XSPEC is invoked by typing
% xspec as in this example:
%xspec
XSPEC
Build Date/Time: Thu Nov 29 12:40:42 2012
XSPEC12>data s54405.pha
1 spectrum in use
Spectral Data File: s54405.pha Spectrum 1
Net count rate (cts/s) for Spectrum:1 3.783e+00 +/- 1.367e-01
Assigned to Data Group 1 and Plot Group 1
Noticed Channels: 1-125
Telescope: EXOSAT Instrument: ME Channel Type: PHA
Exposure Time: 2.358e+04 sec
Using fit statistic: chi
Using test statistic: chi
27
Using Response (RMF) File s54405.rsp for Source 1
The data command tells the program to read the data as well as the response file that is named in the header of the data file. In general, XSPEC commands can be truncated, provided they remain unambiguous. Since the default extension of a data file is
.pha
, and the abbreviation of
data to the first two letters is unambiguous, the above command can be abbreviated to da s54405
, if desired. To obtain help on the data command, or on any other command, type help command followed by the name of the command.
One of the first things most users will want to do at this stage—even before fitting models—is to look at their data. The plotting device should be set first, with the command cpd
( change plotting device). Here, we use the pgplot X-Window server,
/xs
.
XSPEC12> cpd /xs
There are more than 50 different things that can be plotted, all related in some way to the data, the model, the fit and the instrument. To see them, type:
XSPEC12>
plot ? plot data/models/fits etc
Syntax: plot commands: background chain chisq contour counts data delchi dem emodel eemodel efficiency eufspec eeufspec foldmodel goodness icounts insensitivity lcounts ldata margin
Multi-panel plots are created by entering multiple commands
e.g. "plot data chisq" model ratio residuals sensitivity sum ufspec
The most fundamental is the data plotted against instrument channel (data); next most fundamental, and more informative, is the data plotted against channel energy. To do this plot, use the XSPEC command setplot energy
. Figure A shows the result of the commands:
XSPEC12>
setplot energy
XSPEC12>
plot data
Note the label on the y-axis. The word “normalized” indicates that this plot has been divided by the value of the EFFAREA keyword in the response file. Usually this is unity so can be ignored. The label also has no cm
-2
so the plot is not corrected for the effective area of the detector.
We are now ready to fit the data with a model. Models in XSPEC are specified using the
model command, followed by an algebraic expression of a combination of model components.
There are two basic kinds of model components: additive, which represent X-Ray sources of different kinds. After being convolved with the instrument response, the components prescribe the number of counts per energy bin (e.g., a bremsstrahlung continuum); and multiplicative models components, which represent phenomena that modify the observed X-Radiation (e.g. reddening or an absorption edge). They apply an energy-dependent multiplicative factor to the source radiation before the result is convolved with the instrumental response.
Figure A: The result of the command plot data when the data file in question is the EXOSAT ME spectrum of the 6s X-ray pulsar 1E1048.1--5937 available from the HEASARC on-line service
More generally, XSPEC allows three types of modifying components: convolutions and mixing models in addition to the multiplicative type. Since there must be a source, there must be least one additive component in a model, but there is no restriction on the number of modifying components. To see what components are available, just type model :
XSPEC12>model
Additive Models: apec bapec bbody bbodyrad bexrav bexriv bkn2pow bknpower bmc bremss bvapec bvvapec c6mekl c6pmekl c6pvmkl c6vmekl cemekl cevmkl cflow compLS compPS compST compTT compbb compmag comptb compth cplinear cutoffpl disk diskbb diskir diskline diskm disko diskpbb diskpn eplogpar eqpair eqtherm equil expdec ezdiskbb gadem gaussian gnei grad grbm kerrbb kerrd kerrdisk laor laor2 logpar lorentz meka mekal mkcflow nei npshock nsa nsagrav nsatmos nsmax nteea nthComp optxagn optxagnf pegpwrlw pexmon pexrav pexriv plcabs posm powerlaw pshock raymond redge refsch sedov sirf smaug srcut sresc step vapec vbremss vequil vgadem vgnei vmcflow vmeka vmekal vnei vnpshock vpshock vraymond vsedov vvapec zbbody zbremss zgauss zpowerlw
Multiplicative Models:
SSS_ice TBabs TBgrain TBvarabs absori acisabs
28
29
cabs constant cyclabs dust edge expabs expfac gabs highecut hrefl notch pcfabs phabs plabs pwab recorn redden smedge spexpcut spline swind1 uvred varabs vphabs wabs wndabs xion zTBabs zdust zedge zhighect zigm zpcfabs zphabs zredden zsmdust zvarabs zvfeabs zvphabs zwabs zwndabs zxipcf
Convolution Models: cflux gsmooth ireflect kdblur kdblur2 kerrconv lsmooth partcov rdblur reflect rgsxsrc simpl zashift zmshift
Mixing Models: ascac projct suzpsf xmmpsf
Pile-up Models: pileup
Mixing pile-up Models:
Additional models are available at : legacy.gsfc.nasa.gov/docs/xanadu/xspec/newmodels.html
For information about a specific component, type help model
followed by the name of the component):
XSPEC12> help model apec
Given the quality of our data, as shown by the plot, we'll choose an absorbed power law, specified as follows :
XSPEC12>
model phabs(powerlaw)
Or, abbreviating unambiguously:
XSPEC12>
mo pha(po)
The user is then prompted for the initial values of the parameters. Entering
<return>
or
/ in response to a prompt uses the default values. We could also have set all parameters to their default values by entering
/*
at the first prompt. As well as the parameter values themselves, users also may specify step sizes and ranges (
<value>,<delta>
,
<min>
,
<bot>
,
<top>
, and
<max values>
), but here, we'll enter the defaults:
XSPEC12> mo pha(po)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000 1E+06
30
1:phabs:nH>/*
========================================================================
Model: phabs<1>*powerlaw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 1.00000 +/- 0.0
2 2 powerlaw PhoIndex 1.00000 +/- 0.0
3 2 powerlaw norm 1.00000 +/- 0.0
________________________________________________________________________
Fit statistic : Chi-Squared = 4.864244e+08 using 125 PHA bins.
Test statistic : Chi-Squared = 4.864244e+08 using 125 PHA bins.
Reduced chi-squared = 3.987085e+06 for 122 degrees of freedom
Null hypothesis probability = 0.000000e+00
Current data and model not fit yet.
The current statistic is
2
and is huge for the initial, default values—mostly because the power law normalization is two orders of magnitude too large. This is easily fixed using the
renorm command.
XSPEC12> renorm
Fit statistic : Chi-Squared = 852.19 using 125 PHA bins.
Test statistic : Chi-Squared = 852.19 using 125 PHA bins.
Reduced chi-squared = 6.9852 for 122 degrees of freedom
Null hypothesis probability = 7.320332e-110
Current data and model not fit yet.
We are not quite ready to fit the data (and obtain a better
2
), because not all of the 125
PHA bins should be included in the fitting: some are below the lower discriminator of the instrument and therefore do not contain valid data; some have imperfect background subtraction at the margins of the pass band; and some may not contain enough counts for
2
to be strictly meaningful. To find out which channels to discard ( ignore in XSPEC terminology), consult mission-specific documentation that will include information about discriminator settings, background subtraction problems and other issues. For the mature missions in the HEASARC archives, this information already has been encoded in the headers of the spectral files as a list of
“bad” channels. Simply issue the command:
XSPEC12>
ignore bad ignore: 40 channels ignored from source number 1
Fit statistic : Chi-Squared = 799.74 using 85 PHA bins.
Test statistic : Chi-Squared = 799.74 using 85 PHA bins.
Reduced chi-squared = 9.7529 for 82 degrees of freedom
Null hypothesis probability = 3.545928e-118
Current data and model not fit yet.
XSPEC12>
plot ldata chi
31
Giving two options for the plot command generates a plot with vertically stacked windows.
Up to six options can be given to the plot command at a time. Forty channels were rejected because they were flagged as bad—but do we need to ignore any more? Figure B shows the result of plotting the data and the model (in the upper window) and the contributions to
2
(in the lower window). We see that above about 15 keV the S/N becomes small. We also see, comparing Figure
B with Figure A, which bad channels were ignored. Although visual inspection is not the most rigorous method for deciding which channels to ignore (more on this subject later), it's good enough for now, and will at least prevent us from getting grossly misleading results from the fitting.
To ignore energies above 15 keV:
Figure B: The result of the command plot ldata chi after the command ignore bad on the EXOSAT ME spectrum 1E1048.1–5937
XSPEC12>
ignore 15.0-**
78 channels (48-125) ignored in spectrum # 1
Fit statistic : Chi-Squared = 721.57 using 45 PHA bins.
Test statistic : Chi-Squared = 721.57 using 45 PHA bins.
Reduced chi-squared = 17.180 for 42 degrees of freedom
Null hypothesis probability = 1.250565e-124
Current data and model not fit yet.
If the ignore command is handed a real number it assumes energy in keV while if it is handed an integer it will assume channel number. The “**” just means the highest energy. Starting a range with “**” means the lowest energy. The inverse of ignore is notice, which has the same syntax.
32
We are now ready to fit the data. Fitting is initiated by the command fit. As the fit proceeds, the screen displays the status of the fit for each iteration until either the fit converges to the minimum
2
, or we are asked whether the fit is to go through another set of iterations to find the minimum. The default number of iterations before prompting is ten.
XSPEC12>fit
Chi-Squared |beta|/N Lvl 1:nH 2:PhoIndex 3:norm
721.533 1.01892e-10 -3 1.00000 1.00000 0.00242602
471.551 150.854 -4 0.152441 1.67440 0.00415548
367.421 60807.7 -3 0.308661 2.31822 0.00958061
53.6787 25662.3 -4 0.503525 2.14501 0.0121712
43.8123 4706.76 -5 0.549824 2.23901 0.0130837
43.802 118.915 -6 0.538696 2.23676 0.0130385
43.802 0.422329 -7 0.537843 2.23646 0.0130320
========================================
Variances and Principal Axes
1 2 3
4.7883E-08| -0.0025 -0.0151 0.9999
8.6821E-02| -0.9153 -0.4026 -0.0084
2.2915E-03| -0.4027 0.9153 0.0128
----------------------------------------
====================================
Covariance Matrix
1 2 3
7.312e-02 3.115e-02 6.564e-04
3.115e-02 1.599e-02 3.207e-04
6.564e-04 3.207e-04 6.561e-06
------------------------------------
========================================================================
Model phabs<1>*powerlaw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 0.537843 +/- 0.270399
2 2 powerlaw PhoIndex 2.23646 +/- 0.126455
3 2 powerlaw norm 1.30320E-02 +/- 2.56146E-03
________________________________________________________________________
Fit statistic : Chi-Squared = 43.80 using 45 PHA bins.
Test statistic : Chi-Squared = 43.80 using 45 PHA bins.
Reduced chi-squared = 1.043 for 42 degrees of freedom
Null hypothesis probability = 3.949507e-01
There is a fair amount of information here so we will unpack it a bit at a time. One line is written out after each fit iteration. The columns labeled Chi-Squared and Parameters are obvious.
The other two provide additional information on fit convergence. At each step in the fit a numerical derivative of the statistic with respect to the parameters is calculated. We call the vector of these derivatives beta. At the best-fit the norm of beta should be zero so we write out |beta| divided by the number of parameters as a check. The actual default convergence criterion is when the fit statistic does not change significantly between iterations so it is possible for the fit to end while |beta| is still significantly different from zero. The |beta|/N column helps us spot this case. The Lvl column also
33
indicates how the fit is converging and should generally decrease. Note that on the first iteration only the powerlaw norm is varied. While not necessary this simple model, for more complicated models only varying the norms on the first iteration helps the fit proper get started in a reasonable region of parameter space.
At the end of the fit XSPEC writes out the Variances and Principal Axes and Covariance
Matrix sections. These are both based on the second derivatives of the statistic with respect to the parameters. Generally, the larger these second derivatives, the better determined the parameter
(think of the case of a parabola in 1-D). The Covariance Matrix is the inverse of the matrix of second derivatives. The Variances and Principal Axes section is based on an eigenvector decomposition of the matrix of second derivatives and indicates which parameters are correlated.
We can see in this case that the first eigenvector depends almost entirely on the powerlaw norm while the other two are combinations of the nH and powerlaw PhoIndex. This tells us that the norm is independent but the other two parameters are correlated.
The next section shows the best-fit parameters and error estimates. The latter are just the square roots of the diagonal elements of the covariance matrix so implicitly assume that the parameter space is multidimensional Gaussian with all parameters independent. We already know in this case that the parameters are not independent so these error estimates should only be considered guidelines to help us determine the true errors later.
The final section shows the statistic values at the end of the fit. XSPEC defines a fit statistic, used to determine the best-fit parameters and errors, and test statistic, used to decide whether this model and parameters provide a good fit to the data. By default, both statistics are
2
.
When the test statistic is
2
we can also calculate the reduced
2
and the null hypothesis probability. This latter is the probability of getting a value of
2
as large or larger than observed if the model is correct. If this probability is small then the model is not a good fit. The null hypothesis probability can be calculated analytically for
2
but not for some other test statistics so XSPEC provides another way of determining the meaning of the statistic value. The goodness command performs simulations of the data based on the current model and parameters and compares the statistic values calculated with that for the real data. If the observed statistic is larger than the values for the simulated data this implies that the real data do not come from the model. To see how this works we will use the command for this case (where it is not necessary)
XSPEC12>goodness 1000
47.40% of realizations are < best fit statistic 43.80 (nosim)
XSPEC12>plot goodness
Approximately half of the simulations give a statistic value less than that observed, consistent with this being a good fit. Figure C shows a histogram of the
2
values from the simulations with the observed value shown by the vertical dotted line.
So the statistic implies the fit is good but it is still always a good idea to look at the data and residuals to check for any systematic differences that may not be caught by the test. To see the fit and the residuals, we produce figure D using the command
XSPEC12> plot data resid
34
Figure C: The result of the command plot goodness. The histogram shows the fraction of simulations with a given value of the statistic and the dotted line marks that for the observed data. There is no reason to reject the model.
Now that we think we have the correct model we need to determine how well the parameters are determined. The screen output at the end of the fit shows the best-fitting parameter values, as well as approximations to their errors. These errors should be regarded as indications of the uncertainties in the parameters and should not be quoted in publications. The true errors, i.e. the confidence ranges, are obtained using the error command. We want to run error on all three parameters which is an intrinsically parallel operation so we can use XSPEC’s support for multiple cores and run the error estimations in parallel:
XSPEC12> parallel error 3
XSPEC12> error 1 2 3
Parameter Confidence Range (2.706)
1 0.107599 1.00722 (-0.430244,0.469381)
2 2.03775 2.44916 (-0.198717,0.2127)
3 0.00954178 0.0181617 (-0.00349017,0.00512978)
Here, the numbers 1, 2, 3 refer to the parameter numbers in the
Model par
column of the output at the end of the fit. For the first parameter, the column of absorbing hydrogen atoms, the
90% confidence range is
20
N
H
9.3 10 cm
2
. This corresponds to an excursion in
2 of 2.706. The reason these “better” errors are not given automatically as part of the fit output is that they entail further fitting. When the model is simple, this does not require much CPU, but for complicated models the extra time can be considerable. The error for each parameter is determined allowing the other two parameters to vary freely. If the parameters are uncorrelated this is all the information we need to know. However, we have an indication from the covariance matrix at the
Figure D: The result of the command plot data resid with: the ME data file from
1E1048.1—5937; “bad” and negative channels ignored; the best-fitting absorbed power-law model; the residuals of the fit.
end of the fit that the column and photon index are correlated. To investigate this further we can use the command steppar to run a grid over these two parameters:
XSPEC12> steppar 1 0.0 1.5 25 2 1.5 3.0 25
Chi-Squared Delta nH PhoIndex
Chi-Squared 1 2
162.65 118.84 0 0 0 1.5
171.59 127.79 1 0.06 0 1.5
180.87 137.06 2 0.12 0 1.5
190.44 146.64 3 0.18 0 1.5
200.29 156.49 4 0.24 0 1.5
. . . . . . .
316.02 272.22 4 0.24 25 3
334.68 290.88 3 0.18 25 3
354.2 310.4 2 0.12 25 3
374.62 330.82 1 0.06 25 3
395.94 352.14 0 0 25 3 and make the contour plot shown in figure E using:
XSPEC12> plot contour
What else can we do with the fit? One thing is to derive the flux of the model. The data by themselves only give the instrument-dependent count rate. The model, on the other hand, is an estimate of the true spectrum emitted. In XSPEC, the model is defined in physical units
35
36
Figure E: The result of the command plot contour. The contours shown are for one, two and three sigma. The cross marks the best-fit position.
independent of the instrument. The command flux integrates the current model over the range specified by the user:
XSPEC12> flux 2 10
Model Flux 0.003539 photons (2.2321e-11 ergs/cm^2/s) range (2.0000 - 10.000 keV)
2.2x10
Here we have chosen the standard X-ray range of 2—10 keV and find that the energy flux is
-11
erg/cm
2
/s. Note that flux will integrate only within the energy range of the current response matrix. If the model flux outside this range is desired—in effect, an extrapolation beyond the data---then the command energies should be used. This command defines a set of energies on which the model will be calculated. The resulting model is then remapped onto the response energies for convolution with the response matrix. For example, if we want to know the flux of our model in the ROSAT PSPC band of 0.2—2 keV, we enter:
XSPEC12> energies extend low 0.2 100
Models will use response energies extended to:
Low: 0.2 in 100 log bins
Fit statistic : Chi-Squared = 43.80 using 45 PHA bins.
Test statistic : Chi-Squared = 43.80 using 45 PHA bins.
Reduced chi-squared = 1.043 for 42 degrees of freedom
Null hypothesis probability = 3.949504e-01
Current data and model not fit yet.
37
XSPEC12> flux 0.2 2.
Model Flux 0.004352 photons (8.847e-12 ergs/cm^2/s) range (0.20000 - 2.0000 keV)
The energy flux, at 8.8x10
-12
ergs/cm
2
/s is lower in this band but the photon flux is higher.
The model energies can be reset to the response energies using energies reset
.
Calculating the flux is not usually enough, we want its uncertainty as well. The best way to do this is to use the cflux model. Suppose further that what we really want is the flux without the absorption then we include the new cflux model by:
XSPEC12> editmod pha*cflux(pow)
Input parameter value, delta, min, bot, top, and max values for ...
0.5 -0.1( 0.005) 0 0 1e+06
1e+06
2:cflux:Emin>0.2
10 -0.1( 0.1) 0 0 1e+06
1e+06
3:cflux:Emax>2.0
-12 0.01( 0.12) -100 -100 100
100
4:cflux:lg10Flux>-10.3
Fit statistic : Chi-Squared = 3459.85 using 45 PHA bins.
Test statistic : Chi-Squared = 3459.85 using 45 PHA bins.
Reduced chi-squared = 84.3867 for 41 degrees of freedom
Null hypothesis probability = 0.000000e+00
Current data and model not fit yet.
========================================================================
Model phabs<1>*cflux<2>*powerlaw<3> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 0.537843 +/- 0.270399
2 2 cflux Emin keV 0.200000 frozen
3 2 cflux Emax keV 2.00000 frozen
4 2 cflux lg10Flux cgs -10.3000 +/- 0.0
5 3 powerlaw PhoIndex 2.23646 +/- 0.126455
6 3 powerlaw norm 1.30320E-02 +/- 2.56146E-03
________________________________________________________________________
The Emin and Emax parameters are set to the energy range over which we want the flux to be calculated. We also have to fix the norm of the powerlaw because the normalization of the model will now be determined by the lg10Flux parameter. This is done using the freeze command:
XSPEC12> freeze 6
We now run fit to get the best-fit value of lg10Flux as -10.2787 then:
XSPEC12> error 4
Parameter Confidence Range (2.706)
4 -10.4574 -10.0796 (-0.178807,0.199057) for a 90% confidence range on the 0.2—2 keV unabsorbed flux of 3.49x10
-11
– 8.33x10
-11 ergs/cm
2
/s.
38
The fit, as we've remarked, is good, and the parameters are constrained. But unless the purpose of our investigation is merely to measure a photon index, it's a good idea to check whether alternative models can fit the data just as well. We also should derive upper limits to components such as iron emission lines and additional continua, which, although not evident in the data nor required for a good fit, are nevertheless important to constrain. First, let's try an absorbed black body:
XSPEC12>mo pha(bb)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000
1e+06
1:phabs:nH>/*
========================================================================
Model phabs<1>*bbody<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 1.00000 +/- 0.0
2 2 bbody kT keV 3.00000 +/- 0.0
3 2 bbody norm 1.00000 +/- 0.0
________________________________________________________________________
Fit statistic : Chi-Squared = 3.377094e+09 using 45 PHA bins.
Test statistic : Chi-Squared = 3.377094e+09 using 45 PHA bins.
Reduced chi-squared = 8.040700e+07 for 42 degrees of freedom
Null hypothesis probability = 0.000000e+00
Current data and model not fit yet.
XSPEC12>fit
Parameters
Chi-Squared |beta|/N Lvl 1:nH 2:kT 3:norm
1602.34 3.49871e-11 -3 1.00000 3.00000 0.000767254
1535.61 63.3168 0 0.334306 3.01647 0.000673086
1523.48 112166 0 0.157481 2.96616 0.000613283
1491.74 170832 0 0.0668722 2.87681 0.000570110
1444.73 204639 0 0.0228475 2.76753 0.000535213
1387.84 226852 0 0.00205203 2.64901 0.000504579
1325.6 243760 0 0.000843912 2.52648 0.000476503
1256.04 258202 0 0.000287666 2.40140 0.000450137
1179.2 271528 0 3.10806e-05 2.27482 0.000425541
1083.47 283137 0 7.99181e-06 2.13278 0.000401083
Number of trials exceeded: continue fitting? Y
...
...
123.773 25.397 -8 1.87147e-08 0.890295 0.000278599
Number of trials exceeded: continue fitting?
***Warning: Zero alpha-matrix diagonal element for parameter 1
Parameter 1 is pegged at 1.87147e-08 due to zero or negative pivot element, likely
caused by the fit being insensitive to the parameter.
123.773 1.92501 -3 1.87147e-08 0.890205 0.000278596
==============================
Variances and Principal Axes
2 3
39
2.8677E-04| -1.0000 -0.0000
2.2370E-11| 0.0000 -1.0000
------------------------------
========================
Covariance Matrix
1 2
2.868e-04 9.336e-09
9.336e-09 2.267e-11
------------------------
========================================================================
Model phabs<1>*bbody<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 1.87147E-08 +/- -1.00000
2 2 bbody kT keV 0.890205 +/- 1.69343E-02
3 2 bbody norm 2.78596E-04 +/- 4.76176E-06
________________________________________________________________________
Fit statistic : Chi-Squared = 123.77 using 45 PHA bins.
Test statistic : Chi-Squared = 123.77 using 45 PHA bins.
Reduced chi-squared = 2.9470 for 42 degrees of freedom
Null hypothesis probability = 5.417115e-10
Note that after each set of 10 iterations you are asked whether you want to continue.
Replying no at these prompts is a good idea if the fit is not converging quickly. Conversely, to avoid having to keep answering the question, i.e., to increase the number of iterations before the prompting question appears, begin the fit with, say fit
100
. This command will put the fit through
100 iterations before pausing. To automatically answer yes to all such questions use the command
query yes
.
Note that the fit has written out a warning about the first parameter and its estimated error is written as -1. This indicates that the fit is unable to constrain the parameter and it should be considered indeterminate. This usually indicates that the model is not appropriate. One thing to check in this case is that the model component has any contribution within the energy range being calculated. Plotting the data and residuals again we obtain Figure F.
The black body fit is obviously not a good one. Not only is
2
large, but the best-fitting
N
H
is indeterminate. Inspection of the residuals confirms this: the pronounced wave-like shape is indicative of a bad choice of overall continuum.
Let's try thermal bremsstrahlung next:
XSPEC12>mo pha(br)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000
1e+06
1:phabs:nH>/*
Figure F: As for Figure D, but the model is the best-fitting absorbed black body. Note the wave-like shape of the residuals which indicates how poor the fit is, i.e. that the continuum is obviously not a black body.
========================================================================
Model phabs<1>*bremss<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 1.00000 +/- 0.0
2 2 bremss kT keV 7.00000 +/- 0.0
3 2 b remss norm 1.00000 +/- 0.0
________________________________________________________________________
Fit statistic : Chi-Squared = 4.534834e+07 using 45 PHA bins.
Test statistic : Chi-Squared = 4.534834e+07 using 45 PHA bins.
Reduced chi-squared = 1.079722e+06 for 42 degrees of freedom
Null hypothesis probability = 0.000000e+00
Current data and model not fit yet.
XSPEC12>fit
Parameters
Chi-Squared |beta|/N Lvl 1:nH 2:kT 3:norm
156.921 6.92228e-11 -3 1.00000 7.00000 0.00863005
106.765 24.2507 -4 0.264912 6.25747 0.00718902
...
...
40.0331 190.876 0 8.46112e-05 5.28741 0.00831314
========================================
40
41
Variances and Principal Axes
1 2 3
1.9514E-08| -0.0016 0.0007 1.0000
1.1574E-02| 0.9738 0.2272 0.0014
5.3111E-01| 0.2272 -0.9738 0.0011
----------------------------------------
====================================
Covariance Matrix
1 2 3
3.839e-02 -1.150e-01 1.427e-04
-1.150e-01 5.043e-01 -5.396e-04
1.427e-04 -5.396e-04 6.287e-07
------------------------------------
========================================================================
Model phabs<1>*bremss<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 8.46112E-05 +/- 0.195940
2 2 bremss kT keV 5.28741 +/- 0.710133
3 2 bremss norm 8.31314E-03 +/- 7.92890E-04
________________________________________________________________________
Fit statistic : Chi-Squared = 40.03 using 45 PHA bins.
Test statistic : Chi-Squared = 40.03 using 45 PHA bins.
Reduced chi-squared = 0.9532 for 42 degrees of freedom
Null hypothesis probability = 5.576222e-01
Bremsstrahlung is a better fit than the black body—and is as good as the power law— although it shares the low
N
H
. With two good fits, the power law and the bremsstrahlung, it's time to scrutinize their parameters in more detail.
First, we reset our fit to the powerlaw (output omitted):
XSPEC12>mo pha(po)
From the EXOSAT database on HEASARC, we know that the target in question, 1E1048.1--
5937, has a Galactic latitude of 24 , i.e., almost on the plane of the Galaxy. In fact, the database also provides the value of the Galactic
N
H
based on 21-cm radio observations. At 4x10
22
cm
-2
, it is higher than the 90 percent-confidence upper limit from the power-law fit. Perhaps, then, the powerlaw fit is not so good after all. What we can do is fix (freeze in XSPEC terminology) the value of
N
H
at the Galactic value and refit the power law. Although we won't get a good fit, the shape of the residuals might give us a clue to what is missing. To freeze a parameter in XSPEC, use the command freeze followed by the parameter number, like this:
XSPEC12> freeze 1
The inverse of freeze is thaw:
XSPEC12> thaw 1
42
Figure G: As for Figure D & F, but the model is the best-fitting power law with the absorption fixed at the Galactic value. Under the assumptions that the absorption really is the same as the 21-cm value and that the continuum really is a power law, this plot provides some indication of what other components might be added to the model to improve the fit.
Alternatively, parameters can be frozen using the newpar command, which allows all the quantities associated with a parameter to be changed. We can flip between frozen and thawed states by entering 0 after the new parameter value. In our case, we want
N
H
frozen at 4x10
22
, so we go back to the power law best fit and do the following :
cm
-2
XSPEC12>newpar 1
Current value, delta, min, bot, top, and max values
0.537843 0.001(0.00537843) 0 0 100000
1e+06
1:phabs[1]:nH:1>4,0
Fit statistic : Chi-Squared = 823.34 using 45 PHA bins.
Test statistic : Chi-Squared = 823.34 using 45 PHA bins.
Reduced chi-squared = 19.148 for 43 degrees of freedom
Null hypothesis probability = 6.151383e-145
Current data and model not fit yet.
1 4, 0
The same result can be obtained by putting everything onto the command line, i.e., newpar
, or by issuing the two commands, newpar
1 4
followed by freeze
1
. Now, if we fit and plot again, we get the following model (Fig. G).
XSPEC12>fit
...
========================================================================
Model phabs<1>*powerlaw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
43
par comp
1 1 phabs nH 10^22 4.00000 frozen
2 2 powerlaw PhoIndex 3.59784 +/- 6.76670E-02
3 2 powerlaw norm 0.116579 +/- 9.43208E-03
________________________________________________________________________
Fit statistic : Chi-Squared = 136.04 using 45 PHA bins.
The fit is not good. In Figure G we can see why: there appears to be a surplus of softer photons, perhaps indicating a second continuum component. To investigate this possibility we can add a component to our model. The editmod command lets us do this without having to respecify the model from scratch. Here, we'll add a black body component.
XSPEC12>editmod pha(po+bb)
Input parameter value, delta, min, bot, top, and max values for ...
3 0.01( 0.03) 0.0001 0.01 100
200
4:bbody:kT>2,0
1 0.01( 0.01) 0 0 1e+24
1e+24
5:bbody:norm>1e-5
Fit statistic : Chi-Squared = 132.76 using 45 PHA bins.
Test statistic : Chi-Squared = 132.76 using 45 PHA bins.
Reduced chi-squared = 3.1610 for 42 degrees of freedom
Null hypothesis probability = 2.387580e-11
Current data and model not fit yet.
========================================================================
Model phabs<1>(powerlaw<2> + bbody<3>) Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 4.00000 frozen
2 2 powerlaw PhoIndex 3.59784 +/- 6.76670E-02
3 2 powerlaw norm 0.116579 +/- 9.43208E-03
4 3 bbody kT keV 2.00000 frozen
5 3 bbody norm 1.00000E-05 +/- 0.0
________________________________________________________________________
Notice that in specifying the initial values of the black body, we have frozen kT at 2 keV
(the canonical temperature for nuclear burning on the surface of a neutron star in a low-mass X-ray binary) and started the normalization at zero. Without these measures, the fit might “lose its way”.
Now, if we fit, we get (not showing all the iterations this time):
========================================================================
Model phabs<1>(powerlaw<2> + bbody<3>) Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 4.00000 frozen
2 2 powerlaw PhoIndex 4.89584 +/- 0.158997
3 2 powerlaw norm 0.365230 +/- 5.25376E-02
44
Figure H: The result of the command plot model in the case of the ME data file from 1E1048.1—5937. Here, the model is the best-fitting combination of power law, black body and fixed Galactic absorption. The three lines show the two continuum components (absorbed to the same degree) and their sum.
4 3 bbody kT keV 2.00000 frozen
5 3 bbody norm 2.29697E-04 +/- 2.04095E-05
________________________________________________________________________
Fit statistic : Chi-Squared = 69.53 using 45 PHA bins.
The fit is better than the one with just a power law and the fixed Galactic column, but it is still not good. Thawing the black body temperature and fitting does of course improve the fit but the powerl law index becomes even steeper. Looking at this odd model with the command
XSPEC12> plot model
We see, in Figure H, that the black body and the power law have changed places, in that the power law provides the soft photons required by the high absorption, while the black body provides the harder photons. We could continue to search for a plausible, well-fitting model, but the data, with their limited signal-to-noise and energy resolution, probably don't warrant it (the original investigators published only the power law fit).
There is, however, one final, useful thing to do with the data: derive an upper limit to the presence of a fluorescent iron emission line. First we delete the black body component using
45
delcomp then thaw N
H
and refit to recover our original best fit. Now, we add a gaussian emission line of fixed energy and width then fit to get:
========================================================================
Model phabs<1>(powerlaw<2> + gaussian<3>) Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 0.753989 +/- 0.320344
2 2 powerlaw PhoIndex 2.38165 +/- 0.166973
3 2 powerlaw norm 1.59131E-02 +/- 3.94947E-03
4 3 gaussian LineE keV 6.40000 frozen
5 3 gaussian Sigma keV 0.100000 frozen
6 3 gaussian norm 7.47368E-05 +/- 4.74253E-05
________________________________________________________________________
The energy and width have to be frozen because, in the absence of an obvious line in the data, the fit would be completely unable to converge on meaningful values. Besides, our aim is to see how bright a line at 6.4 keV can be and still not ruin the fit. To do this, we fit first and then use the error command to derive the maximum allowable iron line normalization. We then set the normalization at this maximum value with newpar and, finally, derive the equivalent width using the eqwidth command. That is:
XSPEC12>err 6
Parameter Confidence Range (2.706)
***Warning: Parameter pegged at hard limit: 0
6 0 0.000151164 (-7.476e-05,7.64036e-05)
XSPEC12>new 6 0.000151164
Fit statistic : Chi-Squared = 46.03 using 45 PHA bins.
Test statistic : Chi-Squared = 46.03 using 45 PHA bins.
Reduced chi-squared = 1.123 for 41 degrees of freedom
Null hypothesis probability = 2.717072e-01
Current data and model not fit yet.
XSPEC12>eqwidth 3
Data group number: 1
Additive group equiv width for Component 3: 0.784168 keV
Things to note:
The true minimum value of the gaussian normalization is less than zero, but the error command stopped searching for a
limit of the parameter. Hard limits can be adjusted with the newpar command, and they correspond to the quantities min
and max
associated with the parameter values.
The command eqwidth takes the component number as its argument.
The upper limit on the equivalent width of a 6.4 keV emission line is high (784 eV)!
4.3 Simultaneous Fitting
XSPEC has the very useful facility of allowing models to be fitted simultaneously to more than one data file. It is even possible to group files together and to fit different models simultaneously. Reasons for fitting in this manner include:
46
The same target is observed at several epochs but, although the source stays constant, the
response matrix has changed. When this happens, the data files cannot be added together; they have to be fitted separately. Fitting the data files simultaneously yields tighter constraints.
The same target is observed with different instruments. All the instruments on Suzaku, for example, observe in the same direction simultaneously. As far as XSPEC is concerned, this is just like the previous case: two data files with two responses fitted simultaneously with the same model.
Different targets are observed, but the user wants to fit the same model to each data file
with some parameters shared and some allowed to vary separately. For example, if we have a series of spectra from a variable AGN, we might want to fit them simultaneously with a model that has the same, common photon index but separately vary the normalization and absorption.
Other scenarios are possible---the important thing is to recognize the flexibility of XSPEC in this regard.
As an example we will look at a case of fitting the same model to two different data files but where not all the parameters are identical. Again, this is an older dataset that provides a simpler illustration than more modern data. The massive X-ray binary Centaurus X-3 was observed with the LAC on Ginga in 1989. Its flux level before eclipse was much lower than the level after eclipse.
Here, we'll use XSPEC to see whether spectra from these two phases can be fitted with the same model, which differs only in the amount of absorption. This kind of fitting relies on introducing an extra dimension, the group, to the indexing of the data files. The files in each group share the same model but not necessarily the same parameter values, which may be shared as common to all the groups or varied separately from group to group. Although each group may contain more than one file, there is only one file in each of the two groups in this example. Groups are specified with the data command, with the group number preceding the file number, like this:
XSPEC12>data 1:1 losum 2:2 hisum
2 spectra in use
Spectral Data File: losum.pha Spectrum 1
Net count rate (cts/s) for Spectrum:1 1.401e+02 +/- 3.549e-01
Assigned to Data Group 1 and Plot Group 1
Noticed Channels: 1-48
Telescope: GINGA Instrument: LAC Channel Type: PHA
Exposure Time: 1 sec
Using fit statistic: chi
Using test statistic: chi
Using Response (RMF) File ginga_lac.rsp for Source 1
Spectral Data File: hisum.pha Spectrum 2
Net count rate (cts/s) for Spectrum:2 1.371e+03 +/- 3.123e+00
Assigned to Data Group 2 and Plot Group 2
Noticed Channels: 1-48
Telescope: GINGA Instrument: LAC Channel Type: PHA
Exposure Time: 1 sec
Using fit statistic: chi
Using test statistic: chi
Using Response (RMF) File ginga_lac.rsp for Source 1
Here, the first group makes up the file losum.pha
, which contains the spectrum of all the low, pre-eclipse emission. The second group makes up the second file, hisum.pha
, which contains
47
all the high, post-eclipse emission. Note that file number is “absolute” in the sense that it is independent of group number. Thus, if there were three files in each of the two groups ( lo1.pha
, lo2.pha
, lo3.pha
, hi1.pha
, hi2.pha
,
and hi3.pha
, say), rather than one, the six files would be specified as da
1:1 lo1 1:2 lo2 1:3 lo3 2:4 hi1 2:5 hi2 2:6 hi3
. The
ignore command works on file number, and does not take group number into account. So, to ignore channels 1–3 and 37–48 of both files:
XSPEC12> ignore 1-2:1-3 37-48 cut-off:
The model we'll use at first to fit the two files is an absorbed power law with a high-energy
XSPEC12> mo phabs * highecut (po)
After defining the model, we will be prompted for two sets of parameter values, one for the first group of data files ( losum.pha
), the other for the second group ( hisum.pha
). Here, we'll enter the absorption column of the first group as 10
24
cm
–2
and enter the default values for all the other parameters in the first group. Now, when it comes to the second group of parameters, we enter a column of 10
22
cm
–2
and then enter defaults for the other parameters. The rule being applied here is as follows: to tie parameters in the second group to their equivalents in the first group, take the default when entering the second-group parameters; to allow parameters in the second group to vary independently of their equivalents in the first group, enter different values explicitly:
XSPEC12> mo phabs*highecut(po)
Input parameter value, delta, min, bot, top, and max values for ...
Current: 1 0.001 0 0 1E+05 1E+06
DataGroup 1:phabs:nH>100
Current: 10 0.01 0.0001 0.01 1E+06 1E+06
DataGroup 1:highecut:cutoffE>
Current: 15 0.01 0.0001 0.01 1E+06 1E+06
DataGroup 1:highecut:foldE>
Current: 1 0.01 -3 -2 9 10
DataGroup 1:powerlaw:PhoIndex>
Current: 1 0.01 0 0 1E+24 1E+24
DataGroup 1:powerlaw:norm>
Current: 100 0.001 0 0 1E+05 1E+06
DataGroup 2:phabs:nH>1
Current: 10 0.01 0.0001 0.01 1E+06 1E+06
DataGroup 2:highecut:cutoffE>/*
========================================================================
Model phabs<1>*highecut<2>*powerlaw<3> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
1 1 phabs nH 10^22 100.000 +/- 0.0
2 2 highecut cutoffE keV 10.0000 +/- 0.0
3 2 highecut foldE keV 15.0000 +/- 0.0
4 3 powerlaw PhoIndex 1.00000 +/- 0.0
5 3 powerlaw norm 1.00000 +/- 0.0
Data group: 2
6 1 phabs nH 10^22 1.00000 +/- 0.0
7 2 highecut cutoffE keV 10.0000 = 2
8 2 highecut foldE keV 15.0000 = 3
9 3 powerlaw PhoIndex 1.00000 = 4
48
10 3 powerlaw norm 1.00000 = 5
________________________________________________________________________
Notice how the summary of the model, displayed immediately above, is different now that we have two groups, as opposed to one (as in all the previous examples). We can see that of the 10 model parameters, 6 are free (i.e., 4 of the second group parameters are tied to their equivalents in the first group). Fitting this model results in a huge
2
(not shown here), because our assumption that only a change in absorption can account for the spectral variation before and after eclipse is clearly wrong. Perhaps scattering also plays a role in reducing the flux before eclipse. This could be modeled (simply at first) by allowing the normalization of the power law to be smaller before eclipse than after eclipse. To decouple tied parameters, we change the parameter value in the second group to a value—any value—different from that in the first group (changing the value in the first group has the effect of changing both without decoupling). As usual, the newpar command is used:
XSPEC12> newpar 10 1
Fit statistic : Chi-Squared = 2.062941e+06 using 66 PHA bins.
Test statistic : Chi-Squared = 2.062941e+06 using 66 PHA bins.
Reduced chi-squared = 34965.10 for 59 degrees of freedom
Null hypothesis probability = 0.000000e+00
Current data and model not fit yet.
XSPEC12> fit
...
========================================================================
Model phabs<1>*highecut<2>*powerlaw<3> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
1 1 phabs nH 10^22 20.1531 +/- 0.181904
2 2 highecut cutoffE keV 14.6846 +/- 5.59251E-02
3 2 highecut foldE keV 7.41660 +/- 8.99545E-02
4 3 powerlaw PhoIndex 1.18690 +/- 6.33054E-03
5 3 powerlaw norm 5.88294E-02 +/- 9.30380E-04
Data group: 2
6 1 phabs nH 10^22 1.27002 +/- 3.77708E-02
7 2 highecut cutoffE keV 14.6846 = 2
8 2 highecut foldE keV 7.41660 = 3
9 3 powerlaw PhoIndex 1.18690 = 4
10 3 powerlaw norm 0.312117 +/- 4.49061E-03
________________________________________________________________________
Fit statistic : Chi-Squared = 15423.79 using 66 PHA bins.
After fitting, this decoupling reduces
2
by a factor of six to 15,478, but this is still too high. Indeed, this simple attempt to account for the spectral variability in terms of “blanket” cold absorption and scattering does not work. More sophisticated models, involving additional components and partial absorption, should be tried.
49
4.4 Multiple Models: a Background Modeling Example
In the previous section we showed how to fit the same model to multiple datasets. We now demonstrate how to fit multiple models, each with their own response, to the same dataset. There are several reasons why this may be useful, for instance:
We are using data from a coded aperture mask. If there are multiple sources in the field they will all contribute to the spectrum from each detector. However, each source may have a different response due to its position.
We are observing an extended source using a telescope whose PSF is large enough that the
signal from different regions are mixed together. In this case we will want to analyze spectra from all regions of the source simultaneously with each spectrum having a contribution from the model in other regions.
We wish to model the background spectrum that includes a particle component. The particle background will have a different response from the X-ray background because the particles come from all directions, not just down the telescope.
We will demonstrate the third example here. Suppose we have a model for the background spectrum that requires a different response to that for the source spectrum. Read in the source and background spectra as separate files:
XSPEC12>data 1:1 source.pha 2:2 back.pha
The source and background files have their own response matrices:
XSPEC12>response 1 source.rsp 2 back.rsp
Set up the model for the source. Here we will take the simple case of an absorbed power-law:
XSPEC12>model phabs(pow)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000
1e+06
1:data group 1::phabs:nH>
1 0.01( 0.01) -3 -2 9
10
2:data group 1::powerlaw:PhoIndex>
1 0.01( 0.01) 0 0 1e+24
1e+24
3:data group 1::powerlaw:norm>
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000
1e+06
4:data group 2::phabs:nH>
1 0.01( 0.01) -3 -2 9
10
5:data group 2::powerlaw:PhoIndex>
1 0.01( 0.01) 0 0 1e+24
1e+24
6:data group 2::powerlaw:norm>0 0
50
Note that we have fixed the normalization of the source model for the background dataset at zero so it doesn't contribute. Now we need to set up the background model for both datasets with its own response matrix.
XSPEC12>response 2:1 back.rsp 2:2 back.rsp
This tells XSPEC that both these datasets have a second model which must be multiplied by the back.rsp response matrix. We now define the background model to be used. In this case take the simple example of a single power-law
XSPEC12>model 2:myback pow
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01( 0.01) -3 -2 9
10
1:myback:data group 1::powerlaw:PhoIndex>
1 0.01( 0.01) 0 0 1e+24
1e+24
2:myback:data group 1::powerlaw:norm>
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01( 0.01) -3 -2 9
10
3:myback:data group 2::powerlaw:PhoIndex>
1 0.01( 0.01) 0 0 1e+24
1e+24
4:myback:data group 2::powerlaw:norm>
We have now set up XSPEC so that the source data is compared to a source model multiplied by the source response plus a background model multiplied by the background response and the background data is compared to the background model multiplied by the background response. The background models fitted to the source and background data are constrained to be the same.
XSPEC12>show param
Parameters defined:
========================================================================
Model phabs<1>*powerlaw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
1 1 phabs nH 10^22 1.00000 +/- 0.0
2 2 powerlaw PhoIndex 1.00000 +/- 0.0
3 2 powerlaw norm 1.00000 +/- 0.0
Data group: 2
4 1 phabs nH 10^22 1.00000 = 1
5 2 powerlaw PhoIndex 1.00000 = 2
6 2 powerlaw norm 1.00000 = 3
________________________________________________________________________
========================================================================
Model myback:powerlaw<1> Source No.: 2 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
51
1 1 powerlaw PhoIndex 1.00000 +/- 0.0
2 1 powerlaw norm 1.00000 +/- 0.0
Data group: 2
3 1 powerlaw PhoIndex 1.00000 = myback:1
4 1 powerlaw norm 1.00000 = myback:2
________________________________________________________________________
It is often the case that the response information is split into an RMF and ARF, where the
RMF describes the instrument response and the ARF the telescope effective area. The particle background can then be included by using the RMF but not the ARF:
XSPEC12>data 1:1 source.pha 2:2 back.pha
XSPEC12>response 1 source.rmf 2 source.rmf
XSPEC12>arf 1 source.arf
XSPEC12>response 2:1 source.rmf 2:2 source.rmf
4.5 Using XSPEC to Simulate Data: an Example for Chandra
In several cases, analyzing simulated data is a powerful tool to demonstrate feasibility. For example:
To support an observing proposal. That is, to demonstrate what constraints a proposed observation would yield.
To support a hardware proposal. If a response matrix is generated, it can be used to demonstrate what kind of science could be done with a new instrument.
To support a theoretical paper. A theorist could write a paper describing a model, and then show how these model spectra would appear when observed. This, of course, is very like the first case.
Here, we will illustrate the first example. The first step is to define a model on which to base the simulation. The way XSPEC creates simulated data is to take the current model, convolve it with the current response matrix, while adding noise appropriate to the integration time specified.
Once created, the simulated data can be analyzed in the same way as real data to derive confidence limits.
Let us suppose that we want to measure the intrinsic absorption of a faint high-redshift source using Chandra. Our model is thus a power-law absorbed both by the local Galactic column and an intrinsic column. First, we set up the model. From the literature we have the Galactic absorption column and redshift so:
XSPEC12>mo pha*zpha(zpo)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001( 0.01) 0 0 100000
1e+06
1:phabs:nH>0.08
1 0.001( 0.01) 0 0 100000
1e+06
2:zphabs:nH>1.0
0 -0.01( 0.01) -0.999 -0.999 10
10
3:zphabs:Redshift>5.1
52
1 0.01( 0.01) -3 -2 9
10
4:zpowerlw:PhoIndex>1.7
0 -0.01( 0.01) -0.999 -0.999 10
10
5:zpowerlw:Redshift>5.1
1 0.01( 0.01) 0 0 1e+24
1e+24
6:zpowerlw:norm>
========================================================================
Model phabs<1>*zphabs<2>*zpowerlw<3> Source No.: 1 Active/Off
Model Model Component Parameter Unit Value
par comp
1 1 phabs nH 10^22 8.00000E-02 +/- 0.0
2 2 zphabs nH 10^22 1.00000 +/- 0.0
3 2 zphabs Redshift 5.10000 frozen
4 3 zpowerlw PhoIndex 1.70000 +/- 0.0
5 3 zpowerlw Redshift 5.10000 frozen
6 3 zpowerlw norm 1.00000 +/- 0.0
Now suppose that we know that the observed 0.5—2.5 keV flux is 1.1x10
-13
ergs/cm
2
/s. We now can derive the correct normalization by using the commands energies, flux and newpar. That is, we'll determine the flux of the model with the normalization of unity. We then work out the new normalization and reset it:
XSPEC12> energies 0.5 2.5 1000
XSPEC12> flux 0.5 2.5
Model Flux 0.052736 photons (1.0017e-10 ergs/cm^2/s) range (0.50000 - 2.5000 keV)
XSPEC12>
newpar 6 1.1e-3
3 variable fit parameters
XSPEC12> flux
Model Flux 2.6368e-05 photons (5.0086e-14 ergs/cm^2/s) range (0.50000 - 2.5000 keV)
1.1x10
Here, we have changed the value of the normalization (the fifth parameter) from 1.0 to
-13
/ 1.00x10
-10
= 1.1x10
-3
to give the required flux.
The simulation is initiated with the command fakeit. If the argument none
is given, we will be prompted for the name of the response matrix. If no argument is given, the current response will be used. We also need to reset the energies command before the fakeit to ensure that the model is calculated on the entire energy range of the response:
XSPEC12> energies reset
XSPEC12> fakeit none
For fake data, file #1 needs response file: aciss_aimpt_cy15.rmf
... and ancillary response file: aciss_aimpt_cy15.arf
There then follows a series of prompts asking the user to specify whether he or she wants counting statistics (yes!), the name of the fake data (file test.fak
in our example), and the
53
integration time (40,000 seconds -- the correction norm and background exposure time can be left at their default values).
Use counting statistics in creating fake data? (y):
Input optional fake file prefix:
Fake data file name (aciss_aimpt_cy15.fak): test.fak
Exposure time, correction norm, bkg exposure time (1.00000, 1.00000, 1.00000):
40000.0
No background will be applied to fake spectrum #1
1 spectrum in use
Fit statistic : Chi-Squared = 350.95 using 1024 PHA bins.
***Warning: Chi-square may not be valid due to bins with zero variance
in spectrum number(s): 1
Test statistic : Chi-Squared = 350.95 using 1024 PHA bins.
Reduced chi-squared = 0.34407 for 1020 degrees of freedom
Null hypothesis probability = 1.000000e+00
***Warning: Chi-square may not be valid due to bins with zero variance
in spectrum number(s): 1
Current data and model not fit yet.
The first thing we should note is that the default statistics are not correct for these data. For
Poisson data and no background we should cstat
for the fit statistic and pchi
for the test statistic:
XSPEC12>statistic cstat
Default fit statistic is set to: C-Statistic
This will apply to all current and newly loaded spectra.
Fit statistic : C-Statistic = 513.63 using 1024 PHA bins and 1020 degrees of freedom.
Test statistic : Chi-Squared = 350.95 using 1024 PHA bins.
Reduced chi-squared = 0.34407 for 1020 degrees of freedom
Null hypothesis probability = 1.000000e+00
***Warning: Chi-square may not be valid due to bins with zero variance
in spectrum number(s): 1
Current data and model not fit yet.
XSPEC12>statistic test pchi
Default test statistic is set to: Pearson Chi-Squared
This will apply to all current and newly loaded spectra.
Fit statistic : C-Statistic = 513.63 using 1024 PHA bins and 1020 degrees of freedom.
Test statistic : Pearson Chi-Squared = 639.35 using 1024 PHA bins.
54
Reduced chi-squared = 0.62682 for 1020 degrees of freedom
Null hypothesis probability = 1.000000e+00
***Warning: Pearson Chi-square may not be valid due to bins with zero model value
in spectrum number(s): 1
Current data and model not fit yet.
As we can see from the warning message we need to ignore some channels where there is no effective response. Looking at a plot of the data and model indicates we should ignore below
0.15 keV and above 10 keV so:
XSPEC12>ignore **-0.15 10.0-**
11 channels (1-11) ignored in spectrum # 1
340 channels (685-1024) ignored in spectrum # 1
Fit statistic : C-Statistic = 510.55 using 673 PHA bins and 669 degrees of freedom.
Test statistic : Pearson Chi-Squared = 635.19 using 673 PHA bins.
Reduced chi-squared = 0.94947 for 669 degrees of freedom
Null hypothesis probability = 8.217205e-01
Current data and model not fit yet.
We assume that the Galactic column is known so freeze the first parameter. We then perform a fit followed by the error command:
XSPEC12> freeze 1
...
XSPEC12>fit
...
XSPEC12>parallel error 3
XSPEC12>err 2 4 6
Parameter Confidence Range ( 2.706)
2 1.16302 5.64805 (-2.00255,2.48247)
4 1.73345 1.95111 (-0.106137,0.111521)
6 0.00126229 0.00221906 (-0.000397759,0.000559019)
Note that our input parameters do not lie within the 90% confidence errors however since this will happen one times in ten (by definition) this should not worry us unduly. For a real observing proposal we would likely repeat this experiment with different input values of the intrinsic absorption to learn how well we could constrain it given a range of possible actual values.
4.6 Producing Plots: Modifying the Defaults
The final results of using XSPEC are usually one or more tables containing confidence ranges and fit statistics, and one or more plots showing the fits themselves. So far, the plots shown have generally used the default settings, but it is possible to edit plots to improve their appearance.
The plotting package used by XSPEC is PGPLOT, which is comprised of a library of lowlevel tasks. At a higher level is QDP/PLT, the interactive program that forms the interface between
55
the XSPEC user and PGPLOT. QDP/PLT has its own manual; it also comes with on-line help.
Here, we show how to make some of the most common modifications to plots.
In this example, we'll take the simulated Chandra spectrum and make a better plot. Figure I shows the basic data and folded model plot. The only additional changes we have made to this plot are to increase the line widths to make them print better. We made this plot as follows:
XSPEC12>setplot energy
XSPEC12>iplot data
PLT>lwidth 3
PLT>lwidth 3 on 1..2
PLT>time off
PLT>hard figi.ps/ps
The first lwidth command increases the line widths on the frame while the second increases it on the data and model. The time off command just removes a username and time stamp from the bottom right of the plot. The hard command makes a “hardcopy”, in this case a PostScript file.
Before looking at other PLT commands we can use to modify the plot there is one more thing we can try at the XSPEC level. The current bin sizes are much smaller than the resolution so we may as well combine bins in the plot (but not in the fitting) to make it clearer.
XSPEC12>setplot rebin 100 4
Combines four spectral bins into one. The setplot rebin command combines bins till either a S/N of the first argument is reached or the number of bins in the second argument have been combined. We do an iplot again then do the following modifications:
PLT> viewport 0.2 0.2 0.8 0.7
The first thing we'll do is change the aspect ratio of the box that contains the plot ( viewport in QDP terminology). The viewport is defined as the coordinates of the lower left and upper right corners of the page. The units are such that the full width and height of the page are unity. The labels fall outside the viewport, so if the full viewport were specified, only the plot would appear.
The default box has a viewport with corners at (0.1, 0.1) and (0.9, 0.9). For our purposes, we want a viewport with corners at (0.2, 0.2) and (0.8, 0.7): with this size and shape, the hardcopy will fit nicely on the page and not have to be reduced for photocopying.
Figure I: The data and folded model for the simulated Chandra ACIS-S spectrum.
56
Next we want to change some of the labels:
PLT> label top Simulated Spectrum
PLT> label file Chandra ACIS-S
PLT> label y counts s\u-1\d keV\u-1\d
Note the change in the y-axis label is to remove the string “normalized”. The normalization referred to is almost always unity so this label can generally be changed. To get help on a PLT command, just type help followed by the name of the command. Note that PLT commands can be abbreviated, just like XSPEC commands. To see the results of changing the viewport and the labels, just enter the command plot.
The two changes we want to make next are to rescale the axes and to change the y-axis to a logarithmic scale. The commands for these changes also are straightforward: the rescale command takes the minimum and maximum values as its arguments, while the log command takes x
or y
as arguments:
PLT> rescale x 0.3 6.0
PLT> rescale y 1.0e-4 0.03
PLT> log y
PLT> plot
To revert to a linear scale, use the command log off y
. The only remaining extra change is to reduce the size of the characters. This is done using the csize command, which takes the normalization as its argument. One (1) will not change the size, a number less than one will reduce it and a number bigger than one will increase it.
Figure J: A simulated Chandra ACIS-S spectrum produced to show how a plot can be modified by the user.
57
PLT> csize 0.8
PLT> plot
We make the PostScript file and also save the plot information using the wenv command that, in this case, writes files figj.qdp and figj.pco containing the plot data and commands, respectively.
PLT> hardcopy figj.ps/ps
PLT> wenv figj
PLT> quit
The result of all this manipulation is shown proudly in Figure J.
Markov Chain Monte Carlo Example
To illustrate MCMC methods we will use the same data as the first walkthrough.
XSPEC12> data s54405
...
XSPEC12> model phabs(pow)
...
XSPEC12> renorm
...
XSPEC12> chain type gw
XSPEC12> chain walkers 8
XSPEC12> chain length 10000
We use the Goodman-Weare algorithm with 8 walkers and a total length of 10,000. For the
G-W algorithm the actual number of steps are 10,000/8 but we combine the results from all 8
Figure K: The statistic from an MCMC run showing the initial burn-in phase.
58
walkers into a single output file. We start the chain at the default model parameters except that we use the renorm command to make sure that the model and the data have the same normalization. If we had multiple additive parameters with their own norms then a good starting place would be to use the fit
1
command to initially set the normalizations to something sensible.
XSPEC12> chain run test1.fits
The first thing to check is what happened to the fit statistic during the run.
XSPEC12> plot chain 0
The result is shown in Figure K, which plots the statistic value against the chain step. It is clear that after about 2000 steps the chain reached a steady state. We would usually have told
XSPEC to discard the first few thousand steps but included them for illustrative purposes. Let us do this again but specifying a burn-in phase that will not be stored.
XSPEC12> chain burn 5000
XSPEC12> chain run test1.fits
The output chain now comprises 10,000 steady-state samples of the parameter probability distribution. Repeating plot chain
0
will confirm that the chain is in a steady state. The other parameter values can be plotted either singly using eg plot chain
2
for the power-law index or in pairs eg plot chain
1 2
giving a scatter plot as shown in Figure L.
Using the error command at this point will generate errors based on the chain values.
XSPEC12>error 1 2 3
Errors calculated from chains
Figure L: The scatter plot from a 10,000 step MCMC run.
59
Parameter Confidence Range (2.706)
1 0.264971 0.919546
2 2.1134 2.41307
3 0.0107304 0.0171814
The 90% confidence ranges are determined by ordering the parameter values in the chain then finding the center 90%.
4.7 INTEGRAL/SPI
4.7.1 A Walk Through Example
Consider an observation of the Crab, for which a (standard) 5
5dithering observation strategy was employed. Since the Crab (pulsar and nebular components are of course un-resolvable at INTEGRAL's spatial resolution) is by far the brightest source in it immediate region of the sky, and its position is precisely known, we can opt not to perform SPI or IBIS imaging analysis prior to
XSPEC analysis. We thus run the standard INTEGRAL/SPI analysis chain on detectors 0-18 up to the SPIHIST level for (or BIN_I level in the terminology of the INTEGRAL documentation), selecting the "PHA" output option. We then run SPIARF, providing the name of the PHA-II file just created, and selecting the "update" option in the spiarf.par parameter file (you should refer to the SPIARF documentation prior to this step if it is unfamiliar). The celestial coordinates for the
Crab are provided in decimal degrees (RA,Dec = 83.63,22.01) interactively or by editing the parameter file. This may take a few minutes, depending on the speed of your computer and the length of your observation. Once completed, SPIARF must be run one more time, setting the
"bkg_resp" option to "y"; this creates the response matrices to be applied to the background model, and updates the PHA-II response database table accordingly. Then SPIRMF, which interpolates the template RMFs to the users desired spectral binning, also writes information to the PHA response database table to be used by XSPEC. Finally, you should run SPIBKG_INIT, which will construct a set of bbackground spectral templates to initialize the SPI background model currently installed in
XSPEC (read the FTOOLS help for that utility carefully your first time). You are now ready to run
XSPEC; a sample session might look like this (some repetitive output has been suppressed):
%
% xspec
XSPEC version: 12.2.1
Build Date/Time: Wed Nov 2 17:14:21 2005
XSPEC12>package require Integral 1.0
1.0
XSPEC12>data ./myDataDir/rev0044_crab.pha{1-19}
19 spectra in use
RMF # 1
Using Response (RMF) File resp/comp1_100x100.rmf
RMF # 2
Using Response (RMF) File resp/comp2_100x100.rmf
RMF # 3
Using Response (RMF) File resp/comp3_100x100.rmf
60
Using Multiple Sources
For Source # 1
Using Auxiliary Response (ARF) Files
resp/rev0044_100ch_crab_cmp1.arf.fits
resp/rev0044_100ch_crab_cmp2.arf.fits
resp/rev0044_100ch_crab_cmp3.arf.fits
For Source # 2
Using Auxiliary Response (ARF) Files
resp/rev0044_100ch_bkg_cmp1.arf.fits
resp/rev0044_100ch_bkg_cmp2.arf.fits
resp/rev0044_100ch_bkg_cmp3.arf.fits
Source File: ./myDataDir/rev0044_crab.pha{1}
Net count rate (cts/s) for Spectrum No. 1 3.7011e+01 +/- 1.2119e-01
Assigned to Data Group No. : 1
Assigned to Plot Group No. : 1
Source File: ./myDataDir/rev0044_crab.pha{2}
Net count rate (cts/s) for Spectrum No. 2 3.7309e+01 +/- 1.2167e-01
Assigned to Data Group No. : 1
Assigned to Plot Group No. : 2
...
Source File: ./myDataDir/rev0044_crab.pha{19}
Net count rate (cts/s) for Spectrum No. 19 3.6913e+01 +/- 1.2103e-01
Assigned to Data Group No. : 1
Assigned to Plot Group No. : 19
XSPEC12>mo 1:crab po
Input parameter value, delta, min, bot, top, and max values for ...
1 PhoIndex 1.0000E+00 1.0000E-02 -3.0000E+00
-2.0000E+00 9.0000E+00 1.0000E+01 crab::powerlaw:PhoIndex>2.11 0.01 1.5 1.6 2.5 2.6
2 norm 1.0000E+00 1.0000E-02 0.0000E+00
0.0000E+00 1.0000E+24 1.0000E+24 crab::powerlaw:norm>8. 0.1 1. 2. 18. 20.
…
XSPEC12>mo 2:bkg spibkg5
Input parameter value, delta, min, bot, top, and max values for ...
1 Par_1 0.0000E+00 1.0000E-02 -2.0000E-01
-1.5000E-01 1.5000E-01 2.0000E-01 bkg::spibkg5:Par_1>/*
…
________________________________________________________________________________
_____________________
XSPEC12>ign 1-19:68-80
...
XSPEC12>ign 1-19:90-100
...
XSPEC12>fit
Number of trials and critical delta: 10 1.0000000E-02
...
========================================================================
61
Model bkg:spibkg5 Source No.: 2 Active/On
Model Component Name: spibkg5 Number: 1
N Name Unit Value Sigma
1 Par_1 9.0650E-03 +/- 2.8651E-03
2 Par_2 1.6174E-02 +/- 3.4778E-03
…
25 Par_25 -1.9537E-02 +/- 6.1429E-03
26 norm 9.7286E-01 +/- 1.3527E-03
________________________________________________________________________
========================================================================
Model crab:powerlaw Source No.: 1 Active/On
Model Component Name: powerlaw Number: 1
N Name Unit Value Sigma
1 PhoIndex 2.1163E+00 +/- 1.8946E-02
2 norm 1.1390E+01 +/- 8.1414E-01
________________________________________________________________________
Chi-Squared = 1.8993005E+03 using 1463 PHA bins.
Reduced chi-squared = 1.3235544E+00 for 1435 degrees of freedom
Null hypothesis probability = 1.5268098E-15
XSPEC12>
Note that the syntax used for the data statement (appended curly bracket, specifying use of spectra 1-19), and the separate model commands, which are indexed and named (in this case simply
"crab" for the source of interest and "bkg" for the background model, "spibkg_lo". These commands are described in detail elsewhere in this document, as are the the spibkg_lo, spibkg_med and spibkg_hi models. In this case, 100 logarithmically-spaced energy bins spanning the nominal
20-8000 keV band of the SPI instrument were used.
In this example, only one dither-point was used to solve for the Crab spectrum, and the background. The simple assumption of a single background spectrum (i.e. no detector-to-detector variations) was assumed. In general, and particularly for fainter sources, a much larger number of spectra will be needed for a solution (and even for the Crab, the quality of the fit, and the accuracy of the inferred parameters can be improved). Also, detector-to-detector and/or time (i.e. pointingto-pointing) variations will need to be considered. This can be accomplished using the datagrouping feature of XSPEC, which will be described subsequently. Also notice that channels between about 70 and 80 were ignored; this is because there are detector electronic effects contaminating the single-event data for energies from ~1250-1400 keV (refer to the
SPI data analysis manual
for additional discussion), and that there are a lot of (scientifically uninteresting) background model parameters. Also, the highest energies were ignored, since the source flux becomes insignificant relative to the background.
Some results are illustrated below. These plots were generated with the sequence of commands:
XSPEC12> setplot group 1-19
XSPEC12> plot ldata res
62
…
XSPEC12> plot ufspec
Note that without the "setplot group" command, XSPEC would plot 19 sets of spectral data, models and residuals. The can become confusing, especially as the number of spectra included in an analysis becomes much larger than 19! On the other hand, it can be useful to divide the data into subsets for plotting purposes, e.g. setplot group 1-6 7-12 13-19, to get an idea of relative shadowing effects of the coded-mask. The left hand plot illustrates the source model, the background model, the total model (i.e. source + background), and the data (here in count rates per channel). The right hand plot illustrates the "unfolded model" (blue, power-law curve), the summed model, and the data as a photon flux. A possible source of confusion is the similarity of the background model curves plotted in theses two separate representations. The explanation is that the background, which is dominated by instrumental contributions, is modeled in detector count space (i.e. the background response matrix has unit effective area. Thus, to be strictly correct, the right-hand plot is a hybrid of the photon source model and the detector-rate background model. We further note that at the present time, XSPEC does not have the capability to plot (or store and manipulate) the background subtracted data. This is a feature under consideration for a future release.
If we had chosen a observation containing more than a single source, the procedure would have been similar, except that the sequence of model commands would be extended, e.g.
XSPEC12>data ./MyDataDir/GCDE_aug_03.pha{1-475}
…
XSPEC12> model 1:1e1740 po
…
XSPEC12> model 2:gx1_4 po
…
XSPEC12> model 3:bkg spibkg_lo
…
63
Here data from the Galactic Center deep exposure campaign were loaded, and two sources are sought. In this case, a much larger number of spectra were loaded (475 spectra corresponds to one full 5
5 dither using all 19 detectors.
In this case, the simple approach of applying constant background (i.e. no detector-todetector or pointing-to-pointing variation) to the full data set is likely to be a poor approximation. A more realistic approach would be to use the XSPEC grouping capability to handle such variations in the background solution. This can be accomplished in the usual manner (refer to the description of the grouping command in this document), however, it can become tedious in terms of the required command line inputs. For example, to establish a separate data group for each detector for a long (e.g. 5
5 dither) observations, a sequence of commands such as this would be required:
XSPEC12> data 1:1 ./MyDataDir/rev0044_Crab.pha.fits{1}
XSPEC12> data 2:2 ./MyDataDir/rev0044_Crab.pha.fits{2}
XSPEC12> data 3:3 ./MyDataDir/rev0044_Crab.pha.fits{3}
...
XSPEC12> data 19:19 ./MyDataDir/rev0044_Crab.pha.fits{19}
XSPEC12> data 1:20 ./MyDataDir/rev0044_Crab.pha.fits{20}
XSPEC12> data 2:21 ./MyDataDir/rev0044_Crab.pha.fits{21}
XSPEC12> data 3:22 ./MyDataDir/rev0044_Crab.pha.fits{22}
...
XSPEC12> data 19:38 ./MyDataDir/rev0044_Crab.pha.fits{38}
XSPEC12> data 1:39 /MyDataDir/rev0044_Crab.pha.fits{39}
XSPEC12> data 2:40 ./MyDataDir/rev0044_Crab.pha.fits{40}
XSPEC12> data 3:41 ./MyDataDir/rev0044_Crab.pha.fits{41}
...
XSPEC12> data 18:474 ./MyDataDir/rev0044_Crab.pha.fits{474}
XSPEC12> data 19:475 ./MyDataDir/rev0044_Crab.pha.fits{475}
One might then for example, make a first cut attempt by fitting a constant background.
Then, as a next step, one might allow the normalization terms of the background model to vary over the groups (i.e. over the detector plane). This is accomplished with the "untie" command, using the following sequence:
XSPEC12> untie bkg:52
XSPEC12> untie bkg:78
XSPEC12> untie bkg:104
XSPEC12> untie bkg:130
XSPEC12> untie bkg:156
XSPEC12> untie bkg:182
XSPEC12> untie bkg:208
XSPEC12> untie bkg:234
XSPEC12> untie bkg:260
XSPEC12> untie bkg:286
XSPEC12> untie bkg:312
XSPEC12> untie bkg:338
XSPEC12> untie bkg:364
XSPEC12> untie bkg:390
XSPEC12> untie bkg:416
64
XSPEC12> untie bkg:442
XSPEC12> untie bkg:468
XSPEC12> untie bkg:487
Note that use of the "bkg" identifier, which associates the parameters index with the background model. The specific sequence of numbers use here requires some explanation; the particular background model employed has 25 parameters (which simply correspond in rank order to the 25 most variable individual bins), and a normalization term, i.e. parameter 26. Thus, the normalization for the second detector group is parameter 52, for the third parameter 78, and so on.
Similar command sequences can be used to untie additional background model parameters.
Supposing that we did this and refitted the data. We then might, for example wish to go back and freeze the individual normalization terms with the freeze command:
XSPEC12> freeze bkg:26
XSPEC12> freeze bkg:52
…
XSPEC12> freeze bkg:487
By now though, you probably get the idea that this all requires an unreasonable amount of command-line input. To circumvent this problem, a number of INTEGRAL/SPI specific "tcl" scripts are available which greatly streamline this process.
4.7.2 INTEGRAL Specific Command Line Scripts
SPIdata
The SPIdata procedure, which when installed can be treated as an XSPEC command, greatly facilitates the data initialization step. For example, the command
XSPEC12> SPIdata ./MyData/Dir/rev0044_crab.pha 475 det Y
Opens the Crab observation spectral data file, reads the 475 spectra into memory, grouping them by detector. The "Y" then indicates that, yes, I wish to ignore the spectral data channels corresponding to the known detector-electronic noise contamination (this is the default). Instead of
"det" as the grouping option I could have selected "time" to group by time (quantized into ditherpointing intervals). A "-" lead to the data being initialzed into a single group. The command:
XSPEC12> SPIdata ./MyData/Dir/rev0044_crab.pha 475
65
Reads the 475 spectra into a single data group, and ignores the undesirable channels. If you forget all this, the command
XSPEC12> SPIdata -h will remind you. The scripts SPIuntie, and SPIfreeze have similar command-line syntax.
SPIuntie and SPIfreeze
XSPEC12> SPIuntie bkg 475 19 -1
The SPIuntie command script will accomplish the same result as the sequence of "untie" commands in the INTEGRAL/SPI example presented in this document. In that case, we had loaded 475 spectra associated with a single 5
5-dither pattern centered on the Crab nebula. The spectra were grouped by detector, which is a common approach to SPI analysis given the known detector-to-detector variations in the background rates. Suppose after an initial fitting pass, for which we assumed a single background spectrum, we know wish to untie the individual data group
(i.e. detector) background models. This can be accomplished by issuing 25 "untie" commands as previously noted, or in a single command line using the SPIuntie command:
XSPEC12> SPIuntie bkg 475 19 -1 untie bkg:52
Chi-Squared = 1.2030200E+04 using 1615 PHA bins.
Reduced chi-squared = 7.5852458E+00 for 1586 degrees of freedom
Null hypothesis probability = 0.0000000E+00
untie bkg:78
Chi-Squared = 1.2030200E+04 using 1615 PHA bins.
Reduced chi-squared = 7.5900314E+00 for 1585 degrees of freedom
Null hypothesis probability = 0.0000000E+00
untie bkg:104
renorm: no renormalization necessary
Chi-Squared = 1.2030200E+04 using 1615 PHA bins.
Reduced chi-squared = 7.5948231E+00 for 1584 degrees of freedom
Null hypothesis probability = 0.0000000E+00
…
One might then make a second pass at fitting the data, hopefully leading to improved statistics. Subsequently, additional background model parameters could be untied using the
66
SPIuntie procedure as well. For example, to untie three additional parameters over the full data set the command syntax is:
XSPEC12> SPIuntie bkg 475 19 1 3
…
This will untie the first 3 parameters of the background model identified by "bkg", i.e. equivalent to issuing (475-1)
3 individual untie commands. Note that you can always be reminded of the command-line argument definitions by typing "SPIuntie -h" at the XSPEC prompt.
Suppose now that you are satisfied with the relative background normalization terms, and wish to freeze them at their current values for subsequent fitting passes. This could be accomplished using the SPIfreeze command script:
XSPEC12> SPIfreeze bkg 475 -1
XSPEC12>SPIfreeze bkg 19 1 -1 freeze bkg:52 1
Chi-Squared = 6.6232600E+05 using 1805 PHA bins.
Reduced chi-squared = 3.7589444E+02 for 1762 degrees of freedom
Null hypothesis probability = 0.0000000E+00 freeze bkg:78
Chi-Squared = 6.5791894E+05 using 1805 PHA bins.
Reduced chi-squared = 3.7318148E+02 for 1763 degrees of freedom
Null hypothesis probability = 0.0000000E+00
…
As with the SPIuntie command script, typing "SPIfreeze -h" at the XSPEC prompt will scroll the command-line definitions to your screen.
2
Note that the current SPI background models, which are documented elsewhere, are designed so that the parameter list is hierarchically ordered in terms of decreasing criticality. Thus, freeing the first parameter is likely to have the most significant impact on the statistics, the second parameter, the next most significant, and so on.
5. XSPEC commands
5.1 Summary of Commands
The following is a list of the commands available in XSPEC, together with a brief description of the purpose of each. The commands have been categorized under six headings:
Control, Data, Fit, Model, Plot, Script, and Setting. The Control commands contain the interface with the operating system: they cause commands to be executed, or user input written to disk, or control how much is output. The Data commands manipulate the data being analyzed, by reading data into the program or replacing spectra or their ancillary detector, background, correction, or efficiency (auxiliary response) arrays. Additionally data commands control the channels under analysis. The fit commands invoke the fitting routines, modify their behavior by interchanging fitting algorithms or statistics in use, fixing parameters, or perform statistical testing. The Model commands create or manipulate the model, adding or editing components, modifying parameters, or alternatively performing analytical calculations from a model. The Plot commands deal with all aspects of plotting. The scripts are auto-loaded Tcl scripts that can be used in the same ways as commands. Finally the Setting commands sets variables that affect theoretical models.
Command Category Description
abund addcomp addline arf autosave backgrnd bayes chain chatter corfile cornorm cosmo
S
ETTING
Set the abundance table.
M
ODEL
Add a component to the model.
M
ODEL
Add lines to a model
D
ATA
Read an auxiliary response file.
C
ONTROL
Periodically save the XSPEC status.
D
ATA
Reset the files to be used for background subtraction.
F
IT
Set up for Bayesian inference.
F
IT
Run a Monte Carlo Markov Chain.
C
ONTROL
Control the verbosity of XSPEC.
D
ATA
D
ATA
Reset the files to be used for background correction.
Reset the normalization to be used in correcting the background.
S
ETTING
Set
H
0
,
q
0
, and
67
Command Category
cpd data delcomp diagrsp dummyrsp editmod energies eqwidth error (rerror) exec exit extend fakeit fit flux freeze (rfreeze)
Description
P
LOT
D
ATA
Alias for setplot device
.
Input one or more PHA data files.
M
ODEL
Delete a component from the model.
D
ATA
Diagonalize the current response for an ideal response.
M
ODEL
Create a dummy response, covering a given energy range.
M
ODEL
Add, delete, or replace one component in the model.
M
ODEL
Specify new energy binning for model fluxes.
M
ODEL
Calculate a model component’s equivalent width.
F
IT
Determine a single parameter confidence region. rerror is for response parameters.
C
ONTROL
Execute a shell command from within
XSPEC.
C
ONTROL
Wind up any hardcopy plots and exit from XSPEC.
M
ODEL
This is now obsolete. See energies command.
D
ATA
Produce simulated data files for sensitivity studies.
F
IT
F
IT
Find the best fit model parameters.
M
ODEL
Calculate the current model's flux over an energy range.
Do not allow a model parameter to vary during the fit. rfreeze is for response parameters.
68
Command Category
ftest gain goodness hardcopy help identify ignore initpackage iplot lmod log lrt lumin margin mdefine method model (rmodel)
Description
F
IT
Calculate the F-statistic between two model fits
M
ODEL
Perform a simple modification of the response gain.
F
IT
Monte Carlo calculation of goodness-offit.
P
LOT
Spool the current plot to the printer.
C
ONTROL
Obtain help on XSPEC commands.
M
ODEL
List possible lines in the specified energy range.
D
ATA
Ignore a range of PHA channels in future fit operations.
M
ODEL
Compile, build, and initialize a package of local models.
P
LOT
As plot command but interactive using
PLT.
M
ODEL
Load a package of local models.
C
ONTROL
Open the log file to save output.
S
CRIPT
Likelihood ratio test between two models.
M
ODEL
Calculate the current model's luminosity over a given rest frame energy range and redshift.
F
IT
MCMC probability distribution.
M
ODEL
Define a simple model using an arithmetic expression.
S
ETTING
Set the minimization method.
M
ODEL
Define the model to be used when fitting the data.
69
Command Category
modid multifake newpar
(rnewpar) notice parallel plot query quit renorm rescalecov response save script setplot show simftest
Description
M
ODEL
Guess line IDs in the model.
S
CRIPT
Perform many iterations of fakeit and save the results in a FITS file.
M
ODEL
Modify the model parameters (use rnewpar for response parameters).
D
ATA
Restore a range of PHA channels for future operations.
CONTROL
Enable parallel processing for particular tasks in XSPEC.
P
LOT
Plot various information on the current plot device.
C
ONTROL
Switch on/off prompt to continue fitting.
C
ONTROL
An alias for exit
F
IT
Adjust the model norms, and/or control automatic renorming.
S
CRIPT
Rescale the covariance matrix used in the proposal chain command.
D
ATA
Reset the files used to determine the detector responses.
C
ONTROL
Save aspects of the current state to a command file.
C
ONTROL
Open the script file to save all commands input.
P
LOT
Modify the plot device and other values used by the plot routines.
C
ONTROL
Display current file and model information.
S
CRIPT
Generate simulated datasets to estimate the F-test probability for adding a model component.
70
Command Category
source statistic steppar syscall systematic tclout tcloutr thaw (rthaw) thleqw time uncertain untie (runtie) version weight writefits xsect xset
Description
C
ONTROL
Execute a script file.
S
ETTING
Change the fit statistic in use.
F
IT
Step through a range of parameter values; perform a fit at each step.
C
ONTROL
Run a shell command.
M
ODEL
Set the model systematic error.
C
ONTROL
write xspec data to a tcl variable
C
ONTROL
tclout with return value
F
IT
Allow a model parameter to vary during the fit. rthaw is for response parameters.
M
ODEL
Calculates expected fluorescent line equivalent width.
C
ONTROL
Display elapsed time and other statistical information.
F
IT
Alias for error
M
ODEL
Untie linked parameters. runtie is for response parameters.
C
ONTROL
Print XSPEC version and build date/time
F
IT
Change the weighting function used for chi-squared fits.
S
CRIPT
Write information about the current fit and errors to a FITS file.
S
ETTING
Change the photoelectric absorption cross-sections in use.
S
ETTING
Modify a number of XSPEC internal switches
71
72
5.2 Description of Syntax
The individual commands are treated in alphabetical order in the following section. The novice would be well-served by reading the treatments of the data, model, newpar, and fit commands, in that order, then the other commands as needed. The write-up for each command includes a brief description of the purpose, an outline of the correct syntax, a more detailed discussion of the command assumptions and purpose, and a series of examples. Some commands have one or more subcommands that are similarly described following the command.
In the command description, the syntax uses the following conventions.
<arg>
<arg c> =:: <arg a> <arg b>
<arg>... an argument to the command defines
<arg c> as
<arga>
followed by
<argb> a repeated string of arguments of the same type
[<arg>] is an optional argument
<arg a> | <arg b> indicates a choice between an argument of
<arg a>
or
<arg b>
Exceptional responses to the command prompt are : empty line or line containing only spaces and tab characters nothing performed, prompt repeated
/
<EOF> (Ctrl-D on Unix)
/*
?, ?command, command ? any remaining arguments will have the values given on the last invocation of the command same as quit skip input and return to prompt. Defaults for prompted values will be used.
Print list of commands, or summary help for a single command
5.3 Control Commands
5.3.1 autosave: set frequency of saving commands
Set or disable autosave, which saves the XSPEC environment to a file periodically.
Syntax:
autosave
<option> where
<option>
is either off
or a non-zero positive integer
N
. If the option is off
, then auto-saving is disabled.If the option is
N, the XSPEC environment is saved every
N
commands.
The saving of the environment is equivalent to the command
XSPEC12>save all xautosav.xcm ., i.e. both the file and model information is saved to the file xautosav.xcm, placed in the directory ~/.xspec/cache. Thus in case of an unexpected crash, the state of XSPEC before the crash can be restored by running
@xautosav.xcm
. The default value for the auto-save option is 1.
73
5.3.2 chatter: set verboseness level
Control the verbosity of XSPEC.
Syntax:
chatter
<chatter level> <log chatter> where
<chatter level
> and
<log chatter
> are integer values.The initial value for each argument is 10. Higher values will encourage XSPEC to tell the user more, lower values tell the user less, or make XSPEC “quieter.”
<chatter level
> applies to the terminal output, while
<log chatter
> controls the verbosity in the log file. Currently, the maximum chattiness is
25.Values below five should be avoided, as they tend to make XSPEC far too obscure.Some commands may temporarily modify the chattiness, such as the error command. A chattiness of 25 will generate a lot of debug output.
Examples:
XSPEC12>
chatter 10
// Set the terminal chattiness to 10, same as the initial value.
XSPEC12>
chatter ,0
//Set the chattiness for the log file to very low.
//This setting essentially disables the log file output.
XSPEC12>
chatter 5
//Make XSPEC very quiet.
XSPEC12>
chatter 10 25
// Restore the terminal chattiness to the initial level,
// while in the log file XSPEC will tell all
// (particularly when new data files are read in)
5.3.3 exit, quit: exit program
The command to end the current XSPEC run.
Syntax:
exit
After an exit
, the current plot files are closed.An <EOF> will have an identical result.
5.3.4 help: display manual or help for a specific command/theoretical model component
Obtain help on the XSPEC commands, their syntax, and examples of their use.
Syntax:
help
[<topic list>]
On the first invocation of the help command, an instance of a pdf file reader (by default
Adobe Acrobat Reader) is started (a shortly delay may ensue), or the XSPEC manual is accessed online. Please see the subsection “Customizing XSPEC” in the XSPEC Overview section for details on how to control this behavior. The Acrobat reader must be in the user’s path. If this default is used, then subsequent calls to help will use this instance to display other help pages. help without arguments displays the XSPEC manual, with a bookmark index that allows random access to the help system, or in the online mode will open to the XSPEC manual homepage.
74
The design allows for users to add help files for local models and scripts to the help system if they are placed in the help search path.
Examples:
XSPEC12> help
//show the entire manual.
XSPEC12> help fit
//Go to the help text for the fit command.
XSPEC12> help model pow
//Go to the help text for the powerlaw model. (Entering just “XSPEC12> model” will produce a scrolled-text list of all available model components.)
XSPEC12> help appendices
//show the manual appendices (which document the user interface, the Cash statistic, how to add models to XSPEC, a summary of PLT commands, and associated FTOOLS and other programs for manipulating data).
XSPEC12>help appendix local
//show the appendix describing how to add local models
Help also displays the following information as scrolling text:
XSPEC12> help ?
//Show a list of all available commands.
XSPEC12> help ??
//Show a brief summary and usage syntax of all available commands.
XSPEC12> <command> ?
// Show brief summary and syntax of <command>.
5.3.5 log: log the session output
Open a log file.
Syntax:
log
[STAMP] <log file> where
<log file>
is the name of the file to be opened (default extension is
.log
).If no arguments are on the line, then the default file name is xspec.log
. If
<log file>
matches the string none
, then the current log file is closed. If the string
STAMP
is given as an argument then the log filename will include a data and time stamp. If
<log file>
has no suffix then the stamp is appended to the name and a
.log
suffix added. To change the chattiness level for the log file (ie. the amount ofinformation written to the log file) use the chatter
command. The default chatter level for the log file is 10.
Examples:
XSPEC12> log
//Turn on the log file (default xspec.log).}
XSPEC12> log none
//Close the log file.
XSPEC12> log mylog
//Open the log file (mylog.log)
XSPEC12> chatter ,, 12
//Set the log file chattiness to 12.
75
5.3.6 parallel: enable parallel processing for particular tasks in XSPEC.
where <task> is currently limited to leven, error, or steppar. For best results, it is recommended that you set <max num of processes> to the number of CPU cores on your machine. Set <max num processes> back to 1 to turn parallel processing off for the particular task. To display current settings, type ‘parallel’ with no arguments.
The leven option will spawn up to <max num> processes during the Levenberg-Marquardt fitting, specifically to perform the N independent calculations of the parameter first-order partial derivatives (N being the number of variable fit parameters). [This will not apply if the
USE_NUMERICAL_DIFFERENTIATION variable in the user’s Xspec.init file is changed from the default ‘false’ to ‘true’.]
The speed-up that one can expect is highly dependent upon the model in use. For simpler models with quick calculation times, you will probably see little to no speed gain with parallel leven. But with multi-core CPUs, gains should be quite noticeable when the model calculation consumes a large fraction of the overall fitting time. For example, with fits using the time-intensive sedov model on a 4-core machine, we’ve typically seen about a 40% reduction in fit time compared with the single processing case.
The error option is for running parallel computations within XSPEC’s error command. This enables the error calculations for multiple parameters to be performed simultaneously. The speedup here should simply be proportional to the number of cores available. However for cases where complications are reported (such as a new minimum found, or a non-monotonicity in the statistic space), it is recommended that you perform the error calculations in standard single-process mode.
When the steppar option is set, XSPEC will divide the N-dimensional steppar grid into <max num> sections of equal size, and spawn a separate process for calculating each section.
If both parallel leven and error or steppar are in use, XSPEC will temporarily disable the lowerlevel leven parallelization when running the higher-level parallel error or steppar command calculations.
Examples:
XSPEC12>
model cflow
// Using a model with 5 variable fit parameters.
XSPEC12>
parallel leven 4
XSPEC12>
fit
// Calculations for the 5 parameters will be divided amongst
// 4 processes during the fit.
XSPEC12> parallel leven 1
// Restores single-process calculation to the
//
XSPEC12> parallel error 3
// Allow up to 3 simultaneous ‘error’ parameter calculations
// to be performed in parallel.
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XSPEC12> error 2 3 6
// Perform error calculations on parameters 2, 3, and 6 in parallel.
XSPEC12> parallel steppar 4
// The following 20x30 steppar grid will be split amongst
// 4 parallel processes.
XSPEC12> steppar 1 10. 11. 20 2 .5 .8 30
// Display current settings:
XSPEC12> parallel
Maximum number of parallel processes:
error: 3
leven: 1
steppar: 4
5.3.7 query: set a default answer for prompts in scripts
Switch on/off the continue fitting questions.
Syntax:
query
<option> where
<option>
is yes
, no
, or on
. If on
then the continue fitting question in
fit
,
steppar
, and
error
will be asked when the number of trials is exceeded. Also, when the number of trials to find the error
is exceeded a question will be asked. For either of the other two options the questions will not be asked but the answer will be assumed to be yes
or no
depending on the
value
set. To ensure that fitting continues without any questions being asked use the command
XSPEC12>
query yes
5.3.8 save: save the current session commands
Save aspects of the current state to a command file.
Syntax: save
<option> <filename>
If no
<filename>
is given, then the file
savexspec.xcm
is created.
If you don't give the extension to the file name the default is
.xcm
.
The values of
<option>
allowed are
model
, files,
and
all
. The
model
option writes out commands to recreate the current model and parameter values; the
files
option writes out commands to read-in the current spectra, and the all
option does both of the above. The default option is
model
. To recover the saved context use the command
XSPEC12>@filename
Examples:
XSPEC12> save model fname
// Write out model commands to the file fname.xcm
XSPEC12> save
// Same as above, but save into file savexspec.xcm.
XSPEC12> save files fname
// Write out data file commands.
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5.3.9 script: write commands to a script file
Open a script file.
Syntax:
script
<script file> where
<script file>
is the name of the file to be opened (default extension is
.xcm
).If no arguments are on the line, then the default file name is xspec.xcm
.If
<script file> matches the string none
, then the current script file is closed. The script file saves all commands that are input. This command is useful for users who use the same set of commands repeatedly.
Once a script file is written and saved, the user then can re-run the same set of commands on other data by
XSPEC12>
source <script file>
Examples:
XSPEC12> script
// Turn on the script file (default xspec.xcm)
XSPEC12> script none
// Close the script file.
XSPEC12> script myscript
// Open the script file (myscript.xcm)
5.3.10 show: output current program state
List selected information to the user's terminal (and the log file, if open).
Syntax:
show
[<selection>] where
<selection>
is a key word to select the information to be printed. If omitted, it is the information last asked for. Initially, the default selection is all
. (Note: to better integrate the usage of OGIP type-II files, much of the information given by “show files” in previous versions is now displayed by “show data.”)
Selections are:
XSPEC12> show abund
//show current solar abundance table
XSPEC12>
show all
//All the information
XSPEC12>
show allfile
// All file information = files + noticed + rates
XSPEC12>
show control
// XSPEC control information
XSPEC12> show data
// File names, associated coefficients, and net count rates,
// displayed in order of spectrum number. For higher chatter,
// also displays grouping map.
XSPEC12>
show free
// Free parameters
XSPEC12>
show files
// Equivalent to “show data” but displayed in order of file name.
XSPEC12>
show fit
//Fit information
XSPEC12>
show model
//The model specification
XSPEC12>
show noticed
//Channel ranges noticed for each file.
XSPEC12>
show parameters
//All current parameter values (including gain parameters, if any).
XSPEC12>
show parameters <par range>
// Show subset of all model parameters given by <par range>,
// e.g. show parameters 1,3,5-8
XSPEC12>
show pha
// Current data, error and model values for each channel.
XSPEC12>
show plot
//Current plot settings from setplot command, includes rebinning info.
XSPEC12>
show rates
//Folded model, correction rates for each file.
XSPEC12> show response
//show responses loaded
XSPEC12> show rparameters
// All current gain (response) parameters
XSPEC12> show rparameters <par range>
// Show subset of all gain (response) parameters
XSPEC12> show xsect
//show description of cross-section table
5.3.11 syscall: execute a shell command
Execute command in a shell.
Syntax:
syscall{[<shell command>]>
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This command executes its arguments by passing them to the users current shell for execution. Thus file name globbing ( i.e. wildcard expansion) are performed on the command before execution. This is in contrast to the exec
command, which executes commands directly, without first passing them on to a shell.
If no arguments are given, then the command will start an interactive subshell.
79
80
5.3.12 tclout: create tcl variables from current state
Write internal xspec data to a tcl variable. This facility allows the manipulation of xspec data by tcl scripts, so that one can, for example, extract data from xspec runs and store in output files, format xspec output data as desired, use independent plotting software, etc.
Syntax: tclout
<option> [<par1>] [<par2>] [<par3>]> tclout
creates the tcl variable
$xspec_tclout
, which can then of course be set to any named variable. The allowed values of <option> are :
? areascal n <s|b> arf n backgrnd n backscal n <s|b> chain best|last|proposal|stat chatter compinfo [<mod>:]n
[<groupn>] cosmo
Show the valid options. Does not set
$xspec_tclout
.
Writes a string of blank separated values giving the
AREASCAL values for spectrum n. If no second argument is given or it is “s” then the values are from the source file, if “b” from the background file.
The auxiliary response filename(s) for spectrum n.
Background filename for spectrum n
Same as areascal option but for BACKSCAL value.
The best option returns the parameter values corresponding to the smallest statistic value in the loaded chains. The last option returns the final set of parameter values in the loaded chains. The proposal option takes arguments distribution or matrix and returns the name or covariance matrix for the proposal distribution when using
Metropolis-Hastings. The stat option returns the output of the last chain stat command.
Current xspec chatter level.
Name, 1 st
parameter number and number of parameters of model component n, belonging to model w/ optional name <mod> and optional datagroup
<groupn>.
Writes a blank separated string containing the Hubble constant (H0), the deceleration parameter (q0), and the cosmological constant (Lambda0). Note that if
Lambda0 is non-zero the Universe is assumed to be flat and the value of q0 should be ignored.
covariance [m, n] datagrp [n] datasets dof energies [n] eqwidth n [errsims] error [<mod>:]n
(for gain parameters use: rerror [<sourceNum>:]n )
Element (m,n) from the covariance matrix of the most recent fit. If no indices are specified, then entire covariance matrix is retrieved.
Data group number for spectrum n. If no n is given, outputs the total number of data groups.
Number of datasets.
Degrees of freedom in fit, and the number of channels.
Writes a string of blank separated values giving the energies for spectrum n on which the model is calculated. If n is not specified or is 0, it will output the energies of the default dummy response matrix.
Last equivalent width calculated for spectrum n. If
“errsims” keyword is supplied, this will instead return the complete sorted array of values generated for the most recent eqwidth error simulation.
Writes last confidence region calculated for parameter
n of model with optional name <mod>, and a string listing any errors that occurred during the calculation. The string comprises nine letters, the letter is T or F depending on whether or not an error occurred. The 9 possible errors are:
1. new minimum found
2. non-monotonicity detected
3. minimization may have run into problem
4. hit hard lower limit
5. hit hard upper limit
6. parameter was frozen
7. search failed in –ve direction
8. search failed in +ve direction
9. reduced chi-squared too high
So for example an error string of “FFFFFFFFT” indicates the calculation failed because the reduced chi-squared was too high.
81
82
expos n <s|b> filename n flux [n] [errsims] ftest gain
[<sourceNum>:] <specNum> slope | offset goodness [sims] idline e d ignore [<n>] lumin [n] [errsims] margin probability
|
[<modName>:]<parNum> model
Same as areascal option but for EXPOSURE value.
Filename corresponding to spectrum n.
Last model flux or luminosity calculated for spectrum
n. Writes a string of 6 values: val errLow errHigh
(in ergs/cm
2
) val errLow errHigh (in photons).
Error values are .0 if flux was not run with “err” option.
If the “errsims” keyword is supplied, this will instead return the completed sorted array of values generated during the most recent flux error calculation.
The result of the last ftest command.
For gain fit parameters, value,delta,min,low,high,max for the slope or offset parameter belonging to the
[<sourceNum>:]<specNum> response. For nonfit gain parameters, only the value is returned.
The percentage of realizations from the last goodness command with statistic value less than the best-fit statistic using the data. If optional “sims” keyword is specified, this will instead give the full array of simulation values from the last goodness command.
Possible line IDs within the range [e-d, e+d].
The range(s) of the ignored channels for spectrum <n>.
Last model luminosity calculated for spectrum n.
Same output format as flux option, in units of
1.0x10
44
erg/s.
The probability option returns the probability column respectively from the most recent margin command. Otherwise, the parameter column indicated by <parNum> is returned. Note that for multi-dimensional margin the returned parameter column will contain duplicate values, in the same order as they originally appeared on the screen during the margin run.
Description of current model(s).
modcomp [<mod>] modpar [<mod>] Number of model parameters (with optional model name). modval [<specNum>[<mod]] Write to Tcl the last calculated model values for the specified spectrum and optional model name.
Writes a string of blank separated numbers. Note that the output is in units of photons/cm^2/s/bin. nchan [<n>]
Number of components in model (with optional model name). noticed [<n>] noticed energy [<n>] nullhyp
Total number of channels in spectrum n (including ignored channels).
Range (low,high) of noticed channels for spectrum n.
The noticed energies for spectrum n. param [<mod>:]n peakrsid n [lo, hi]
When using chi-square for fits, this will retrieve the reported null hypothesis probability.
(value,delta,min,low,high,max) for model parameter n. pinfo [<mod>:]n
Energies and strengths of the peak residuals (+ve and – ve) for the spectrum n. Optional arguments lo, hi specify an energy range in which to search.
Parameter name and unit for parameter n of model with optional name. plink [<mod>:]n plot <option> <array> [<plot group n>] plotgrp
Information on parameter linking for parameter n. This is in the form true/false (T or F) for linked/not linked, followed by the multiplicative factor and additive constants if linked.
Write a string of blank separated values for the array.
<option> is one of the valid arguments for the plot or iplot commands. <array> is one of x, xerr, y, yerr, or model. xerr and yerr output the 1-sigma error bars generated for plots with errors. The model array is for the convolved model in data and ldata plots. For contour plots this command just dumps the steppar results. The command does not work for genetic plot options.
Number of plot groups.
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query rate <n | all> rerror [<sourceNumber>:]n response n sigma [<modelName>:]n simpars solab stat [test] statmethod [test] steppar varpar version statistic | delstat |
[<modName>:]<parNum>
84
The setting of the query option.
Count rate, uncertainty and the model rate for the specified spectrum n, or for the sum over all spectra.
Writes last confidence region calculated for response parameter n of model with optional source number, and a string listing any errors that occurred during the calculation. See the help above on the error option for a description of the string.
Response filename(s) for the spectrum n.
The sigma uncertainty value for parameter n. If n is not a variable parameter or fit was unable to calculate sigma, -1.0 is returned.
Creates a list of parameter values by drawing from a multivariate Normal distribution based on the covariance matrix from the last fit. This is the same mechanism that is used to get the errors on fluxes and luminosities, and to run the goodness command.
Solar abundance table values.
Value of statistic. If optional ‘test’ argument is given, this outputs the test statistic rather than the fit statistic.
The name of the fit stat method currently in use. If optional ‘test’ argument is given, this will give the name of the test stat method.
The statistic and delstat options return the statistic or delta-statistic column respectively from the most recent steppar run. Otherwise, the parameter column indicated by <parNum> is returned. Note that for multi-dimensional steppars the returned parameter column will contain duplicate values, in the same order as they originally appeared on the screen during the steppar run.
Number of variable fit parameters.
The XSPEC version string.
weight xflt n
Name of the current weighting function.
XFLT#### keywords for spectrum n. The first number written is the number of keywords and the rest are the keyword values.
Examples:
XSPEC12> data file1
XSPEC12>
model pha(po)
...
XSPEC12>
fit
...
XSPEC12> tclout stat
XSPEC12> scan $xspec_tclout “%f” chistat
XSPEC12> tclout param 1
XSPEC12> scan $xspec_tclout “%f”par2
XSPEC12> tclout param 2
XSPEC12> scan $xspec_tclout “%f”par3
XSPEC12> tclout param 3
In this example, scan
is a tcl command that does a formatted read of the variable
$xspec_tclout
. It reads the first floating point number into the variable given by the last argument on the line.This sequence creates a simple model, fits it, and then writes the
2
statistic and the three parameters to tcl variables
$chistat
,
$par1
,
$par2,
and
$par3
. These can now be manipulated in any way permitted by tcl. Examples of using tclout and tcloutr can be found in the Xspec/src/scripts directory.
85
5.3.13 tcloutr: tclout with return value
Syntax: tcoutr
<option> [<par1>] [<par2>] [<par3>]>
tcloutr is identical to the tclout command except that it also provides what is stored in
$xspec_tclout
as a return value. Therefore it can be used in tcl scripts like this: set var1 [tcloutr energies 1]
tcloutr may produce quite a lot of unwanted screen output, which can be avoided by using
tclout.
86
5.3.14 time: print execution time
Get some information about the program run time.
Syntax:
time
The time command prints out elapses CPU time attributed to the user and to the system.
Two output lines are given, one for user/system time since the time command was last called, and one for time elapsed since the program started.
5.3.15 undo: undo the previous command
Undo the affects of the previously entered xspec command.
Syntax:
undo
New for xspec version 12, the undo command will restore the state of the xspec session prior to the most recently entered command. The current implementation does not allow restoration to more than one command back, so calling undo repeatedly will have no effect. Also, a plot command cannot be undone.
5.3.16 version: print the version string
Syntax:
version
version prints out the information about version number and build date and time (not current date, time) displayed when XSPEC is started.
87
5.4 Data Commands
5.4.1 arf: change the efficiency file for a given response
Read in one or more auxiliary response files (ARF). An ARF gives area versus energy and is used to modify the response matrix for a spectrum. The file must be in the
OGIP standard format.
Syntax:
arf
[ <filespec>...] where
<filespec> =:: [
[source #:]
<spectrum num>]
<filename>
[{ranges}]
... and where <spectrum num> is the spectrum number for the first <filename> specified, <spectrum num> plus one is the spectrum number for the next file (or next entry in {ranges} specifier for Type II multi-ARF files), and so on.
<filename> is the name of the auxiliary response file to be used with the associated spectrum. The optional source number defaults to 1, and for ARFs stored in OGIP Type
II files, {ranges} specifies the row numbers of the desired ARF(s). See the data command for allowed range specification.
If no
<spectrum num>
is given in the first
<filespec>
it is assumed to be 1. If no file specifications are entered, then none of the spectrum responses are modified.An error message is printed if the spectrum number is greater than the current number of spectra (as determined from the last use of the data command).A file name none indicates that no auxiliary response is to be used for that spectrum. If a file is not found or cannot be opened for input, then the user is prompted for a replacement auxiliary response file.An
<EOF>
at this point is equivalent to none
. See the data command forways to completely remove the dataset from consideration.
Note: The ARF command is currently not implemented for data formats which use multiple RMFs per spectrum, such as Integral/SPI data.
Examples:
It is assumed that there are currently three spectra:
XSPEC> arf a,b,c
// New files for the auxiliary response are given for all three spectra.
XSPEC> arf 2 none
// No auxiliary response will be used for the second spectrum.
XSPEC> arf ,d.fits
// d.fits becomes the auxiliary response for the second spectrum.
XSPEC> arf 2 e.fits{3-4}
// Rows 3 and 4 of multi-ARF file e.fits become the auxiliary responses for the second and third spectra.
XSPEC> arf 2:1 f.fits
// f.fits becomes the auxiliary response for the second source of spectrum 1.
5.4.2 backgrnd: change the background file for a given spectrum
Modify one or more of the files used in background subtraction.
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Syntax:
backgrnd
[ <filespec>...]
backgrnd
<spectrum number> none where
<filespec> =:: [ <spectrum num>] <filename>...
and where
<filename>
is the name of the PHA file to be used for background subtraction. The numbering scheme is as described for the
data
command, except that the
<spectrum num> must have previously been loaded.
An error message is printed if
<spectrum num>
is greater than the current number of spectra (as determined from the last use of the data command. backgrnd <n> none
indicates that no background subtraction is to be performed for that spectrum. If a file is not found or cannot be opened for input, then the user is prompted for a replacement background file(an
<EOF>
at this point is equivalent to backgrnd
<spectrum number> none
). The current ignore status for channels is not affected by the bkgrnd command. (See the ignore and
notice
commands). Finally, any grouping specification will be overridden by the grouping in the source spectral file so that the source and background are binned in the same way.
The format of the background file must match that of the spectrum file: for this purpose OGIP Type I and II are considered to be the same format.
For details of how to remove spectra see the
data
command documentation.
Examples:
Suppose there are currently three spectra. Then
XSPEC12>
backgrnd a,b,c
// New files for background subtraction are given for all
// three spectra.
XSPEC12>
backgrnd 2 none
// No background subtraction will be done for the second spectrum.
XSPEC12>
backgrnd ,d
// d.pha becomes the background for the second spectrum.
XSPEC12> backgrnd 2 e{4-5}
// Rows 4 and 5 of Type II file e.pha become the background for
// the second and third spectrum respectively.
5.4.3 corfile: change the correction file for a given spectrum
Reset the files used for background correction.
Syntax:
corfile
[<filespec>...] where
<filespec>
is the same as for the backgrnd command. The correction file can be associated with a spectrum to further adjust the count rates. It is a PHA file whose count rate is multiplied by the current associated correction norm (see the
cornorm and recornrm command) and then subtracted from the input uncorrected data.
The correction norm is not changed by running the corfile command. Default values for the correction file and norm are included in the data PHA file.Unlike the background file, the correction data does NOT contribute to the measurement error. A file name of none
is equivalent to no correction file used.If an input file can not be opened or found, an error message is printed and the user prompted for a replacement.As with the backgrnd command, the correction file is checked against the associated spectrum for number of channels, grouping status, and detector ID. The current ignore status for channels is not affected by the corfile command. Note that correction files have the same format as the
PHA files used by the data command.
Examples:
It is assumed that there are currently three spectra:
XSPEC12>
corfile a,b,c
// New correction files are used for all three spectra.>
XSPEC12>
corfile 2 none
// No correction will be done for the second spectrum.}
XSPEC12>
corfile ,d
// The 2nd file now uses d.pha as its correction.
XSPEC12> corfile 2 e{4-5}
// Rows 4 and 5 of Type II file e.pha becom the correction files for the second
// and third spectrum respectively.
5.4.4 cornorm: change the normalization of the correction file
Reset the normalization used in correcting the background.
Syntax:
cornorm
[[ <spectrum range>...] [ <cornorm>]]
... where
<spectrum range>
=::
<first spectrum no.> – <last spectrum no.>
s a range of spectra to which the correction is to be applied and
<cornorm>
is the value to be used for the normalization. A decimal point (.) is used to distinguish a correction norm from a single spectrum
<spectrum range>
. If no correction norm is given, then the last value input is used (the initial value is one (1)). If no range is given, then the last single range input is modified. (See the corfile command.)
Examples:
Assume that there are four spectra, all with associated correction files already defined, either by default in their PHA file, or explicitly by using the corfile command.
XSPEC12>
cornorm 1-4 1.
//The correction norm for all four is set to 1.0
XSPEC12>
cornorm 0. 1-2 0.3
//The correction norm for the last input range (which was 1-4)
// is set to 0., then files 1 and 2 are reset to 0.3.
XSPEC12>
cornorm 4
//file 4 has the correction also set to 0.3.
XSPEC12>
cornorm 1 4 -.3
//files 1 and 4 are set to -.3.
XSPEC12>
cornorm .7
//file 4 (as the last input single range) is set to 0.7.
89
90
5.4.5 data: read data, background, and responses
Input one or more spectra, together with their associated (background, response) files.
Syntax:
data <file spec1>[,…] [ <file spec2>…] [/]
data none
data <spectrum #> none where t he file specification is
<filespec> =:: [[ <data group #:>] <spectrum #>]
<filename>[{ranges}]
If a particular file is not found or cannot be opened for input for some reason, then the user is prompted for a replacement file name. An
<EOF>
at this point is equivalent to typing
none
. The default extension for all files is
.pha
, so all other extensions, (e.g.
.fak
) must be entered explicitly.The default directory is the current user directory when
XSPEC is invoked. When a new file is input, by default all its PHA channels are considered good channels for fitting and plotting purposes (see the ignore
and notice commands).
XSPEC’s “native” data format is the OGIP standard. The standard specifies the representation of spectrum and all related datasets. XSPEC12 is explicitly designed to be able to work with other data formats as required: for example, the Integral/SPI spectral data format, although based on OGIP TypeII, deviates slightly. This was necessary because 3 response/arf pairs are required per spectrum. XSPEC12 has the ability to specify how response and other data are stored on disk, composed, and combined within the spectral fitting problem by adding new data modules at run-time. In XSPEC12, unlike
XSPEC11, the channels that are ignored are a property of the spectrum, and therefore must be reset when the spectrum is replaced by another.
If the file contains multiple spectra, such as an OGIP Type II PHA file, then the desired spectrum can be specified by appending { ranges
} to the end of the filename, where n
is the row number of the spectrum in the file.
XSPEC12 allows any combination of multiple ranges in the parentheses delimited by commas. The wildcard characters *and ** may also be used. A ** on either side of a hyphen indicates either the first or last row in the file, based on whether it is to the left or right of the hyphen. (If a * is entered on the left or right side of a hyphen, it is substituted by the most recently entered left or right value respectively.) All rows in the file may be selected simply with a single * or ** between the brackets with no hyphen.
Examples:
XSPEC12>
data pha2data{1,3,5-8,14-26,75-**}
// In addition to the various specified rows between 1 and 26,
// also load rows 75 through the end of the file.
XSPEC12>
data pha2data{*}
// Select all rows in the file.
91
For files with multiple spectra the data may either specify a header keyword specifying the response, auxiliary response, background and correction files, or these may be string-valued columns specifying a different filename per row.
Consult the
http://heasarc.gsfc.nasa.gov/docs/software/ftools
package documentation for details of how to modify the file.
The individual spectral data files are created outside of XSPEC by detectorspecific software. They are organized as
XSPEC data
files, but often referred to as PHA files. Whatever its format, the PHA file contains such information as integration time, detector effective area, and a scaling factor (BACKSCAL in the OGIP standard) that estimates the expected size of the internal background. The data file also contains the names of the default files to be used for background subtraction and for the detector sensitivity versus incident photon energy (the response and arf files). A data file has the total observed counts for a number of channels and a factor for the size of any systematic error. Each channel is converted to a count rate per unit area (assumed cm
–2
). The default background file is used for background subtraction. An error term is calculated using
Poisson statistics and any systematic error indicated in the file
spectrum numbering
Multiple filespec
clauses can be input on a single data command, or also on multiple data command. Within XSPEC, each set of data is referred to by its associated spectrum number.
<spectrum #>
, as determined by the following rules. For convenience, we denote the number of spectra that have been previously read in by data command as N s
Spectra in XSPEC are numbered sequentially from 1.
If no spectrum number is specified by the user, the spectrum in the first filename specified is assigned to 1. If spectra have already been loaded at this point, they will be replaced, deleted, or added to depending on the command. For example, if there are 3 spectra loaded (N s
= 3) and the user types
XSPEC12> data multidatafile{1-2} then spectra 1 and 2 will be replaced and 3 deleted. The command
XSPEC12> data multidatafile{1-4} will replace all three spectra and add the fourth.
If the user specifies a “load point”, i.e. the first spectrum number to be created by the new command, i.e.
XSPEC12> data 3 multidatafile{1-4}
3
For OGIP files, any FITS NULL values will be converted to the value 1.E-32. This should have no practical effect because any channels with NULL values will presumably be marked as bad or otherwise ignored.
92
then that load point may not exceed N s
+ 1. If it does, XSPEC will correct the number and issue a warning.
A skipped-over argument can be effected by a comma, for example
XSPEC12> data 3 spectrum1, , spectrum2 indicates that the spectrum for that position, as input in an earlier invocation of data, will continue to be used (in this example, spectrum 3 is replaced, 4 is left untouched, and 5 is either replaced or added. Any spectra with numbers great than 5 are removed.
If the filename input is none
, that spectrum is removed, and so are any highernumber spectra unless none is terminated with a / character. For example:
XSPEC12> data 3 none removes all spectra numbered 3 or higher,
XSPEC12>data 3 none/ removes only spectrum 3 and renumbers the rest.
The data command determines the current total number N
T
of spectra: either N
T spectra are implied by the command line, or the highest spectrum number added (after
XSPEC has made corrections as mentioned above) is N
T
This is true UNLESS a / character terminates the data command.
If the line is terminated by a slash (/), then the current number of spectra is the previous total number of datsets N s or the number as determined from the command line, whichever is greater.
The command
XSPEC12> data by itself prints the one-line help summary, as does
XSPEC12> data ?
data groups
XSPEC allows the user to specify separate data groups for different spectra. Each data group has its own set of parameters for the defined model. These parameters can be either independent from data group to data group, or they can be linked across data groups using the standard XSPEC syntax (see the newpar command). This facility can be used for, say, analyzing extended sources. example
Note that the data group number
XSPEC12>
data 2:3 spectrum4
precedes the spectrum number: in the
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which assumes that at least two spectra are already present, the data group number is 2 and the spectrum number is 3.
XSPEC will not allow the data group number to exceed the spectrum number: for example
XSPEC12> data 3:2 spectrum4 is invalid. XSPEC will correct this and issue a warning.
More Examples:
XSPEC12>
data a
//The file a.pha
is read in as the first (and only) spectrum.
XSPEC12>
data ,b
//b.pha becomes the second spectrum, the first spectrum is
// unmodified (i.e. it is still a.pha
)
XSPEC12>
data c 3 d,e,f
//c.pha replaces a.pha
as the first spectrum; d.pha
, e.pha
, and
// f.pha
provide the, third, fourth, and fifth spectra.
XSPEC12>
data g/
//g.pha replaces c.pha
as the first spectrum; the slash (/)
// indicates that the 2nd through the 5th spectra remain as before.
XSPEC12>
data 2 none/
//the string none indicates that the 2nd spectrum ( b.pha
) is to be
// totally removed. The current total number of datasets thus becomes
// one less (4).The current spectra are g.pha
, d.pha
, e.pha
,
// and f.pha.
XSPEC12>
data h,,
//The current total number of spectra becomes 2, the current data
// sets are from h.pha
and d.pha
.
XSPEC12>
data
//There is no change in the data status.
XSPEC12>
data 1
//The number of spectra is set explicitly to one, that being from
// h.pha.
XSPEC12>
data 1:1 a 2:2 b 3:3 c
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//Read a.PHA into data group 1, b.pha
into data group 2, and c.pha
//into data group 3
XSPEC12>
data 1:1 a 1:2 b 2:3 c
//Read a.pha
and b.pha
into data group 1, and c.pha
into data group 2
XSPEC12>
data a{3}
// Read the third spectrum in the file a.pha
.
5.4.6 diagrsp: set a ‘perfect’ response for a spectrum
Diagonalize the current response matrix for ideal response.
Syntax: diagrsp
This command diagonalizes the current response matrix. The response matrix is set so that the channel values are mapped directly into the corresponding energy ranges, based on the channel energies and energy response range of the current response matrix.
This command is very similar to running dummyrsp in mode 1, with two important differences. Unlike dummyrsp, usage of this command requires that an actual response is currently loaded. It takes its energy range and channel binning information from this currently loaded response rather than user input parameters. Secondly, this does not change the effeciency (ie. effective area) as a function of energy stored for the current detector. Invoking this command will simulate a detector with perfect spectral resolution. If you wish to simulate a detector with perfect resolution AND perfect efficiency, use the dummyrsp
command.
The previous response matrices can be reimplemented with the response command, with no arguments. Any use of the data
and notice
commands will replace the dummy diagonal response with the correct set of matrices.
5.4.7 fakeit: simulate observations of theoretical models
Produce spectra with simulated data.
Syntax:
fakeit
[nowrite] [<file spec>...] where
<file spec>
=::
[ <file number>] <file name> [ {ranges}]...
is similar to the syntax used in the backgrnd, corfile, and response command. The fakeit command is used to create a number of spectrum files, where the current model is multiplied by the response curves and then added to a realization of any background.
Statistical fluctuations can be included. The integration time and correction norm are requested for each file. The file names input as command line arguments are used as background. The number of faked spectra produced is the maximum of the number of spectra currently loaded and the number of file specifications in the command line arguments. The special case fakeit none makes one fake spectrum for each spectrum
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loaded (or one fake spectrum if there are none loaded). See the examples below for a clearer description.
If fakeit is immediately followed by the nowrite specifier, no actual output files will be generated. In this case the fake spectra will exist just for the duration of the
Xspec session (or until they are unloaded).
If a faked spectrum is based on a currently loaded spectrum, then by default the background, response, correction file, and numerical information are taken from the currently-defined data, unless a background file is specified on the command line in which case it becomes the background. The fakeit none case prompts for the rmf and arf filenames and sets the default numerical data to 1.0, except the correction norm, which is set to zero. If the output file is type II then the exposure time and correction scale factor will be the same for all spectra in the file.
For each output file, the user will be prompted for an output file name. If a background file is in use then fakeit will also simulate a new background for each spectrum. Background files are given the same names as output spectrum files but with
_bkg appended to the end of the stem.
The simulated spectra automatically become the current data files. The ignore status is completely reset.
Statistical Issues:
The statistical fluctuations used to create the simulated spectra will depend on whether the current spectra have Poisson or Gaussian errors. If a spectrum file has a
STAT_ERR column and the POISSERR keyword is set to false then xspec assumes
Gaussian errors with sigma from the values in the column. Otherwise, errors are assumed to be Poisson based on the number of counts. Note that it is possible for the spectrum and background files to have different error types. For fakeit cases when there is no current file to use, Poisson errors are assumed.
Type I vs. Type II Output:
Fakeit determines whether to place its fake spectra and background data into type
I or type II files based on the following rules.
If fake spectra are based on currently loaded spectra then the output files will have the same format as those loaded. For example: Assume 3 spectra are currently loaded, spectrum 1 from file typeIdata.pha
and spectra 2 and 3 from file typeIIdata.pha
. Then,
XSPEC12> fakeit will produce 3 fake spectra in 2 output files with names prompted from the user. The first file will be type I, the second type II containing 2 spectra. The same is true for any background files produced.
If the user asks for more fake spectra to be created than the number of spectra currently loaded, for example by typing the following when the same 3 spectra above described are loaded:
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XSPEC12> fakeit 5 then fake spectra 1-3 will be placed in the two files as before. For the additional fake spectra (4 and 5), fakeit uses the following rule: If any of the originally loaded spectra were in a type II file, then all of the additional fake spectra will be placed in 1 type II file.
Otherwise, they will each be placed in a separate type I file. In this example, since a type
II file was originally loaded ( typeIIdata.pha
) when fakeit was called, spectra 4 and 5 will be placed together in a type II output file, in addition to the type I and type II files for the first 3 fake spectra.
If there are no currently loaded spectra all output files will be type I unless either of the following situations exist: 1. Any of the background files entered on the command line are type II, as indicated by row specifiers in brackets. 2. The first response file used clearly belongs to a format associated with type II data, such as
SPI/Integral with its multiple RMF format (see section on SPI/Integral usage).
Overall, though the method of determining output format for additional spectra may seem quite complicated, it can be easily summed up: Fakeit will place all additional spectra and backgrounds (ie. those not based on already loaded data) in type I output files, unless it detects any evidence of type II file usage amongst the command line input, in which case it will produce type II output.
Note on grouped spectra
:
If an input spectrum has grouping information (ie a GROUPING column telling
XSPEC how to bin up the data) then fakeit will simulate the number of counts in each of the grouped bins. However, the spectrum that is written out must have the ungrouped number of channels (and a copy of the GROUPING column from the original spectrum).
The solution that XSPEC adopts is to place all the counts from a grouped bin in the first channel which goes to make up that bin. This is of no consequence for future uses of the simulated spectrum provided that the GROUPING column is not changed. So, in this case grppha or similar tools cannot be run on the simulated spectrum.
Note For SPI/Integral Format
:
Since the SPI/Integral format builds its responses from a combination of multiple
RMFs and ARFs, it must use a different scheme than the OGIP type I and II formats for storing RMF and ARF file location information. This information is stored in a FITS extension, named “RESPFILE_DB” , added to the PHA file. Therefore, when fakeit prompts the user for the location of the response file, simply enter the name of a FITS file which contains a RESPFILE_DB extension pointing to the RMFs and ARFs to be applied. When prompted for an ARF name, enter nothing.
The prompts will only appear for the first spectrum in the data set, and the ARFs will be assigned row by row 1 to 1 with the spectra. For example, if no data is currently loaded, to create 3 fake SPI spectra from the RMFs and ARFs named in the
RESPFILE_DB extension of the file realSpiData.pha
:
XSPEC12> fakeit 3
// ...(various prompts will follow)...
For fake spectrum #1 response file is needed: realSpiData.pha
// ...and ancillary file: <Ret>
// ...(more fakeit prompts)...
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This will create 3 fake spectra, each making use of the same RMFs/ARFs, spectrum 1 using the first row of the ARFs, spectrum 2 using the second etc.
*** CAUTION – SPI/Integral ***
As currently implemented, the RESPFILE_DB method of storing ARF locations does not retain specific row information. The assumption is that the rows in the ARF correspond 1 to 1 with the rows in the spectral data extension. Therefore, much confusion can arise when the row numbers of the loaded spectra do not match that of the fake spectra. For example:
XSPEC12> data my_spi_data.pha{3-4}
// my_spi_data.pha contains a RESPFILE_DB table pointing to arf1.fits,
// arf2.fit, arf3.fits.
// ...(fit to some model(s))...
XSPEC12> fakeit
This will produce 2 fake spectra generated from the model*response operation, where the model has parameters based on a fit to the original spectra in rows 3 and 4 of my_spi_data.pha
, which used ROWS 3 AND 4 of the 3 arf files for their own responses. However, the responses used above to generate the 2 fake spectra will use
ROWS 1 AND 2 of the 3 arf files. This is necessary since the fake spectra will be placed in rows 1 and 2 of their fakeit output file.
Examples:
Type I files:
For each of these examples, assume 3 spectra are currently loaded, each in its own type I file, and that the second spectrum has a background file.
XSPEC12> fakeit
This will produce 3 fake spectra each in its own type I output file, and the user will be prompted for the file names. The response file information will come from each of the original spectra. If any response information is invalid, the user will then be prompted.
A fake background file will be produced for the second spectrum.
XSPEC12> fakeit 4
Produces 4 fake spectra, the first 3 created as in the previous example. The fourth will be created with no background spectrum, and this user is prompted for response information.
XSPEC12> fakeit backa,,none 4
Produces 4 fake spectra. For the first spectrum, a fake background file will be generated from the file backa. The second uses its own background file as before. The third fake spectra will no longer use the response information from loaded spectrum 3, the user will be prompted instead, and its default numerical data will be reset to 1. The fourth spectrum will be created as in the previous example.
If no data is currently loaded:
XSPEC12> fakeit 2
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Produces 2 fake spectra in separate type I files, unless the first user entered response file belongs to a format that is explicitly type II (ie. SPI/Integral).
Type II files:
Assume four spectra with no backgrounds have been loaded from one type II file:
XSPEC12> data original_type2_data.pha{5-8}
Then, after model(s) have been entered and a fit:
XSPEC12> fakeit
This will produce 4 fake spectra in rows 1 to 4 of one type II output file, with responses and arfs taken from the columns of original_type2_data.pha
.
XSPEC12> fakeit ,,backb{1-3}
This produces 5 fake spectra in two type II output files, and 3 fake background spectra also placed in two type II output files:
The first 4 fake spectra are placed in one output file since that is how the 4 spectra they were based on were originally organized. The default numerical data for this file are taken from the original spectra. Fake spectra 3 and 4 now have backgrounds, based on backb{1} and backb{2} respectively. These will generate 2 fake background spectra, placed in rows 3 and 4 of the first output fake background file. Rows 1 and 2 of this file will just consist of zeros since the first 2 spectra have no backgrounds.
The fifth fake spectrum will be placed in the second type II PHA file. Response and numerical data will not be based on the existing loaded spectra. A fake background will be generated from backb{3} and placed in row 1 of the second type II fake background file.
Now assume no data is currently loaded:
XSPEC12> fakeit 2 backb{1}
2 fake spectra in one type II output file are produced, as is a corresponding fake background file with 2 rows. The fact that the user has entered a type II background file on the command line tells fakeit to produce type II output. The first fake spectrum will have no associated background, so row 1 in the fake background file will be all zeros.
Row 2 will consist of the fake background generated from backb{1}.
5.4.8 ignore: ignore detector channels
Ignore data channels.(See also
notice
.)
Syntax:
ignore
<range1> [ <range2>] ... [ <rangeN>] where
ignore
bad
<rangeI> =:: <spectrum range>: <channel range> | <channel range>.
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If no
<spectrum range>
is given, then the previous range is used (the initial default range is file one (1) only). The form of
<spectrum range> is
<spectrum range> =::<init spectrum> – <last spectrum> | <spectrum> where
<init spectrum>
,
<last spectrum>
, and
<spectrum>
are spectrum numbers, in the order that they were input with the data
command. The form of channel range is
<channel range> =:: <initial channel> — <last channel> | <channel>
If integers are given for the channel ranges then channels will be used while if reals are given then energies (or wavelengths if setplot wave
has been specified).
Energy and wavelength units are determined by the setplot energy
and wave
settings.
If only the last channel is indicated, then a default value of one (1) is used for the initial channel. Channels remain ignored until they are explicitly noticed with the notice command, or if a spectrum is replaced.
Examples:
Assume that 4 spectra have been read in, the first 2 with 100 channels and the last
2 with 50 channels.
XSPEC12>
ignore **:1-10
//The first 10 channels of all 4 spectra are ignored
XSPEC12>
ignore 80–**
//An attempt will be made to ignore channels
80
in all four data
// sets (as that was the last spectrum range specified). As a result,
// only channels 80-100 will be ignored for spectra 1 and 2.
// No change will occur for spectra 3 and 4, as they have no
// channels greater than 50.
XSPEC12>
ign 4:1-20 3:30-40 45–**
//Channels 11-20 for spectrum 4 are ignored (1-10 were ignored already)
// while channels 30-40 and 45-50 of spectrum 3 are ignored.
XSPEC12>
ignore 1:1-5
//No channels are ignored, as these were ignored at the beginning.
XSPEC12>
ignore 2:1.-5.
//Ignore all channels between 1 and 5 keV in the second dataset
5.4.9 notice: notice data channels
Notice data channels.(See also
ignore
.)
Syntax: notice
<range1> <range2> ... <rangeN>
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notice all where
<rangeI> =:: <spectrum range>: <channel range> | <channel range>.
If no
<spectrum range>
is given, then the previous range is used (the initial default range is file one (1) only). The form of
<spectrum range> is
<spectrum range> =::<init spectrum> – <last spectrum> | <spectrum> where
<init spectrum>
,
<last spectrum>
, and
<spectrum>
are spectrum numbers, in the order that they were input with the data
command. The form of channel range is
<channel range> =:: <initial channel> — <last channel> | <channel>
If <channel range>
are integers then channels will be used or if reals then energies (or wavelengths if setplot wave
has been specified). Energy and wavelength units are determined by the setplot energy
and wave
settings. If only the last channel is indicated, then a default value of
1 is used for the initial channel. Channels remain noticed until they are explicitly ignored with the ignore
command. When a spectrum is replaced by another spectrum, all input channels automatically are noticed.
XSPEC12> notice all resets all the channels to ‘noticed’.
Examples:
Assume that 4 spectra have been read in, the first 2 having 100 channels and the last 2 having 50 channels.Assume also that channels 1–10 of all four spectra are ignored and that channels 80–100 of spectra 1 and 2 are ignored.
In XSPEC12, notice does not force the detector response to be reread (see RESPONSE
DESCRIPTION).
XSPEC12>
notice **:1—10
//The first 10 channels of all 4 spectra are noticed.
XSPEC12>
notice 80—**
//an attempt will be made to notice channels
80
in all 4 spectra
// (as that was the last spectrum range specified) but the result is that
// only channels 80–100 will be noticed for spectra 1 and 2, with no
// change for spectra 3 and 4 as they have no channels greater than 50.
XSPEC12>
notice 1:1—5
//No channels are noticed, as these channels were noticed
//in the beginning.
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5.4.10 response: change the detector response for a spectrum
Modify one or more of the matrices used to describe the response(s) of the associated spectrum to incident X-rays.
Syntax:
where
response
[ <filespec>...]
response [
<source num>
:]
<spectrum num>
none
<filespec> =:: [[<source num>:]<spectrum num>] <file name>..., and
<file name>
is the name of the response file to be used for the response of the associated spectrum.
If <file name> ends in a { n} specifier then the nth response will be read from the file.
<spectrum num>
is the spectrum number for the first file name
in the specification,
and follows similar rules as described in the
data
command description. An important difference however is that the response command may only be used to modify the response of a previously loaded spectrum: a n error message is printed if the
<spectrum num>
is greater than the current number of spectra (as determined from the last use of the data command).
An optional < source num
> may be specified to attach additional responses to a spectrum, and should be paired with < spectrum num
> separated by a ‘:’. This allows the user to assign multiple models, each with their own response file, to a particular spectrum. See the model command for more information. If no < source num
> is specified, it always defaults to 1. Source numbers do not need to be assigned consecutively to a spectrum, and gaps in numbering are allowed. The additional response may be removed with a response < source num
>:< spectrum num
> none command. Both the show data and show response commands will display current information regarding the response(s) to spectrum assignments.
A file name none
indicates that no response is to be used for that spectrum. This situation means that any incident spectrum will produce no counts for those particular channels. If a file is not found or cannot be opened for input, then the user is prompted for a replacement response file. An
<EOF
>
at this point is equivalent to using none
as the response. See the
data
command for ways to totally remove the spectrum from consideration. The user is also prompted for a replacement if the response file has a different number of PHA channels than the associated spectrum. A warning will be printed out if the response detector ID is different from the associated spectrum's. The current ignore status for channels is not affected by the command. (See the
ignore
and
notice
commands).
Examples:
It is assumed that there are currently three spectra:
Single source usage:
XSPEC12>
response a,b,c // New files for the response are given for all three files.
XSPEC12>
response 2 none // No response will be used for the second file.
XSPEC12>
response ,d{2} // The second response in d becomes the response for
//the second file.
102
Multiple source usage:
XSPEC12>
response 2:1 e // A second source with response e.pha is now added to
// the first spectrum. A second model can be assigned
// to this source.
XSPEC12>
response 2:2 f 3:2 g // A second and third source is assigned to spectrum 2.
XSPEC12> response 2:2 none // The second source is now removed from spectrum 2.
5.5 Fit Commands
5.5.1 bayes: set up for Bayesian inference
Syntax:
where <option> =:: [off | on | cons]. If a parameter number is given as the first argument then this command sets up the prior for the specified model parameter but does not turn Bayesian inference on. If the first argument to the `bayes' command is not a parameter number then one of the options ‘off’, ‘on’, or ‘cons’ is used. The first two turn Bayesian inference off or on, while ‘cons’ turns Bayesian inference on and gives all parameters a constant prior. The options for prior types are as follows.
bayes
[<option> | <mod par #>] {<prior type>
<hyperparameters>}
Prior type Log(prior) cons 0 jeffreys -log( par) gauss -0.5log(2π hpar2) – 0.5(hpar1-
par)
2
/
hpar2
2
Where par is the parameter value and hpar# the hyperparameter values. jeff is an abbreviation for the Jeffreys prior, which is 1/x for an assumed Gaussian distribution of the parameter.
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5.5.2 chain: run a Monte Carlo Markov Chain.
Syntax: chain
[burn <length>] [clear] [filetype fits|ascii] [info]
[length <length>] [load <filename>] [proposal [<distr> <source>]|[<userdefined>]] [rand on|off] [run [>]<filename>] [stat <par num>] [temperature
<value>] [type mh|gw] [unload <range>] [walkers <value>]
If the proposal source is set to use the fit correlation matrix (the default), you must perform a fit before running any chains.
When chains are loaded (and their parameters correspond to the currently loaded model), they will be used by the various XSPEC commands that require distributions of parameter values, such as eqwidth or flux when calculating error estimations. The error command itself will also use the loaded chains, determining the error range from a central percentage of the sorted chain values. This is likely to be faster than the error command’s standard algorithm when not using chains. burn <length>
Specifies that the first
<length>
steps should be thrown away prior to storing the chain. clear filetype fits|ascii info length <length>
Does a reset and removes all chains from the list.
Chooses the format of the output chain file. fits
(the default) writes the chain to a binary table in a FITS file. ascii writes the chain to a simple text file. Either format is readable when using the load
command.
Prints out information on the current chains.
Sets the length for new chains. load <filename> Loads a chain which has been run earlier, stored in file given by
<filename>
. proposal
<distr> <source>
Selects the proposal distribution and source of covariance information to be used when running new chains. The default is proposal gaussian fit
. Currently implemented
<distr>
options are: gaussian and cauchy
.
<source> options are:
chain
Covariance is taken from the currently loaded chains. diagonal <values> The values of a diagonal covariance matrix are entered directly on the command line, separated by commas and/or spaces:
C_11 C_22 ... C_nn
.
<filename> Covariance is read in from a userspecified text file. The file must contain the values of an NxN matrix where N is the current number of freely varying parameters. The values of each matrix row should be entered on one line with whitespace separation. Since this matrix is always symmetrical, values above the diagonal may be omitted. For example a
2x2 matrix could be entered as:
0.98
0.15 0.96 fit
Covariance is taken from the correlation information produced by the current fit. matrix <values> The lower half and diagonal of a symmetrical square covariance matrix are entered directly on the command line, separated by commas and/or spaces:
C_11 C_21 C_22 C_31 C_32 C_33 ...
C_nn
Typing chain proposal
with no other arguments will show a list of all available proposal options.
For an alternative to XSPEC’s
<distr> <source> proposal options, the user may instead want to provide their own custom randomization algorithm. This can be done by writing their own C++ class(es) derived from an
XSPEC randomizer base class. The custom class is added at runtime using the same initpackage/lmod command sequence as for local models, and is specified by proposal <name>
where
<name> is the unique name attribute the user provides for their class. Please see
Appendix G for more information on writing a custom randomizing class, and initpackage for building and loading it.
104
rand on|off recalc run [>]<filename>
Specifies whether the chain start point will be randomized, or taken from the current parameters.
A deprecated option that performs the equivalent of proposal gaussian chain
.
Runs a new chain written to the specified file, or append to an already loaded file if the “>” character preceeds the filename. The chain is written to the file as it runs so its performance can be monitored by examining the file. For high-chatter settings, additional information is printed to the screen. A long run may be interrupted with Ctrl-C, in which case the chain file will still exist but will not be automatically loaded. If appending to a file, the current filetype setting must match the format of the file or XSPEC will prevent it. stat
[<modName>:]<parIdx>
Writes out statistical information on a particular parameter of the chain, specified by the parameter index number (with optional model name).
The information displayed is: line1: The mean of the parameter over each chain file. line2: The parameter mean over all chain files and the variance between chain means. line3: The variance within the chains. line4: The Rubin-Gelman convergence criterion. line5: The fraction of repeats, defined as the number of lines in the chain file for which all parameter values are identical to the previous line, divided by the number of lines in the file.
105
106
temperature
<value> type mh | gw unload <range>
Sets the temperature parameter used in the Metropolis-Hastings algorithm for the proposal acceptance or rejection.
The default value is 1.0 and zero or negative values are forbidden. By using the run append option, it is possible for different sections of the chain file to use different temperatures. The temperatures and the line numbers to which they apply are stored in the header of the FITS format chain files, or in the metadata section at the top of the
ASCII text format files.
Determines the algorithm used to generate the chain. Choices are “mh”
(Metropolis-Hastings) or “gw”
(Goodman-Weare, the default). If using
Goodman-Weare, must also set the walkers
parameter.
Removes the chains specified by
<range> from the list in xspec. Note that this does NOT delete the chain files.
walkers <value> Sets the walkers parameter for the
Goodman-Weare chain algorithm (see type
). This must be an even integer, and both the chain length and burn length should be divisible by it (XSPEC will adjust the lengths to make them so if necessary).
All loaded chains must contain the same fit parameters. xspec will prevent the loading of a chain with a different number of parameters from the currently loaded chains.
Examples:
XSPEC12>chain length 100
//Sets length of chains produced by the run command to 100.
XSPEC12>chain run chain_file1.out
//Runs a chain based on current valid fit parameters, output to
107
//chain_file1.out
XSPEC12>chain run >chain_file1.out
//Appends another run of length 100 to the end of chain_file1.out
XSPEC12>chain load chain_old.out
//Loads a pre-existing chain file, the result of an earlier run
//command. Warning is issued if not the same length as
//chain_file1.out
XSPEC12>chain stat 3
//Prints statistical information on the 3 rd
parameter of the chain.
XSPEC12>chain proposal gaussian myfile.txt
//New chain proposals will be a normal distribution using
//covariance values stored in myfile.txt rather than fit
//correlation matrix.
XSPEC12>chain prop gauss diag .1 .001 .0001
// New chain proposals will be a normal distribution using a 3x3
// diagonal covariance matrix with the values from the
// command line.
XSPEC12>chain temperature .8
// Sets the Metropolis-Hastings temperature value to .8 for
// future chain runs, replacing the default 1.0.
XSPEC12>chain clear
//Removes the 2 loaded chains from xspec’s chain list.
5.5.3 error, uncertain: determine confidence intervals of a fit
Determine the confidence region for a model parameter.
Syntax:
error [[stopat <ntrial> <toler>] [maximum <redchi>]
[ <delta fit statistic>] [ <model param range>...]] where
<model param range> =:: [<modelName:>]<first param>-- <last param> determines the ranges of parameters to be examined, and
<delta fit statistic>
(distinguished from the model parameter indices by the inclusion of a decimal point), is the change in fit statistic used.
For response parameters (see gain command), use rerror with identical syntax except:
<response param range> =:: [<sourceNum:>]<first param>-- <last param>
The error command uses one of two algorithms. If Monte Carlo Markov Chains are loaded
(see chain command) the error range is determined by sorting the chain values, and then taking a
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central percentage of the values corresponding to the confidence level as indicated by
<delta fit statistic>.
This is likely to be the faster of the two algorithms.
When chains are not loaded, error’s algorithm is as follows:
Each indicated parameter is varied, within its allowed hard limits, until the value of the fit statistic, minimized by allowing all the other non-frozen parameters to vary, is equal to the last value of fit statistic determined by the fit
command plus the indicated
<delta fit statistic>
, to within an absolute (not fractional) tolerance of
<toler>
. Note that before the
error command is executed, the data must be fitted. The initial default values are the range 1—1 and the
<delta fit statistic>
of 2.706, equivalent to the 90% confidence region for a single interesting parameter. The number of trials and the tolerance for determining when the critical fit statistic is reached can be modified by preceeding them with the stopat
keyword. Initially, the values are 20 trials with a tolerance of 0.01 in fit statistic.
If a new minimum is found in the course of finding the error, then the calculation is aborted and control returned to the user. The maximum
keyword ensures that error will not be run if the reduced chi-squared of the best fit exceeds
<redchi>
. The default value for
<redchi>
is 2.0.
Since there are very many scenarios which may cause an error calculation to fail, it is highly recommended that you check the results by viewing the 9-letter error string, which is part of the output from the tclout error command (see tclout for a description of the error string). If everything went well, the error string should be “FFFFFFFFF”.
Examples:
Assume that the current model has four model parameters.
XSPEC12>
error 1-4
//Estimate the 90% confidence ranges for each parameter.
XSPEC12>
error 9.0
//Estimate the confidence range for parameters 1-4 with delta fit
// statistic = 9.0, equivalent to the 3 sigma range.
XSPEC12>
error 2.706 1 3 1. 2
//Estimate the 90% ranges for parameters 1 and 3, and the 1. sigma
// range for parameter 2.
XSPEC12>
error 4
//Estimate the 1. sigma range for parameter 4.
XSPEC12>
error stop 20,,3
//Estimate the 1-sigma range for parameter 3 after resetting the number
// of trials to 20.Note that the tolerance field had to be included
//(or at least skipped over).
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5.5.4 fit: fit data
Find the best fit model parameters for the current data by minimizing the current statistic.
Syntax:
fit
<fit method parameters>
The arguments to fit depend on the fitting method currently in use. See the method command for details (and for the usage of the USE_NUMERICAL_DIFFERENTIATION option in the user’s startup Xspec.init file). Output from the fit command also depends on the fitting method currently in use.
Using the Levenberg-Marquardt algorithm, the parameters accepted are the maximum
<number of iterations>
before the user is prompted, the
<critical delta>
, which is the
(absolute, not fractional) change in the statistic between iterations less than which the fit is deemed to have converged, and
<critical beta>
.
The
<critical beta>
provides an optional second stopping criterion, and it refers to the
|beta|/N value reported during a Levenberg-Marquardt fit. This is the norm of the vector derivatives of the statistic with respect to the parameters divided by the number of parameters. At the best fit this should be zero, and so provides another measure of how well the fit is converging.
<critical beta>
is set to a negative value by default, which renders it inactive.
Including the string delay as an argument to fit turns on delayed gratification. It is turned off by nodelay.
Delayed gratification modifies the way the damping parameter is set and has been shown in many cases to speed up convergence. The default is nodelay.
If
<number of iterations>
,
<critical delta>
,
<critical beta>, delay, or nodelay
is entered through the fit command, it also becomes the future default value for the currently loaded fit method (ie. Levenberg-Marquardt).
Examples:
XSPEC12>
fit
// Fit with the default number of iterations and critical delta
// chi-squared.
XSPEC12>
fit 60
// Fit with 60 as the number of iterations.
XSPEC12>
fit 50 1.e-3
// Fit with 1.e-3 as the critical delta.
XSPEC12> fit 50 1.e-3 20.
// Same fit, but will now use |beta|/N = 20.0 as another stopping criterion in addition
// to that of the critical delta.
XSPEC12> fit delay
// Same fit, but will now use delayed gratification.
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5.5.5 freeze: set parameters as fixed
Do not allow indicated model parameters to vary. (See also
thaw
.)
Syntax:
freeze
[ <param range>...] where
<param range =:: [modelName:] <param#> | <param#> — <param#>.
For response parameters (see gain command):
rfreeze
[ <param range>...] where
<param range =:: [source number:] <param#> | <param#> — <param#>.
The indicated model parameter or range of model parameters will be marked so they cannot be varied by the fit
command. By default,the range will be the last range input by either a freeze or thaw command.
Examples:
Currently there are six parameters, initially all unfrozen.
XSPEC12>
freeze 2
//Parameter 2 is frozen
XSPEC12>
freeze 4-6
//Parameters 4, 5, and 6 are frozen.
XSPEC12>
thaw 2 3-5
//Parameters 2, 4, and 5 are thawed, parameter 3 is unaffected.
XSPEC12>
freeze
//Parameters 3,4,5 are frozen (the last range input by a freeze
//or thaw command).
XSPEC12> rfreeze 4-6
//Response parameters 4, 5, and 6 are frozen.
5.5.6 ftest: calculate the F-statistic from two chi-square values
Calculate the F-statistic and its probability given new and old values of degrees of freedom (DOF).
2
and number of
Syntax:
ftest chisq2 dof2 chisq1 dof1
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The new
2
and DOF, chisq2 and dof2, should come from adding an extra model component to (or thawing a frozen parameter of) the model which gave chisq1 and dof1.If the Ftest probability is low then it is reasonable to add the extra model component. WARNING : it is not correct to use the F-test statistic to test for the presence of a line (see Protassov et al 2002, ApJ 571,
545). WARNING: this command can only be used if the extra model component is additive, this does not give the correct result if the component is multiplicative (see Orlandini et al. 2012, ApJ
748, 86).
5.5.7 goodness: perform a goodness of fit Monte-Carlo simulation
Perform a Monte Carlo calculation of the goodness-of-fit.
Syntax:
goodness
[ <# of realizations>] [sim | nosim]
This command simulates
<# of realizations> spectra based on the model and writes out the percentage of these simulations with the fit statistic less than that for the data. If the observed spectrum was produced by the model then this number should be around 50%. This command only works if the sole source of variance in the data is counting statistics. The sim|nosim
switch determines whether each simulation will use parameter values drawn from a
Gaussian distribution centered on the best fit with sigma from the covariance matrix. The sim switch turns on this option, nosim
turns it off in which case all simulations are drawn from the best-fit model. The default starting setting is nosim
.
5.5.8 margin: MCMC probability distribution.
Use the currently loaded MCMC chains to calculate a multi-dimensional probability distribution.
Syntax: margin
<step spec.> [<step spec.> ...] where
<step spec.> ::= [{LOG or NOLOG}] [<model name>:]<fit param index>
<low value> <high value> <no. steps>.
The indicated fit parameter is stepped from ‘<low value>’ to ‘<high value>’ in ‘<no. steps>+1’ trials. The stepping is either linear or log. Initially, the stepping is linear but this can be changed by the optional string ‘log’ before the fit parameter index. ‘nolog’ will force the stepping to be returned to the linear form. The number of steps is set initially to ten. The results of the most recently run margin command may be examined with plot
margin (for 1-D and 2-D distributions only). This command does not require that spectral data files are loaded, or that a valid fit must exist.
Examples:
Assuming chain(s) are loaded consisting of 4 parameters.
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XSPEC12>margin 1 10.0 12.0 20 log 3 1.0 10.0 5
//Calculate a 2-D probability distribution of parameter 1 from 10.0-12.0 in 20 linear bins, and parameter 3 from 1.0-10.0 in 5 logarithmic bins.
XSPEC12>margin 2 10.0 100.0 10 nolog 4 20. 30. 10
//Now calculate for parameter 2 in 10 log bins and parameter 4 in 10 linear bins.
5.5.9 renorm: renormalize model to minimize statistic with current parameters
Renormalize model, or change renorm
conditions.
Syntax:
renorm
[AUTO | NONE | PREFIT]
The renorm
command will adjust the normalizations of the model by a single multiplication factor, which is chosen to minimize the fit statistic.Such a renorm will be performed explicitly whenever the command is used without a key-word, or during certain XSPEC commands, as determined by the following key-words:
AUTO – Renormalize after a model or
newpar
command, and at the beginning of a fit
PREFIT – Renormalize only at the beginning of a fit
NONE – Perform no automatic renormalizations, i.e., only perform them when a renorm
command is given explicitly.
5.5.10 steppar: generate the statistic “surface” for 1 or more parameters
Perform a fit while stepping the value of a parameter through a given range. Useful for determining confidence ranges in situations where greater control is needed than given with the error
command.
Syntax: steppar
[<current|best>] <step spec> [ <step spec>...] where
<step spec> ::= [<log | nolog>] [<modelName>:]<param index> <low value> <high value> <# steps> or
<step spec> ::= [<log | nolog>] [<modelName>:]<param index> delta <step size> <# steps> steps>
In the first case the parameter is stepped from
<low value>
to
<high value>
in
<#
plus one trials. In the second case the parameter is stepped from <best fit value>-<step size>*<# steps> to <best fit value>+<step size>*<# steps>, ie a total of 2<# steps>+1 trials. The stepping is either linear or log. Initially, the stepping is linear but it can be changed by the optional string log
before the parameter index. nolog
will force the stepping to be returned to the linear form. If more than one parameter is entered, then <# steps> must be entered for each one except
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the last. Note that every variable parameter whose <param index> is NOT entered in the command will still be allowed to vary freely during each steppar iteration.
To perform a steppar run on gain (or response) parameters, the optional
[<modelName>:] specifier is replaced by an optional
[<sourceNumber>:]
specifier, and the letter ‘r’ needs to be attached as a prefix to the
<parameter index>
. For example: steppar 2:r3 1.5 2. 10 will step the third response parameter belonging to source number 2.
The number of steps is set initially to 10. At each value, the parameter is frozen, a fit performed, and the resulting value of chi-squared given. If best
is given as an argument then the non-stepped parameters are reset to the best-fit values at each grid point. Alternatively, if current
is given as an argument then the non-stepped parameters are started at their values after the last grid point (the default).
If multiple
<step spec>
are given for different parameters, then a raster scan of the parameter ranges is performed. At the end of the set, the parameters and chi-squared are restored to the values they had initially.
If the model is in a best-fit state when a steppar run is started and a new best fit is found during the run, the user will be prompted at the end of the run to determine if they wish to accept the new best-fit values for their parameters. This prompting can be disabled by the setting of the
query flag.
Depending on the machine, a steppar run may be sped up significantly by assigning it to multiple processes. See the parallel command with the steppar option for more details.
Examples:
Assume that the current model has four parameters:
XSPEC12>
steppar 3 1.5 2.5
//Step parameter 3 from 1.5 to 2.5 in steps of .1.
XSPEC12>
steppar log
//Repeat the above, only use multiplicative steps of 1.0524.
XSPEC12>
step nolog 2 -.2 .2 20
//Step parameter 2 linearly from -.2 to .2 in steps of 0.02.
XSPEC12>
step 2 delta 0.02 5
//Step parameter 2 linearly from the best-fit value-0.1 to
//the best-fit value+0.1 in a total of 11 steps.
5.5.11 thaw: allow fixed parameters to vary.
Allow indicated parameters to vary. (See also freeze)
.
Syntax:
where
thaw{[ <param range>...]}
<param range> =:: [modelName:] <param #> | <param #>-- <param #>
For response parameters (see gain command):
rthaw {[ <param range>...]}
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where
<param range> =:: [sourceNum:] <param #> | <param #>-- <param #>
The indicated parameter, or range of parameters, will be marked as variable by the fitting commands and treated as a fitting parameter in subsequent fits. By default, the range will be the last range input by either a
freeze
or
thaw
command. See the
freeze
examples
for an example of the use of the thaw
command.
5.5.12 weight: change weighting used in computing statistic
Change the weighting function used in the calculation of chi-squared.
Syntax:
weight
[standard | gehrels | churazov | model ]
Standard weighting uses N or the statistical error given in the input spectrum. Gehrels weighting uses 1
N
0.75
, a better approximation when N is small (Gehrels, N. 1986, ApJ 303, 336).
Churazov weighting uses the suggestion of Churazov et al. (1996, ApJ 471, 673) to estimate the weight for a given channel by averaging the counts in surrounding channels. Model weighting uses the value of the model, not the data, to estimate the weight.
5.6 Model Commands
Overview of XSPEC12 Changes: In XSPEC12 several models can exist simultaneously, unlike XSPEC11. Different models are distinguished by name, which is a character string assigned by the user. The purpose of this is to allow an intuitive syntax for creating multiple models simultaneously fit to data, assigned to a corresponding number of sources. The familiar XSPEC11 syntax is, however, fully supported by assigning an internal symbol name.
For example, INTEGRAL/SPI data is modeled using 2 or more sources, one assigned to the background, and one or more assigned to objects resolved by the coded mask.
XSPEC12>data rev_001234{1-19}
…
XSPEC12>model 1:source1 phabs(cutoffpl)
XSPEC12>model 2:source2 phabs(powerlaw)
XSPEC12>model 3:bkg spibk
…
Note that a source number must precede the name to avoid confusion with model expressions. The “normal” case, fitting to a single source, corresponds to source 1.
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When the fit command is given the parameters of the model will be labeled source1:1, source1:2,…source2:1, source2:2,…bkg:1, bkg:2, etc.
Another use for multiple models is to name a model, fit with it, and then mark it as
“inactive,” i.e. not fit to data. A second model may then be defined and fit to the data, and afterward be interchanged. This is designed to allow the user to compare the fits from competing models without recalculation.
Apart from the removal of the pre-XSPEC10 model expression format, which was previously declared deprecated and is now no longer recognized, this new functionality provides a proper superset of the XSPEC11 syntax. The command
XSPEC12> model wa(po)
Creates a “default” model which takes an internal (hidden) symbol as a name. Its parameters are sequenced from 1 as in XSPEC11.
Another enhancement is in the newpar command. XSPEC12’s expression analyzer developed for parsing model expressions is also used for parameter links. Thus newpar link expressions can be polynomials in multiple parameters, such as
XSPEC12> newpar par1 = par2*par2 or
XSPEC12> newpar par1 = 0.5*par3 + 1.5*par4
In sum, most of the syntax enhancements added to XSPEC12 support the presence of multiple models. The need to identify parameters of different models uniquely requires that their name and number be specified, which requires enhancements in the syntax not only in the modelrelated commands
model
,
addcomp
,
delcomp
, and
editmod
but also the parameter-related commands
newpar
,
freeze
,
thaw
,
untie
,
steppar
, and
error
. However, if the model is not named, all of these commands can be used identically as in XSPEC11.
5.6.1 addcomp: add component to a model
Add a component to the model.
Syntax:
addcomp [modelName:] n <comp> where n
is the component number before which the new component is to be inserted, and
<comp> is the name of the new component. Components are numbered in sequence in order of appearance in the expression entered. The new component is regarded as an operator on the component added if it is not additive.
The optional modelName qualifier allows the user to address a named model.
The user is prompted for parameter values for the component. If there are m components in the current model, then acceptable values for the component number added are 1 to m+1.
116
XSPEC detects the type of the model (additive, multiplicative etc), checks the correctness of the syntax of the output model, and adds the component if the resulting models obeys the syntax rules documented in the model command.
Thus,
XSPEC12> mo wa(po)
Followed by
XSPEC12> addcomp 2 bb
Yields the model achieved by
XSPEC12> mo wa(bb + po)
See also delcomp (delete component by number).
Other Examples will serve to clarify addcomp’s behavior.
Suppose that the current model specification is ga+po which using the show command would yield the description model = gaussian[1] + powerlaw[2]
The comments give the model expression following the entry of addcomp and delcomp commands:
XSPEC12> addcomp 2 wab
//gaussian[1]+wabs[2](powerlaw[3])
XSPEC12> addcomp 4 pha
//(gaussian[1]+wabs[2](powerlaw[3]))phabs[4]}
XSPEC12> delcomp 1
//(wabs[1](powerlaw[2]))phabs[3]}
XSPEC12> addcomp 2 zg
//(wabs[1](zgauss[2]+powerlaw[3]))phabs[4]}
XSPEC12> delcomp 3
//(wabs[1](zgauss[2]))phabs[3]
XSPEC12> mo wa(po)
XSPEC12>
addcomp
1 ga
// gauss[1] + wabs[2]*powerlaw[3]
XSPEC12>
delcomp
1
XSPEC12>
addcomp
1 pha
// phabs[1]*wabs[2]*powerlaw[3]
XSPEC12>mo wabs(po)
XSPEC12>
addcomp
3 bb
// wabs[1]*powerlaw[2] + bbody[3]
XSPEC12>
delcomp
1
XSPEC12>
addcomp
3 pha
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// wabs[1]*powerlaw[2]*pha[3]
XSPEC12>
addcomp
3 po
// ERROR: po (additive) is interpreted as being added to the multiplicative
// model pha[3], which is a context error.
For multiply nested models…
XSPEC12> mo wa(po + pha(bb + ga))
XSPEC12>
addcomp
6 po
// wabs[1](powerlaw[2] + phabs[3](bbody[4] + ga[5]) + powerlaw[6])
XSPEC12>
addcomp
5 peg
// wabs[1](powerlaw[2] + phabs[3](bbody[4] + pegpwlw[5] ga[6]) + powerlaw[7])
XSPEC12>
addcomp
7 wa
// wabs[1](powerlaw[2] + phabs[3](bbody[4] + pegpwlw[5] ga[6]) + wabs[7]*powerlaw[8])
5.6.2 addline: add spectral lines to a model
Tcl script to add one or more lines to the current model in an optimum fashion.
Syntax:
addline [<nlines>] [<modeltype>] [{fit|nofit}]
<nlines>
additional lines are added one at a time. Line energies are set to that of the largest residual between the data and the model. For each line a fit is performed with the line width and normalization as the only free parameters. The default option is one gaussian line. The other
<modeltype> that can be used is lorentz. If no third argument is given then the sigma and normalization of each line are fit. If ``nofit'' is specified then the fit is not performed but if ``fit'' is specified then all free parameters are fit. addline currently will only work with the default model (i.e. not for named models).
5.6.3 delcomp: delete a model component
Delete one or more components from the current model.
Syntax:
delcomp [modelName:]
<comp num range> where
<comp num range> is range of positions in the model specification of the components to be deleted.
Examples:
Suppose that the current model specification is wa(po+ga+ga)
.
Then
118
XSPEC12>
delcomp 3-4
//Changes the model to wa(po)
XSPEC12>
delcomp 1
//Changes the model to po
5.6.4 dummyrsp: create and assign dummy response
Create a “dummy” response, covering a given energy range.
Syntax:
dummyrsp [ <low Energy> [ <high Energy> [ <# of ranges>[ <log or linear> [ <channel offset> [ <channel width> [<source_Num:spec_Num>] ]]]]]]
This command creates a dummy response matrix based on the given command line arguments, which will either temporarily supersede the current response matrix, or create a response matrix if one is not currently present. There are two main uses for this command: to do a
“quick and dirty” analysis of uncalibrated data (mode 1), and to examine the behaviour of the current model outside the range of the data's energy response (mode 2). Note that mode 2 usage has now been rendered redundant by the more flexible energies command.
All parameters are optional. The initial default values for the arguments are 0.01 keV, 100 keV, 200 logarithmic energy steps, 0.0 channel offset, and 0.0 channel width. The default values of the first 5 parameters will be modified each time the parameter is explicitly entered. The channel width parameter however always defaults to 0.0 which indicates mode 2 operation, described below.
In addition to the 6 optional parameters allowed for versions 11.x and earlier, a seventh optional parameter has been added allowing the user to apply the dummy response to just one particular source of a spectrum. It consists of two integers for (1-based) source number and spectrum number, separated by a colon. Either both integers should be entered, or they should be left out entirely. ie. A dummy response is either made for EVERY source in every spectrum, or just 1 source in 1 spectrum. This parameter always defaults to all sources and all spectra.
For mode 1 usage, simply enter a non-zero value for the channel width. In this instance, one has a spectrum for which typically no response matrix is currently available. This command will create a diagonal response matrix with perfect efficiency, allowing for the differences in binning between the photon energies and the detector channel energies (see example below). The response matrix will range in energy from
<low Energy>
to
<high Energy>
, using
<# of ranges>
as the number of steps into which the range is logarithmically or linearly divided. The detector channels are assigned to have widths of energy
<channel width>
(specified in keV), the lower bound of the first channel starting at an energy of
<channel offset>
. Then the data can be fit to models, etc., under conditions that assume a perfect detector response.
For mode 2 usage (channel width = 0.0), one can use this command to examine the current model outside the range of the energy response of the detector. When examining several aspects of the current model, such as plotting it or determining flux, XSPEC uses the current evaluation array.
This, in turn, is defined by the current response files being used, which depend on the various detectors. For example, low energy datasets (such as those from the
EXOSAT LEs) may have responses covering 0.05 to 2 keV, while non-imaging proportional counters can span the range from 1 to 30 keV. If the user wishes to examine the behavior of the model outside of the current
119
range, then he or she temporarily must create a dummy response file that will cause the model to be evaluated from
<low energy>
to
<high energy>
, using
<# of ranges>
as the number of steps into which the range is logarithmically or linearly divided. If one wishes only to set the energy response range, than the
<channel width>
argument may be omitted. In this case, or in the case where no data file has been read in, all entries of the dummy response matrix are set to zero. Under these circumstances the dummyrsp has no physically correct way of mapping the model into the data PHA channels, so the user should not try to fit–or plot–the data while the dummyrsp is active in this mode. Also, data need not even be loaded when calling this command in mode 2.
The previous response matrices can be reimplemented with the response
command, with no arguments. Any use of the data
and notice
commands will replace the dummy response with a correct set of matrices, or with no response matrix if none was originally present.
Examples:
XSPEC12>
dummyrsp
//Create the dummy response for all spectra and sources with the
//default limits, initially .01, 100, and 200 bins.
XSPEC12>
dummyrsp .001 1
//Create a dummy response with 200 bins that cover the range from
//0.001 to 1 keV.
XSPEC12>
dummyrsp ,,,500
//The same range, but now with 500 bins.
XSPEC12>
dummyrsp ,,,,lin
//The same range, but now with linearly spaced bins.
XSPEC12>
dummyrsp ,,,,,0.1
//The same range, but now create a diagonal response matrix, with
//channel widths of 0.1 keV.
XSPEC12>
response
//Restore any previous correct responses.
Example dummy response matrix:
Assume a spectrum with 4 channels, then
XSPEC12> dummyrsp .0 30.0 3 lin 5.0 8.0 will produce the following response:
5.0 – 13.0
0.0 – 10.0 0.5
10.0 – 20.0 0.3
20.0 – 30.0 0
Detector channel energies
13.0 – 21.0 21.0 – 29.0
0
0.7
0.1
0
0
0.8
29.0 – 37.0
0
0
0.1
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5.6.5 editmod: edit a model component
Add, delete, or replace one component in the current model.
Syntax:
editmod
[ <delimiter>] <component1> <delimiter> <component2>
<delimiter> ... <componentN> [ <delimiter>] where
<delimiter> is some combination of
(
,
+
,
*
,and
)
, and
<componentJ>
is one of the models known to XSPEC.
The arguments for this command should specify a new model, with thesame syntax as the previous model, except for one component whichmay be either added, deleted, or changed to a different component type. XSPEC then compares the entered model with the current model,determines which component is to be modified (prompting the user if necessary to resolve ambiguities) and then modifies the model,prompting the user for any new parameter values which may be needed.
Examples:
XSPEC12>
mo wabs(po)
XSPEC12>
ed wabs(po+ga)
//This command will add the component gauss to model
// in the specified place and prompt the user for its initial
// parameters.
XSPEC12>
mo wabs(po+zg)
XSPEC12>
ed po+zg
//This command will delete the component wabs from the
//model, leaving the other components and their current
//parameter values unchanged
XSPEC12>
mo wabs(po+po)
XSPEC12>
ed wabs(po)
//Here an ambiguity exists as to which component to delete.
//In this case XSPEC will print out the current model,
//showing the component number for each component, and then
//prompt the user for which component he wants deleted.
XSPEC12>
mo wabs(po+ga)
XSPEC12>
ed wabs(po+zg)
//The component gauss will be replaced by the component zgauss,
//and the user will be prompted for parameter values for the new
// component
5.6.6 energies: specify new energy binning for model fluxes
Supply an energy-binning array to be used in model evaluations in place of their associated response energies. The calculated model spectra are then interpolated onto the response energy arrays before multiplying by the response matrix. This command replaces and enhances the extend command from earlier versions.
Syntax:
energies <range specifier> [<additional range specifiers>…]
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energies <input ascii file>
energies extend <extension specifier>
energies reset where the first <range specifier> ::= <low E> <high E> <nBins> log | lin
<additional range specifiers> ::= <high E> <nBins> log | lin
<extension specifier> ::= low | high <energy> <nBins> log | lin
All energies are in keV. Multiple ranges may be specified to allow for varied binning in different segments of the array, but note that no gaps are allowed in the overall array. Therefore only the first range specifier accepts a <low E> parameter. Additional ranges will automatically begin at the
<high E> value of the previous range.
The extend option provides the same behavior as the old extend command. Models will use associated response energy arrays, with an additional low and/or high array extension. <energy> is the value to which the array is extended, using <nBins> additional log or linear bins.
With the <input ascii file> option, the user can instead supply a customized energy array from a text file. The format requirements are simply that the bin values must appear 1 to a line and in ascending sorted order. Blank lines are allowed and so are comments, which must be preceded by a ‘#’. A simple example:
# myEnergyBinning.txt
.1
1.0
10. # now some linear bins
15.
20.
25. which would actually produce the same energy array as: energies .1 10. 2 log 25. 3 lin
Once an energy array is specified, it will apply to all models, and will be used in place of any response energy array (from actual or dummy responses) for calculating and binning the model flux. It will also apply to any models that are created after it is specified. To turn off this behavior and return all models back to using their response energies, simply type “energies reset”.
Similarly, an array extension created by the “extend” option will continue to be applied to all models until it is either overwritten by another extension, replaced by a new energies array, or removed with the “reset” option. This allows both low and high extensions to exist together.
When a custom-energy binned model flux array needs to be multiplied by a response matrix, xspec will temporarily rebin the flux array to match up with the response energy binning. This is done by simply scaling the flux by the fractional overlap between the custom and response bins. If there is no overlap between the custom and response energies, then the response will be multiplied by zero.
The energies command saves the most recently entered range and extension specifiers to be used as default values the next time it is called. The initial default range specifier is 1 range with <low E>
122
= .1, <high E> = 10., <nBins> = 1000, and lin
. The initial default extension specifier is high
with
<energy> = 100., <nBins> = 200, and
log
.
Examples:
XSPEC12>
energies ,50,,log
// Creates an array from .1 to 50. of 1000 logarithmic bins.
XSPEC12>
energies ,,,,100. 5 lin
// Modifies previous array by adding 5 linear bins from 50. to 100.
XSPEC12> energies ,,,,200.
// The 2 nd
range is now 50. to 200. in 5 linear bins.
XSPEC12> energies 1.,,100
// Array is now just 1 range, 1. to 50. in 100 logarithmic bins.
XSPEC12> energies myFile.txt
// Array is replaced with values stored in myFile.txt
XSPEC12> energies extend ,75.,,lin
// Models will go back to using response energies, but with an
// extension of the high end to 75. keV in 100 additional linear bins.
XSPEC12> energies extend low .01
// Add a low-end extension to .01 keV with 100 new linear bins.
XSPEC12> energies reset
// All models will go back to using the original energy arrays
// from responses.
5.6.7 eqwidth: determine equivalent width
Determine the equivalent width of a model component.
Syntax:
eqwidth [[RANGE <frac range>] <
[err <number> <level> | noerr]
[model name:] model component number>]
The command calculates the integrated photon flux produced by an additive model component
(combined with its multiplicative and/or convolution pre-factors) (FLUX), the location of the peak of the photon spectrum (E), and the flux (photons per keV) at that energy of the continuum
(CONTIN). The equivalent width is then defined as {EW = FLUX / CONTIN} in units of keV.
New for version 12: the continuum is defined to be the contribution from all other components of the model.
There are certain models with a lot of structure where, were they the continuum, it might be inappropriate to estimate the continuum flux at a single energy. The continuum model is integrated
(from
E(1—<frac range
)
>
to
E(1+<frac range
)
>
. The initial value of
<frac range>
is
0.05 and it can changed using the
RANGE
keyword.
The err/noerr
switch sets whether errors will be estimated on the equivalent width. The error algorithm is to draw parameter values from the distribution and calculate an equivalent width.
<number>
of sets of parameter values will be drawn. The resulting equivalent widths are ordered and the central
<level>
percent selected to give the error range. You can get the full array of simulated equivalent width values by calling ‘tclout eqwidth’ with the ‘errsims’ option (see tclout command).
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When Monte Carlo Markov Chains are loaded (see chain command), they will provide the distribution of parameter values for the error estimate. Otherwise the parameter values distribution is assumed to be a multivariate Gaussian centered on the best-fit parameters with sigmas from the covariance matrix. This is only an approximation in the case that fit statistic space is not quadratic.
Examples:
The current model is assumed to be
M
1
multiplicative and the
A x
models are additive.
(A
1
+A
2
+A
3
+A
4
+M
2
(A
5
)), where the M
x
models are
XSPEC12>
eqwidth 3
// Calculate the total flux of component M
1
(A
1
+A
3
+A
1
A
2
(the third
// component of the model with its multiplicative pre-factor)
// and find its peak energy (E). The continuum flux is
// found by the integral flux of M
4
+M
2
(A
5
))
, using the
// range of 0.95E to 1.05E to estimate the flux.
XSPEC12>
eqwidth range .1 3
// As before, but now the continuum is estimated from
// its behavior over the range 0.9E to 1.1E.
XSPEC12>
eqwidth range 0 3
// Now the continuum at the single energy range (E)
// will be used.
XSPEC12>
eqwidth range .05 2
// Now the component M
1
A
1
// M1(A
2
+A
3
+A
4
+M
2
(A
5
is used as the feature, and
))
are used for the continuum. The range
// has been reset to the original value.
XSPEC12>
eqwidth 1
// Illegal, as M
1
is not an additive component.
5.6.8 flux: calculate fluxes
Calculate the flux of the current model between certain limits.
Syntax:
flux
[<lowEnergy> [ <hiEnergy>]] [err <number> <level> | noerr] where
<lowEnergy>
and
<hiEnergy>
are the values over which the flux is calculated.Initial default values are 2 to 10 keV.
The flux is given in units of photons cm
–2
s
–1
and ergs cm
–2
s
–1
. The energy range must be contained by the range covered by the current spectra (which determine the range over which the model is evaluated).Values outside this range will be reset automatically to the extremes. Note that the energy values are two separate arguments, and are NOT connected by a dash. (see parameter ranges in the freeze command).
The flux will be calculated for all loaded spectra. If no spectra are loaded (or none of the loaded spectra have a response), the model is evaluated over the energy range determined by its dummy response. (In XSPEC12, models are automatically assigned default dummy responses when there is no data, so the dummyrsp command need not be given.) If more than 1 model has been loaded, whichever model the user has specified to be the active one for a given source is the one used for the flux calculation.
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The results of a flux command may be retrieved by the “tclout flux <n>” command where n is the particular spectrum of interest. If the flux was calculated for the case of no loaded spectra, the results can be retrieved by “tclout flux” with the <n> argument omitted.
The err/noerr
switch sets whether errors will be estimated on the flux. The error algorithm is to draw parameter values from the distribution and calculate a flux.
<number>
of sets of parameter values will be drawn. The resulting fluxes are ordered and the central
<level> percent selected to give the error range. You can get the full array of simulated flux values by calling ‘tclout flux’ with the ‘errsims’ option (see tclout command).
When Monte Carlo Markov Chains are loaded (see chain command), they will provide the distribution of parameter values for the error estimate. Otherwise the parameter values distribution is assumed to be a multivariate Gaussian centered on the best-fit parameters with sigmas from the covariance matrix. This is only an approximation in the case that fit statistic space is not quadratic.
There is also a model component cflux which can be used to estimate fluxes and errors for part of the model. For instance, defining the model as wabs(pow + cflux(ga)) provides a fit parameter which gives the flux in the gaussian line.
Examples:
The current data have significant responses to data within 1.5 to 18 keV.
XSPEC12>
flux
//Calculate the current model flux over the default range.
XSPEC12>
flux 6.4 7.0
//Calculate the current flux over 6.4 to 7 keV
XSPEC12>
flux 1 10
//The flux is calculated from 1.5 keV (the lower limit of the
//current response's sensitivity) to 10 keV.
5.6.9 gain: modify a response file gain
Modify a response file gain, in a particularly simple way. *CAUTION* This command is to be used with extreme care for investigation of the response properties. To properly fit data, the response matrix should be recalculated explicitly (outside of XSPEC) using any modified gain information derived.
The gain command shifts the energies on which the response matrix is defined and shifts the effective area curve to match. The effective area curve stored by XSPEC is either the ARF, if one was in use, or is calculated from the RSP file as the total area in each energy range. This means that if there are sharp features in the response then these will only be handled correctly by the gain command if they are in the ARF or if no ARF is input. The new energy is calculated by
E' = E/<slope> - <intercept> where <intercept> is in units of keV.
Syntax:
gain [<sourceNum>:]<specNum> <slope> <intercept>
gain fit [[<sourceNum>:]<specNum>]
gain nofit { [[<sourceNum>:]<specNum>] | all }
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gain off
The first variant of the gain command shown above will apply the gain shift specified by the <slope> and <intercept> parameters to the response belonging to spectrum <specNum>, and optionally specified <sourceNum> if the data is analyzed with multiple models. The initial default
<specNum> is 1; later, the default is the number of the spectrum last modified. Initially, all responses are assumed to have nominal gains, determined implicitly by the data in the response files. This is equivalent to a <slope> of 1 and an <intercept> of zero. All responses can be reset back to this original state by entering gain off. Note that in this mode of usage, the slope and intercept values do NOT become variable fit parameters. They are simply fixed values used to modify the response.
The gain fit mode is used when the user wishes to have the slope and intercept parameters determined by the results of a fit. The <specNum> and optional <sourceNum> parameters specify to which response the fit gain values are to be applied. These may be omitted only if a single spectrum is loaded, with a single model source. Otherwise at least a spectrum number is required.
The user will then be prompted for slope and intercept parameter information in the same way as model parameters are normally entered. These values are then immediately applied to the response, and will be adjusted the next time a fit is run.
Gain fit parameters belong to the more general category of response parameters in
XSPEC, and may be modified using an equivalent set of commands to those used for regular model parameters. The command names are the same except prefixed by the letter ‘r’:
XSPEC commands for editing/viewing model parameters
Equivalent commands for gain (or response) parameters newpar rnewpar freeze rfreeze thaw rthaw untie runtie error rerror model rmodel show par show par, show rpar
For example after assigning gain fit parameters to source 1 of spectrum 1 (with “gain fit
1”):
XSPEC12> rfreeze 1
XSPEC12> rnewpar 2 .05
XSPEC12> show rpar
126
Response parameters defined:
========================================================================
Source No.: 1
Rpar Spectrum Rmodel Rpar_name Unit Value
1 1 gain slope 1.00000 frozen
2 1 gain offset 5.00000E-02 +/- 0.0
________________________________________________________________________
Rnewpar can also link gain parameters to one another and can adjust the hard and soft parameter limits, as newpar does for model parameters. The default gain parameter hard limits are hardcoded in XSPEC, but these can be overridden by setting GSLOP_MIN, GSLOP_MAX,
GOFFS_MIN, and GOFFS_MAX keywords in the matrix extension of your response file.
The gain operation itself belongs to the category of response functions, which in future versions of XSPEC may be defined with rmodel just as regular XSPEC model functions are defined with model. Though gain is currently the only available response function, the following command will work:
// Apply gain to the response belonging to source 2 of spectrum 1
XSPEC12>rmodel 2:1 gain which is equivalent to:
XSPEC12>gain fit 2:1
The nofit argument switches off the fitting and leaves the gain at the current values of the parameters. Unless the argument all is given, it is applied to a single response specified by
<specNum> and optional <sourceNum>. As with gain fit, both arguments may be omitted if only a single spectrum with 1 source is loaded. When all is specified, fitting is switched off for the gain parameters of all responses. gain off will switch off fitting for all gain parameters, and will reset all of them to their nominal value.
Whenever a new response file is defined for a spectrum, the response will return to the nofit state with nominal value. The ignore and notice commands however will not affect the current gain of the response. THE GAIN COMMAND IS NOT CURRENTLY IMPLEMENTED FOR
DUMMY RESPONSES.
Examples:
XSPEC12>gain 1 0.98
// The response belonging to spectrum 1 is adjusted with a slope of 0.98.
// The 1 may be omitted if only 1 spectrum (with 1 source) is loaded.
XSPEC12>gain 1,,.03
// The offset also is moved now by 0.03 keV.
XSPEC12>gain 2:4 1.1 0.1
// The response belonging to source number 2, spectrum 4, is adjusted with slope 1.1
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// and offset 0.1 keV.
XSPEC12>gain off
// The above 2 responses, and any others that have been adjusted, are reset to slope
// 1.0, offset 0.0.
XSPEC12> gain fit 3
// Variable fit parameters are created for spectrum 3 response. User will be prompted
// for starting fit parameter values of slope and offset.
XSPEC12> fit
// Best fit gain values will now be determined for and applied to spectrum 3 response.
XSPEC12> gain nofit 3
// Spectrum 3 response will retain its current gain values, but values will not be
// adjusted during future fits.
NOTE: Current gain information may be easily viewed with the show response command. Gain fit parameters may also be viewed with the show par or show rpar commands.
The gain command has been slightly revised for XSPEC12. Previously when a user entered a gain command, it was generally interpreted to apply to an entire model. This new implementation clearly defines an applied gain as belonging to a particular response. It also offers less ambiguity for dealing with XSPEC12’s multiple models scheme. So for example if 2 spectra are loaded, each in its own data group, and the user enters a gain fit command, under the old system they would be prompted for 2 sets of parameters since the model is applied to 2 data groups. With the new system, the user specifies which particular response (belonging to either spectrum 1 or 2) they wish to apply the gain fit to, and are then prompted for just the 1 set of gain parameters for that response. This is more clearly demonstrated with the examples below. The new command options “gain nofit all” and “gain off” are also described below.
*** NOTE: Backwards incompatible syntax change ***
Beginning with XSPEC 12.5.1, gain parameters must be specified as
[<sourceNum>:]<specNum> and NOT <specNum>[:<sourceNum>]. This reversal was made so that the gain command conforms to the [<sourceNum>:]<specNum> usage in other XSPEC commands, such as response and arf.
5.6.10 identify: identify spectral lines
List possible lines in the specified energy range.
128
Syntax:
identify
<energy> <delta_energy> <redshift> <line_list>
The energy range searched is
< energy >±Δ < energy >
(keV) in the rest frame of the source. If working in wavelength mode, as set by the
setplot
command, then the <energy> and
<delta energy> parameters should be entered as wavelengths (in Angstroms).
<line list> specifies the list of lines to be searched. The options are bearden
, which searches the Bearden compilation of fluorescence lines (Bearden, J.A., 1967, Rev.Mod.Phys. 39, 78), mekal
, which uses the lines from the mekal model (q.v.) and apec
, which uses the APEC
http://cxc.harvard.edu/atomdb
line list. The apec
option takes an additional two arguments: the temperature of the plasma (keV) and a minimum emissivity of lines to be shown. If the command
xset
has been used to set
APECROOT
then identify
uses the
APECROOT
value to define the new atomic physics data files. See the help on the apec
model for details.
5.6.11 initpackage: initialize a package of local models
The initpackage command initializes a package of local models from their source code and from a model component description file in “model.dat” format which defines the component’s name, type, function call, and its parameter names and initial settings. Further details of the file format, function and parameter specifications are given in Appendix C,
Adding Local Models To
XSPEC
. [Note: initpackage is now also supported on Cygwin. The former Cygwin-only static_initpackage command has been removed.]
The <name> argument names the package. For internal reasons package names must be lowercase: the initpackage command will force lower case and warn the user if the argument contains uppercase letters. Also there should be no numerals in the package name.
The <description file> argument specifies the model component description file. The third argument <directory> is optional and specifies the location of the source code. If it is not given, the value of the setting LOCAL_MODEL_DIRECTORY given in the user’s Xspec.init file will be used. Finally, the <description file>, if not specified as an absolute pathname, will be read from the same directory as the source code.
Another optional argument is “-udmget”, for local model libraries containing Fortran code which makes use of XSPEC’s now-obsolete udmget function for dynamic memory allocation.
None of the functions in XSPEC’s built-in models library use udmget anymore, and the necessary xsudmget.cxx file no longer resides there. If a user still requires this code for their own local models, they should add “-udmget” (without the quotes) at the end of the comamnd line.
initipackage will then copy the files xsudmget.cxx and xspec.h into the user’s local model directory.
initpackage performs the following tasks: reads the model description file writes code that will load the new component calculation functions writes a makefile that will drive the compilation and installation of the new code invokes the compiler and builds the library.
129
A separate command, lmod, actually loads the library.This two step process makes it easier to determine where the user is during the process if compilation failures arise. Further, if the model is complete and working correctly, only the lmod command need be invoked.
Initpackage can also be run as a stand-alone program outside of XSPEC. When used like this however, after initpackage has finished the user must manually run hmake to build their library. XSPEC performs this part automatically using a script file.
5.6.12 lmod, localmodel: load a package of local models
The lmod command (localmodel is an alias for this command) loads a user model package
Further details are given in Appendix C. [Note: This command is now also supported on
Cygwin.]
Syntax: lmod <
name> [directory]
As for initpackage, the
<name>
argument is the name of the model package being loaded, and the
<directory>
is the its location, defaulting to the setting of
LOCAL_MODEL_DIRECTORY given in the user’s Xspec.init
lmod performs the following tasks:
loads the library corresponding to the package named
<name>
reads the model description file supplied by the initpackage command for the library
adds the new model components to the list of models recognized by the model command.
Note that lmod requires that the user has write-access to <directory> (please see Appendix
C for details).
5.6.13 lumin: calculate luminosities
Calculate the luminosity of the current model for a given redshift and rest frame energy range.
Syntax:
|noerr]
lumin
[<lowEnergy> [<hiEnergy>] [<redshift>] [err <number> <level> where
<low Energy>
and
<hi Energy> are the rest frame energies over which the luminosity is calculated and
<redshift>
is the source redshift.Initial default values are 2 to 10 keV for 0 redshift. The luminosity is given in units of ergs/s. The energy range redshifted to the observed range must be contained by the range covered by the current spectra (which determine the range over which the model is evaluated). Values outside this range will be automatically reset to the extremes. Note that the energy values are two separate arguments and are NOT connected by a dash (see parameter ranges in the freeze command description).
The lumin will be calculated for all loaded spectra. If no spectra are loaded (or none of the loaded spectra have a response), the model is evaluated over the energy range determined by its dummy response. (In XSPEC12, models are automatically assigned default dummy responses
130
when there is no data, so the dummyrsp command need not be given.) If more than 1 model has been loaded, whichever model the user has specified to be the active one for a given source is the one used for the lumin calculation.
The results of a lumin command may be retrieved by the “tclout lumin <n>” command where n is the particular spectrum of interest. If lumin was calculated for the case of no loaded spectra, the results can be retrieved by “tclout lumin” with the <n> argument omitted.
The err/noerr
switch sets whether errors will be estimated on the luminosity. The error algorithm is to draw parameter values from the distribution and calculate a luminosity.
<number> of sets of parameter values will be drawn. The resulting luminosities are ordered and the central
<level> percent selected to give the error range. You can get the full array of simulated lumin values by calling ‘tclout lumin’ with the ‘errsims’ option (see tclout command).
The parameter values distribution is assumed to be a multivariate Gaussian centered on the best-fit parameters with sigmas from the covariance matrix. This is only an approximation in the case that fit statistic space is not quadratic.
Examples:
The current data have significant response to data within 1 to 18 keV.
XSPEC> lumin,,,0.5
//Calculate the current model luminosity over the default range for z=0.5
XSPEC> lumin 6.4 7.0
//Calculate the current luminosity over 6.4 to 7 keV.
5.6.14 mdefine: Define a simple model using an arithmetic expression.
Syntax: mdefine
[name [expression [: [type] [emin emax]]] where 'name' = the name of the model. If "name" is a previously defined model with mdefine, the current definition will overwrite the old one, and the user is warned; if it is a built-in model, however, the user will be asked to use a different name.
'expression' = a string of arithmetic expression. Simple rules for expression:
1) The energy term, must be 'e' or 'E' in the expression. Other words, which are not numerical constants nor internal functions, are assumed to be model parameters.
2) If a convolution model varies with the location on the spectrum to be convolved, the special variable ".e" or ".E" may be used to refer to the convolution point.
3) The expression may contain spaces for better readability.
'type' = user may optionally specify the type of the model, the valid types are (add, mul, con). (Mix models are not yet implemented as of v12.5.0) Please note that the character
":" must be used to separate the options from the "expression". If "type" is not given default is add.
'emin emax' = user may also specify the minimum and maximum energy values for the model, the default values are 1.e-20 and 1.e+20, respectively.
131
Note that MDEFINE can also be used to display and delete previously defined models:
1) To display the name, type and expression of all previously defined models:
XSPEC12>mdefine
2) To display the name, type and expression of a previously defined model by the name,
MNAME:
XSPEC12> mdefine MNAME
3) To delete a previously defined model by the name, MNAME:
XSPEC12> mdefine MNAME :
Operators:
The following operators are recognized in an expression:
+ = plus operator
- = minus operator
* = multiplying operator
/ = dividing operator
** = exponentiation operator
^ = exponentiation operator
Functions:
The following internal functions are supported:
Unary Functions .............................
EXP (expr) = exp of a vector expression
SIN (expr) = sine of vector expression in rad
SIND (expr) = sine of a vector expression in degree
COS (expr) = cosine of a vector expression in rad
COSD (expr) = cosine of a vector expression in degree
TAN (expr) = tangent of a vector expression in rad
TAND (expr) = tangent of a vector expression in degree
LOG (expr) = base 10 log of a vector expression
LN (expr) = natural log of a vector expression
SQRT (expr) = sqrt of a vector expression
ABS (expr) = absolute value of a vector expression
INT (expr) = integer part of a vector expression
ASIN (expr) = sin^-1 of a vector expression in rad
ACOS (expr) = cos^-1 of a vector expression in rad
MEAN (expr) = mean value of a vector expression
DIM (expr) = dimension of a vector expression
SMIN (expr) = minimum value of a vector expression
SMAX (expr) = maximum value of a vector expression
132
Binary Functions ............................
MAX (expr1, expr2) = maximum of the two vector expressions
MIN (expr1, expr2) = minimum of the two vector expressions
Examples:
XSPEC12> mdef dplaw E**p1 + f*E**p2 ! define a model named "dplaw" with
3 parameters, p1, p2, f
XSPEC12> mdef junk a*e+b*log(e)/sin(e) ! define a model named "junk" with
2 parameters (a, b)
XSPEC12> mdef junk2 exp(-a*e) : mul ! define a model named "junk2" with
1 parameter, a; the option following ":" says that it will be a multiplicative model.
XSPEC12> mdef junk3 0.2+B*e : mul
XSPEC12> mdef bb E**2/T**4/(exp(E/T)-1) ! try to define a blackbody model with name "bb", you get warning:
! define a model named "junk3" with
1 parameter, B, options following
":" says that this will be a multiplicative model
***Warning: bb is a pre-defined model
Please use a different name for your model.
XSPEC12> mdef sg exp(-E^2/(2*A*.E)) / sqrt(6.283*A*sqrt(.E)) : con
! this defines a Gaussian convolution model with sigma varying with square root of energy.
XSPEC12> mdef junk2 :
XSPEC12> mdef
-- Name ---- Type ------ Expression ----- dplaw add E**p1+f*E**p2
! delete junk2
! display all user-defined models junk add a*E+b*LOG(E)/SIN(E) junk3 mul a+b*E
EXP(-E^2/(2*A*.E))/SQRT(6.283*A*SQRT(.E))
-----------------------------------------
5.6.15 model: define a theoretical model
Define the form of the theoretical model to be fit to the data.
133 model
[<source num>:<name>] [<delimiter>] <component1> <delimiter>
<component2> <delimiter>... <componentN> [ <delimiter>]
model [
?]
model [<name>|unnamed] none
model clear
model <name>|unnamed active|inactive
rmodel [<source num>:]<spec num> <response function>|none where
<delimiter>
is some combination of
(
,
+
,
*
,
)
, and
<componentJ>
is one of the model components known to XSPEC. The optional name must be preceded by a source number followed by a colon.
To specifically refer to the default model use the string unnamed. Descriptions of these models may be accessed by typing help models
at the prompt.
The source argument and name, if present, assign that model to be used with one of the sources found to be in the spectrum during the data pipelining. These 2 parameters allow one to simultaneously analyze multiple models, each assigned to their own responses. The model will be referred to the channel space using a response corresponding to that source number. To create a model for a source number higher than 1, a detector response must first exist for that number. See the examples below and the response command for more information about using multiple sources.
This ability to assign multiple models both generalizes and replaces the XSPEC11 method of using
‘/b’ to specify background models.
After the model is loaded, if there are data present the model is attached through the instrumental response to the spectra to be fitted, as in XSPEC11. Unlike XSPEC11, however, if there are no data loaded the model will be attached to a default diagonal dummy response. The parameters of that dummy response (energy range, number of flux points, linear/logarithmic intervals) can be set by the user in the Xspec.init file using the DUMMY setting. Thus any model can be plotted in energy or wavelength space as soon as it has been defined.
The model components are of various types depending on what they represent and how they combine with other models additive, multiplicative, convolution, pile-up, and mixing models. Each component may have one or more parameters that can be varied during the fit (see the newpar command writeup).
Additive model components are those directly associated with sources, such as power laws, thermal models, emission lines, etc. The net effect of two independent additive models is just the sum of their individual emissivities.
Multiplicative model components do not directly produce photons, but instead modify (by an energy-dependent multiplicative parameter) the spectrum produced by one or more additive components. Examples of multiplicative models are photoelectric absorption models, edges, absorption lines, etc.
Convolution models components modify the spectrum as a whole, acting like operators rather than simply applying bin by bin multiplication factors. An example of a convolution model is a gaussian smoothing with energy dependent width. Thus, when using convolution models, the ordering of components is in general significant (see below under
syntax rules
).
134
The pile-up model is similar to the operation of the convolution models. The only difference is that the flux is multiplied by the effective area on input and divided by the same factors on output.
Mixing model components implement two-dimensional transformations of model spectra. The data are divided into regions by assigning them to 2 or more datagroups, and the transformation “mixes” the flux among the regions. An example is the projct
(projection) model, which assumes that the regions are 3-dimensional ellipsoidal shells in space, and projects the flux computed from the other components onto 2-dimensional elliptical annuli.
A list of all the currently installed models is given in response to the command model
?
(the ‘?’ is not actually required)
(this will leave the current model in use).
The new command variants have the following uses:
model [<name>] none removes the model of name <name> if given. Without the <name> argument, the command removes the unnamed “default” model, which is of course the XSPEC11 behavior.
model clear removes all models
model <name>|unnamed active|inactive makes the model named <name> active (fit to data) or inactive. Inactive models are tied to a dummy (unit diagonal) response. Making a model assigned to a given source active makes any previous model assigned to that source inactive. Note that to make the default unnamed model active or inactive refer to it by the string unnamed.
See the commands delcomp
, addcomp
and editmod
for details on how to modify the current model without having to enter a completely new model.
rmodel [<source num>:]<spec num> <response function>|none assigns or removes a response function to the response belonging to <source num> of spectrum
<spec num>. Currently the only available <response function> in XSPEC is gain
, which makes
rmodel redundant with the gain command usage: gain fit [<source num>:]<spec num>
The rmodel none option removes the response function and restores the response to its initial state.
Syntax Rules
Model components are combined in the obvious algebraic way, with
+
separating additive models,
*
separating multiplicative models, and parentheses to show which additive models the multiplicative models act on. The
*
need not be included next to parentheses, where it is redundant.
Also, if only one additive model is being modified by one or more multiplicative models, the
135
required brackets may be replaced by a
*
. In this case the additive model must be the last component in the grouping. Thus
M
1
*(A
1
+A
2
) + M
2
*M
3
(A
3
) + M
4
*A
4
+ A
5
is a valid model, where the M's signify multiplicative models and the A's additive models.
The old style syntax for entering models (versions 9.02 and earlier) is not supported in version 12 and will return a syntax error.
XSPEC12’s recursive lexical analyzer and expression parser allows, in principle, infinite nesting depth. It has been tested to 3 levels of parentheses, although it should be said that this new behavior is a by-product of the design rather than fulfilling an important need. Thus, expressions such as
M
1
*(A
1
+ A
2
*(A
3
+ M
2
*M
3
*(A
6
+ A
7
))) + C
1
*(A
8
+ A
9
*(A
10
+ M
2
*A
6
))
are supported.
The model expression is analyzed on entry and syntax errors, or undefined models, will return control to the prompt with an error message. XSPEC12’s model definition algorithm treats expressions delimited by ‘+’ signs that are not within parentheses as separate “Component
Groups”. The Component Group comprises a list of components of the different types, and these are in turn calculated and then combined to produce an internal “Sum Component”. These Sum
Components from each such component group are then added to produce the output model (note that if there is an overall component – for example, a convolution or mixing component – then all of the model will be contained inside one Component Group).
The syntax rules that are checked for are as follows:
Expression must not begin with a “*”
A “*” must be preceded and followed by words or a brace (redundant braces are removed).
A standalone component must be additive. A standalone component is defined as a single component model or a single component at the beginning (end) of the expression followed
(preceded) by a “+”, or in the middle of the expression delimited by 2 “+” signs.
A convolution component must not appear at the end, or followed by a closing brace.
A mixing model component must appear first in the expression and apply to all components (thus a model including a mixing component always has one Component Group.
When using convolution components, the order in which they are applied is in general significant.For example, the two models
C
1
*M
1
(A
1
+A
2
) and M
1
* C
1
(A
1
+A
2
)
are not necessarily equivalent (here the C's represent convolution models).The way XSPEC handles the ordering of components is by first computing the spectrum for the additive components of a given additive group (A1+A2 in the above example). It then applies all multiplicative or convolution components in the additive group from right to left in the order they appear in the model formula.
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N.B. Beginning with v12.5.0, convolutions no longer have to precede the source. Parentheses may also be used to specify convolution precedence, so the following two examples are not equivalent:
C
1
*M
1
(A
1
+A
2
) and (C
1
*M
1
) (A
1
+A
2
)
Mixing models are a special case. The mixing transformation is applied to the entire model once the combination into a single Sum Component has been executed. Note that since XSPEC12 can have multiple models applied to a given spectrum, the mixing transformation can nevertheless be applied to only one of the models being fit. This will be relevant, for example, for the case where the background is fitted by a separate model
Examples
Note that po (= powerlaw)
and ga (= gauss)
are additive models, and that wabs and phabs
(different photoelectric absorption screens) are multiplicative models.
XSPEC12> model po
// The single component po (powerlaw) is the model.
XSPEC12> model po+ga
XSPEC12> model (po+ga)wabs
XSPEC12> model phabs(po+ga)
XSPEC12> model wa(phabs(po)+ga)
XSPEC12> model wa po phabs ga //error: old syntax
XSPEC12> model wa*phabs*po
XSPEC12> model (po+po)phabs
//Note that though the first and second components are the same
// form, their parameters are varied separately.
XSPEC12> model phabs*wa(po)
A complex (and almost certainly unphysical) example is the following:
XSPEC12>model wa(po+pha(peg+edge(disk+bbod)))const + pla(pos+hr*step) + not*gau
Applying multiple models:
Assume 3 spectra are loaded, each with a single response (source 1 by default).
XSPEC12> model wa(po)
// The unnamed model wa(po) will apply to all 3 spectra, accordingly
// multiplied by each spectrum’s response.
XSPEC12> response 2:2 new_resp.pha 2:3 another_new_resp.pha
// Additional responses assigned to source number 2 for spectra 2 and 3.
XSPEC12> model 2:second_mod ga
// The model “second_mod” will now apply to source 2, and is therefore
// multiplied by new_resp.pha and another_new_resp.pha for spectra 2
// and 3 respectively.
XSPEC12> model second_mod inactive
// “second_mod” will no longer apply to spectra 2 and 3, though they
// retain responses for source 2.
OR
XSPEC12> response 2:2 none
XSPEC12> response 2:3 none
// No responses exist for source number 2, second_mod is
// rendered inactive.
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5.6.16 modid: write out possible IDs for lines in the model.
Tcl script to write out possible IDs for gaussian or lorentzian lines in the current model.
Syntax: modid
[{<delta> | conf }
This script runs the identify command for every gaussian or lorentzian line included in the current model. If a number is given as an argument then that is used as the delta energy for identify. If the string “conf” is given as the argument then the last calculated confidence regions are searched for possible line IDs. If no argument is given then “conf” is assumed.
5.6.17 newpar: change parameter values
Adjust one or more of the model parameters.
Syntax: newpar
[modelName:]<index range> [<param spec list> ]
newpar
[modelName:]<index> = <coupling expression>
newpar
0 where
<param spec list> =:: <param value> <delta> <param range spec>
<param range spec> =:: <hard min> <soft min> <soft max> <hard max>
For response parameters (created with the gain or rmodel command):
rnewpar
[<sourceNum>:]<idx range> [<param spec list>]
rnewpar
[<sourceNum>:]<index> = <coupling expression>
The model parameters are accessed through their model parameter indices. For example, the first parameter of the first model component generally is model parameter 1, etc.The first command line argument,
<index range>
, gives the indices’ parameters to be modified by the newpar command. The default value is the range from the previous invocation of newpar
. The remaining arguments can be used to update the parameter specification. If the parameter specification is omitted from the command line, then the user is explicitly prompted for it. The first two arguments of the parameter specification are:
<param value> The trial value of the parameter used initially in the fit
<delta>
The step size used in the numerical determination of the derivatives used during the fitting process. When delta is set to zero, the parameter is not adjustable during the fit. This value may be overriden for all parameters by the xset delta
command
138
option, which will apply a proportional rather than a fixed delta.
The four arguments of the range specification determine the range of acceptable values for the parameter. The soft limits should include the range of expected parameter behavior. Between the hard and soft limits, the parameter is made stiffer to adjustment by the minimization routine invoked by the fit
command. The parameter is never allowed to have a value at or outside the hard limits.
A slash (
/
) will set all the six parameter specification values (value, delta, range specification) to the previous value (default for a new model, current value if the parameter has previously been set or fit).
The sequence
/*
leaves all parameters unchanged (in the case of a new model, to be set to the default).
newpar
0
Prints the current parameter settings.
Parameter Links
Coupling of parameters allows parameters in a model to always have the same value or to be related by an expression. The expression is a polynomial function of the other parameters
(XSPEC will reject attempts to link parameters to themselves!). Also, XSPEC12 allows parameters to be designated in their initialization file to be fixed, i.e. never variable during a fit, or to act as switches that change the mode in which a theoretical component is calculated (i.e. it may be interpolated or analytically calculated). “scale” or “switch” parameters cannot be linked to any other type of parameter, but only to other scale or switch parameters. Details of parameter types are explained in more detail in Appendix C.
The syntax for linking parameters is
XSPEC12> newpar <par> = f( par ), where f is a polynomial in the (other) parameters with real coefficients. N.B. Integers appearing in f that are within the range of existing parameter numbers will be interpreted as parameters: to avoid confusion, if a real number is intended it should include a decimal point. Integers larger than the last parameter number will be interpreted as integers. Parameters of named models must have their index numbers prefixed by
[modelName:]
.
If there are multiple data groups present, then the parameters of models associated with datagroups greater than 1 (“secondary models”) are coupled by default to their “primary” counterparts. For example, if there are 5 parameters in the model and 3 datagroups present, then the model command will prompt for 15 parameters. If the user types
XSPEC12> model <expression>
XSPEC12>/*
Then parameters 1-5 will be set to their values specified in the initialization (“model.dat”) file.
Parameters 6-15 will be linked to their counterparts, i.e. as if the user had typed
XSPEC12> newpar 6 = 1
XSPEC12> newpar 7 = 2
…
XSPEC12> newpar 11 = 1
And so on.
Examples:
The total number of model parameters for the example is four.
XSPEC12>
newpar 2 0.1
//The value of the second parameter is set to 0.1.
XSPEC12>
newpar 3-4
//The program will prompt for a specification for the 3 rd
// parameter (comp gives the name of the corresponding model component) comp:param3>0.001, 0
//which has its value set to 0.001 and its delta set to zero, fixing
// it in later fits.The program now prompts for a specification for
// the 4th parameter comp:param4>21
// which is set to 21.As there is no 5 th
parameter, the program
// displays a summary and returns to command level.
XSPEC12>
newpar ,,.001
//The value of the delta of the 3rd parameter (which is the default
// index as it was the first parameter modified in the previous
// newpar invocation) is set to 0.001, allowing it to be adjusted
// during any fits.
The total number of parameters for this example is eight.
XSPEC12>
newpar 4 = 1
//The value of parameter 4 is set to the value of parameter 1.
//This has the consequence of model parameter 4 being frozen at the
// value of parameter 1 during subsequent fitting procedures.
// If model parameter 1 is a free parameter, then both parameters
// 1 and 4 change their values simultaneously in the fit procedure.
XSPEC12>
newpar 4 = 3/5 + 6.7
//The value of parameter 4 is set to the value of
// (parameter 3/ parameter 5) plus 6.7
XSPEC12>
newpar 6 = 3 * .1 - 9.5
//The value of parameter 6 is set to 0.1 times the
// value of parameter 3 minus 9.5
XSPEC12>
newpar 5 = 2 + 5.
//The value of parameter 5 is set to the value
// of parameter 2 plus 5.
XSPEC12>
newpar 8 = 1 / 4.6
//parameter 8 is set to parameter 1 divided by 4.6
XSPEC12>
untie 6
//Makes parameter 6 independent of parameter 3 and a free
//parameter.
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140
5.6.18 variance systematic: add a model-dependent systematic term to the
Syntax: systematic
[ <model systematic error>]
Set a systematic error term on the model to be added in quadrature to that on the data when evaluating chi-squared. The default value is zero.
5.6.19 untie: unlink previously linked parameters
Untie the specified parameter from any links to other parameters.
Syntax: untie
<param range> where <param range> is of the form
<param range> =:: [modelName:]<param #>
For response parameters (see gain command):
runtie
<param range> where <param range> is of the form
<param range> =:: [sourceNum:]<param #>
Parameters previously linked together with commands such as
XSPEC12> newpar <param spec> are unlinked. The parameter will retain its current value for the next fit.
5.7 Plot Commands
5.7.1 cpd: set current plotting device
Syntax:
cpd
cpd
< plot device>
<filename>
cpd
<filename>/{ps,cps,vps,vcps}
cpd none
Set current plot device. The same can be achieved with the setplot device command, which takes the same options. In XSPEC12 as in previous versions, the plot device options are those allowed by the PGPLOT library.
When plotting to the screen, the most commonly used devices are
/xs
(
/xserve
) and
/xw
(
/xwindow
). If you select
/xs
, the plot window is persistent: it remains visible and in the selected
141
position even after the XSPEC session is finished. With
/xw
the plot window closes at the end of the XSPEC session. Also note that on some platforms, when using
/xs
in multiple desktops, you might not see the window appear in a second desktop if it is still open in the first.
If the second argument does not start with a ‘/’ character, which indicates that the string represents a PGPLOT device, it is taken to be a filename for Postscript output, and the default postscript driver will be used. The default postscript driver produces a monochrome plot in landscape orientation.
The filename argument can be followed by a ‘/’ that specifies a particular postscript driver variant. Allowable variants are: cps (color postscript), vps (monochrome portrait orientation), and vcps (color portrait orientation), as well as the default, ps.
PGPLOT devices
A number of plot device types are supported in XSPEC. PGPLOT devices available on
Unix machines are :
/GIF
/VGIF
/NULL
/PPM
/VPPM
/PS
/VPS
/CPS
/VCPS
/TEK4010
/GF
/RETRO
/GTERM
/XTERM
/ZSTEM
/V603
/KRM3
/TK4100
/VT125DEC
/XDISP
/XWINDOW
/XSERVE
Graphics Interchange Format file, landscape orientation
Graphics Interchange Format file, portrait orientation
Null device, no output
Portable Pixel Map file, landscape orientation
Portable Pixel Map file, portrait orientation
PostScript file, landscape orientation
PostScript file, portrait orientation
Colour PostScript file, landscape orientation
Colour PostScript file, portrait orientation
Tektronix 4010 terminal
GraphOn Tek terminal emulator
Retrographics VT640 Tek emulator
Color gterm terminal emulator
XTERM Tek terminal emulator
ZSTEM Tek terminal emulator
Visual 603 terminal
Kermit 3 IBM-PC terminal emulator
Tektronix 4100 terminals
VT125 and other REGIS terminals pgdisp or figdisp server
X window window@node:display.screen/xw
An /XWINDOW window that persists for re-use
Closes the device. For Postscript output, it flushes the write buffer into the file and closes the file.
Note that in XSPEC12, each plot command produces a separate page in the postscript file, unlike previously where each plot overwrote the previous plot.
Example:
142
// produce a set of color postscript plots in landscape orientation
// … commands to produce a plot.
XSPEC12> cpd dataplot.ps/cps
XSPEC12> plot data chi
XSPEC12> plot ufspec
XSPEC12> plot efficiency
XSPEC12> cpd none
Will produce 3 plots in the file dataplot.ps.
Note, in contrast, that the hardcopy command will print only the plot that is currently in a graphics frame.
5.7.2 hardcopy: print plot
Spool the current plot to the printer.
Syntax:
hardcopy [<filename>] [mono | color]
This command takes whatever is the current display in you plot window, writes it to a postscript file, and then sends it to a printer using the unix lpr
command. It will thus be printed on whatever printer lpr
uses as your default printer. If a filename is specified, the postscript file will be saved (e.g. “hardcopy dataplot.ps color” will produce a color plot saved in the file dataplot.ps).
If mono or color is not given, the hardcopy will be monochrome.
5.7.3 iplot: make a plot, and leave XSPEC in interactive plotting mode
Interactive plotting on the current plot device.
iplot <plot type>
This command works like the plot
command (see the plot
command description), but allows the user to change the plot and to add text to the plot interactively using the PLT package.
See the Overview of PLT in the Appendices for more information.
5.7.4 plot: make a plot
Make one or more plots to the current plot device (see setplot device)
.
Syntax:
plot
<plot type> [<plot type>] [<plot type>] ...
<plot type>
is a keyword describing the various plots allowed. Up to six plot panes can be put on a single page by combining multiple
<plot type>
options. For example: plot data resid ratio model
143
will produce a 4-pane plot. However contour plots may not be combined with other plots in this manner. When a certain plot type takes additional arguments (eg. chain, model
), simply list them in order prior to specifying the next plot type: plot chain 3 4 data ufspec
In multi-pane plots, XSPEC will determine if two consecutive plot types may share a common X-axis (e.g. plot data delchi,
or
plot counts ratio
). If so, the first pane will be stacked directly on top of the second. (Note that the small subset of multi-pane plots that were allowed in earlier versions of XSPEC all belonged in this category.)
For changing plot units, see setplot energy
and setplot wave.
Also see iplot
for performing interactive plots.
background
Plot only the background spectra (with folded model, if defined). To plot both the data and background spectra, use plot data
with the setplot background
option.
chain
Plot a Monte Carlo Markov chain. plot chain [thin <n>] <par1> [<par2>]
Chains must be currently loaded (see chain
command), and
<par1>
and
<par2>
are parameter identifiers of the form
[<model name>:]n
where n
is an integer, specifying the parameter columns in the chain file to serve as the X and Y axes respectively. To select the fitstatistic column, enter ‘0’ for the
<par>
value. If
<par2>
is omitted,
<par1>
is simply plotted against row number.
Use the thin <n>
option to display only 1 out of every <n> chain points. Example:
# plot one in five chain points,
# using parameters 1 and 4 for (X,Y) plot chain thin 5 1 4
The thin
value will be retained for future chain plots until it is reset. Enter thin 1
to remove thinning.
chisq
Plot contributions to chisq
. The contribution is plotted +ve or –ve depending on whether the residual is +ve or –ve.
contour
Plot the results of the last steppar
run. If this was over one parameter then a plot of statistic versus parameter value is produced while a steppar
over two parameters results in a fitstatistic contour plot. plot contour [ <min fit stat> [ <# levels> [ <levels>]]]
144
where
<min fit stat>
is the minimum fit statistic relative to which the delta fit statistic is calculated,
<# levels> is the number of contour levels to use and <levels> :=
<level1
>
... <levelN> are the contour levels in the deltafit statistic. contour
will plot the fit statistic grid calculated by the last steppar
command (which should have gridded on two parameters). A small plus sign “
+
” will be drawn on the plot at the parameter values corresponding to the minimum found by the most recent fit.
The fit statistic confidence contours are often drawn based on a relatively small grid (i.e.,
5x5). To understand fully what these plots are telling you, it is useful to know a couple of points concerning how the software chooses the location of the contour lines. The contour plot is drawn based only on the information contained in the sample grid. For example, if the minimum fit statistic occurs when parameter 1 equal 2.25 and you use steppar 1 1.0 5.0 4
, then the grid values closest to the minimum are 2.0 and 3.0. This could mean that there are no grid points where deltafit statistic is less than your lowest level (which defaults to 1.0). As a result, the lowest contour will not be drawn. This effect can be minimized by always selecting a steppar
range that causes
XSPEC to step very close to the true minima.
For the above example, using steppar 1 1.25 5.25 4
, would have been a better selection.
The location of a contour line between grid points is designated using a linear interpolation. Since the fit statistic surface is often quadratic, a linear interpolation will result in the lines being drawn inside the true location of the contour. The combination of this and the previous effect sometimes will result in the minimum found by the fit
command lying outside the region enclosed by the lowest contour level.
Examples:
XSPEC12>
steppar 2 0.5 1. 4 3 1. 2. 4
//create a grid for parameters 2 and 3
XSPEC12>
plot contour
//Plot out a grid with three contours with
// delta fit statistic of 2.3, 4.61 and 9.21
XSPEC12>
plot cont,,4,1.,2.3,4.61,9.21
//same as above, but with a delta fit statistic = 1 contour.}
counts
Plot the data (with the folded model, if defined) with the y-axis being numbers of counts in each bin.
data
Plot the data (with the folded model, if defined).
delchi
Plot the residuals in terms of sigmas with error bars of size one.
dem
Plot the relative contributions of plasma at different temperatures for multi-temperature models. This is not very clever at the moment and only plots the last model calculated.
145
eemodel
See model.
eeufspec
See ufspec.
efficien
Plot the total response efficiency versus incident photon energy.
emodel
See model.
eufspec
See ufspec.
goodness
Plot a histogram of the statistics calculated for each simulation of the most recent
‘goodness’ command run.
icounts
Integrated counts and folded model. The integrated counts are normalized to unity.
insensitv
Plot the insensitivity of the current spectrum to changes in the incident spectra
(experimental).
lcounts
Plot the data (with the folded model, if defined) with a logarithmic y-axis indicating the count spectrum
ldata
Plot the data (with the folded model, if defined) with a logarithmic y-axis.
margin
Plot the probability distribution from the results of the most recently run margin
command.
(Must be a 1-D or 2-D distribution.)
model, emodel, eemodel
Plot the current incident model spectrum (Note: This is NOT the same as an unfolded spectrum.) The contributions of the various additive components are also plotted. If using a named model, the model name should be given as an additional argument. emodel plots Ef(E) or, if
146
plotting wavelength, λf(λ). eemodel plots E
2 f(E), or if plotting wavelength, λ
2 f(λ). The E (or λ) used in the multiplicative factor is taken to be the geometric mean of the lower and upper energies of the plot bin.
ratio
Plot the data divided by the folded model.
residuals
Plot the data minus the folded model.
sensitvty
Plot the sensitivity of the current spectrum to changes in the incident spectra (experimental).
sum
A pretty plot of the data and residuals against both channels and energy.
ufspec, eufspec, eeufspec
Plot the unfolded spectrum and the model. The contributions to the model of the various additive components also are plotted. WARNING ! This plot is not model-independent and your unfolded model points will move if the model is changed. The data points plotted are calculated by
D*(unfolded model)/(folded model), where D is the observed data, (unfolded model) is the theoretical model integrated over the plot bin, and (folded model) is the model times the response as seen in the standard plot data
. eufspec plots the unfolded spectrum and model in Ef(E), or if plotting wavelength, λf(λ). eeufspec plots the unfolded spectrum and model in E
2 f(E), or if plotting wavelength, λ
2 f(λ). The E (or λ) used in the multiplicative factor is taken to be the geometric mean of the lower and upper energies of the plot bin.
5.7.5 setplot: modify plotting parameters
Set one of the various plot options. setplot <subcommand string> where
<subcommand string>
is a keyword followed in some cases by arguments.
Current settings of all setplot items can be viewed with show plot.
add
Show individual additive model components on the data plots.
The opposite is setplot noadd.
147
area, noarea
After setplot area
is entered, plot data
and plot ldata will show the data divided by the response effective area for each particular channel. plot residuals
will necessarily also be affected by this. Usual plotting is restored by setplot noarea
. If data is associated with more than 1 response, the response effective area is calculated by simply summing the contributions from each response.
background, nobackground
any).
When running plot data or
plot ldata
, also show associated background spectra (if
channel
Change the x-axis on data and residual plots to channels.
command
Add a PLT command to the command list. setplot command <PLT command> where
<PLT command>
is any valid PLT command. very time you use setplot command
, that command is added to the list that is passed toPLT when you use plot
or iplot
.
The most common use of setplot command
is to add a common label to all plots produced. You should be careful when using this command, because XSPEC does not check to see if you have entered a valid PLT command.These commands are appended to the list that XSPEC creates to generate the plot and so setplot command
will override these values (this can either be a bug or a feature, depending on what you have done!) See also setplot delete
and setplot list
.
Example:
XSPEC12>
setp co LA OT Crab {Add the label “Crab” to future plots.
delete
Delete a PLT command from the command list. setplot delete [all | <command #>-<command #> | <command #>] where
<command #>
is the number of a PLT command that had been entered previously using setplot command
.This command is used to delete commands from the list passed to PLT when you use the XSPEC plot
or iplot
commands.
Example:
XSPEC12>
setp co LA OT Testing
//PLT label command
XSPEC12>
setp co LWidth 5
//PLT line-width command
148
XSPEC12>
setplot lis
//List the PLT command stack.
1: LAbel OT Testing
2: LWidth 5
XSPEC12>
setplot del 1
//Delete the first command in the stack.
XSPEC12>
setplot lis
1: LWidth 5
device
Set current plot device.
XSPEC12>setplot device < plot device>
XSPEC12>setplot device <filename>
XSPEC12>setplot device <filename>/{ps,cps,vps,vcps}
XSPEC12>setplot device none
If the second argument does not start with a ‘/’ character, which indicates that the string represents a PGPLOT device, it is taken to be a filename for Postscript output, and the default postscript driver will be used. The default postscript driver produces a monochrome plot in landscape orientation.
The filename argument can be followed by a ‘/’ that specifies a particular postscript driver variant. Allowable variants are: cps (color postscript), vps (monochrome portrait orientation), and vcps (color portrait orientation), as well as the default, ps.
Set the device used for plots.
PGPLOT devices
A number of plot device types are supported in XSPEC. PGPLOT devices available on
Unix machines are :
/GIF
/VGIF
/NULL
/PPM
/VPPM
/PS
/VPS
/CPS
/VCPS
/TEK4010
/GF
/RETRO
/GTERM
/XTERM
/ZSTEM
/V603
Graphics Interchange Format file, landscape orientation
Graphics Interchange Format file, portrait orientation
Null device, no output
Portable Pixel Map file, landscape orientation
Portable Pixel Map file, portrait orientation
PostScript file, landscape orientation
PostScript file, portrait orientation
Colour PostScript file, landscape orientation
Colour PostScript file, portrait orientation
Tektronix 4010 terminal
GraphOn Tek terminal emulator
Retrographics VT640 Tek emulator
Color gterm terminal emulator
XTERM Tek terminal emulator
ZSTEM Tek terminal emulator
Visual 603 terminal
149
/KRM3
/TK4100
/VT125DEC
/XDISP
/XWINDOW
/XSERVE
Examples:
Kermit 3 IBM-PC terminal emulator
Tektronix 4100 terminals
VT125 and other REGIS terminals pgdisp or figdisp server
X window window@node:display.screen/xw
An /XWINDOW window that persists for re-use
XSPEC12>
setplot device /xt
//sets the device to the xterm.
XSPEC12>
setplot device none
//closes the plot file.
energy
Change the X-axis on plots to energies, and optionally change the units. setplot energy [<units>] where
<units>
is an optional string for modifying X-axis energy units. Valid choices currently are: keV, MeV, GeV, and
Hz
, which are case-insensitive and can be abbreviated.
Energy units initially default to keV
. The selection made here also determines the units in
ignore/notice energy range specifiers.
Where applicable, Y-axis units will be modified to match the X-axis selection. The exception is for the choice of
Hz
when emodel/eufspec is in Jy and eemodel/eeufspec in ergs/cm^2/s.
group
Define a range of spectra to be in the same group for plotting purposes only. setplot group <spectrum range>... where
<spectrum range>
is a range of contiguous spectra to be treated as a single spectrum for plotting purposes. The spectra still are fit individually. If multiple ranges are given, each range becomes a single group. Initially, all spectra read in are treated as single spectra. (See also ungroup.)
Examples:
Assume that there are five spectra currently read in, all of them ungrouped initially.
XSPEC12>
setplot group 1-4
//The first four spectra are treated as one group, with the fifth
//spectra on its own. Thus all plots will appear to have two spectra.
XSPEC12>
setplot group 1 2 3 4
//The spectra are reset to each be in their own group.
XSPEC12>
setplot group 2-3 4-5
//Now there are three plot groups, being spectrum 1, by itself, and
150
//spectra 2-3 and 4-5 as groups.
XSPEC12>
setplot group 1-**
//All the spectra are placed in a single plot group.
id
Switch on plotting of line IDs. setplot id <temperature> <emissivity limit> <redshift>
The IDs are taken from the APEC line list for the temperature given by the first argument.
The plot only shows those lines with emissivities above the limit set and the lines are redshifted by the amount specified. Currently theAPEC version used is 1.10. If
xset
apecroot
has been used to reset the APEC files then setplot id uses a filename based on the value of apecroot
as described in the documentation for the apec
model.
list
List all the PLT commands in the command list. setplot list
See setplot delete
for an example of use.
noadd
Do not show individual additive model components on the data plots. setplot noadd
The opposite is setplot add
.
noid
Switch off plotting of line IDs. setplot noid
The opposite is setplot id
.
rebin
Define characteristics used in rebinning the data (for plotting purposes ONLY). setplot rebin <min significance> <max # bins> <plot group> <error type>
151
In plotting the data from a spectrum (or group of spectra, see setplot group
), adjacent bins are combined until they have a significant detection at least as large as
<min significance>
(in
).However, no more than
<max # bins>
may be so combined. Initial values are 0. and 1, respectively. This argument effects only the presentation of the data in plots. It does not change the fitting, in particular the number of degrees of freedom. The values given are applied to all the plotted data in the plot group specified as the final argument. To change the rebinning simultaneously for all the plot groups give anegative value of the plot group.
The
<error type>
argument specifies how to calculate the error barson the new bins. The default is quad
which sums in quadrature the errors on the original bins. sqrt
uses N where N is the number of counts in the new bin, poiss-1
uses 1
N
0.75
, poiss-2
uses
N
0.25
, and poiss-3
is the arithmetic mean of poiss-1
and poiss-2
. If background is present its error is calculated by the same method then added in quadrature to the source error.
Examples:
XSPEC12>
setplot rebin 3 5 1
//Bins in plot group 1 are plotted that have at least 3
//or are grouped in sets of 5 bins.
XSPEC12>
setplot rebin 5 5
//The significance is increased to 5
significance criterion.
,
.
XSPEC12>
setplot rebin,,10,-1
//All plotted bins can be grouped into up to 10 bins in reaching the
//5
XSPEC12>
setplot rebin ,,,sqrt}
//Uses
N
to calculate error bars.
redshift
Apply a redshift to the X-axis energy and wavelength values. setplot redshift <z>
This will multiply X-axis energies by a factor of (1+z) to allow for viewing in the source frame. Y-axis values will be equally affected in plots which are normalized by energy or wavelength. Note that this is not connected in any way to redshift parameters in the model (or the setplot id redshift parameter) and should only be used for illustrative purposes.
splashpage (on|off)
When set to off, the usual XSPEC version and build date information will not be printed to the screen when the first plot window is initially opened. This is intended primarily for the HERA installation of XSPEC.
ungroup
Remove previous grouping set up by setplot group, resetting all spectra to be in a distinct plot group.
152
wave
Change the x-axis on plots to wavelength, and optionally change the units. setplot wave [<units>] setplot wave perhz [off] where <units> is an optional string for modifying X-axis wavelength units. Valid choices currently are: angstom, cm, micron, and
nm
, which are case-insensitive and can be abbreviated. Wavelength units initially default to angstrom
.
Where applicable, Y-axis units will be modified to match the X-axis selection. However this behavior can be changed by the command setplot wave perhz
, which will cause Y-axis units to be in
1/Hz
. This feature is turned off by setplot wave perhz off
, and its initial setting is determined by the WAVE_PLOT_UNITS setting in the user’s ~/.xspec/Xspec.init file. Also note that when perhz
is selected, emodel/eufspec and eemodel/eeufspec will have the same Y-axis units as for setplot energy hz
.
This command makes ignore and notice operate in terms of wavelength rather than energies. The units setting here also determines the units in the ignore/notice range specifiers.
.
xlog (on | off)
Set the x-axis to logarithmic or linear respectively for energy or wavelength plots. xlog has no effect on plots in channel space (recall that the default for energy plots is logarithmic: xlog allows the user to override this setting). xlog and ylog will not work for model-related plots (eg. model, ufspec, and their variants) as their axes are always set to log scale.
ylog (on | off)
Set the y-axis to logarithmic or linear respectively for energy or wavelength plots. For plot instructions that are explicitly logarithmic ( plot ldata, plot lcounts) the state of the ylog setting is ignored. xlog and ylog will not work for model-related plots (eg. model, ufspec, and their variants) as their axes are always set to log scale.
5.8 Setting Commands
5.8.1 abund: set the Solar abundances
Set the abundance table used in the plasma emission and photoelectric absorption models.
Syntax: abund
<option> where
<option>
is:
153
F
Ne
Na
Mg
Al
Si
P
H
He
Li
Be
B
C
N
O angr
, from Anders E. & Grevesse N. (1989, Geochimica et Cosmochimica Acta 53,
197) aspl
, from Asplund M., Grevesse N., Sauval A.J. & Scott P. (2009, ARAA, 47,
481) feld
, from Feldman U.(1992, Physica Scripta 46, 202 except for elements not listed which are given grsa abundances),
2363), aneb
, from Anders E. & Ebihara (1982, Geochimica et Cosmochimica Acta 46, grsa
from Grevesse, N. & Sauval, A.J. (1998, Space Science Reviews 85, 161) wilm
from Wilms, Allen & McCray (2000, ApJ 542, 914 except for elements not listed which are given zero abundance) lodd,
from Lodders, K (2003, ApJ 591, 1220) file filename
, where filename
is an ASCII file containing 30 lines with one number on each line. All abundances are number relative to H.
The tables are:
Element angr aspl feld aneb grsa wilm lodd
1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00
9.77e-02 8.51e-02 9.77e-02 8.01e-02 8.51e-02 9.77e-02 7.92e-02
1.45e-11 1.12e-11 1.26e-11 2.19e-09 1.26e-11 0.00
1.41e-11 2.40e-11 2.51e-11 2.87e-11 2.51e-11 0.00
1.90e-09
2.57e-11
3.98e-10 5.01e-10 3.55e-10 8.82e-10 3.55e-10 0.00 6.03e-10
3.63e-04 2.69e-04 3.98e-04 4.45e-04 3.31e-04 2.40e-04 2.45e-04
1.12e-04 6.76e-05 1.00e-04 9.12e-05 8.32e-05 7.59e-05 6.76e-05
8.51e-04 4.90e-04 8.51e-04 7.39e-04 6.76e-04 4.90e-04 4.90e-04
3.63e-08 3.63e-08 3.63e-08 3.10e-08 3.63e-08 0.00 2.88e-08
1.23e-04 8.51e-05 1.29e-04 1.38e-04 1.20e-04 8.71e-05 7.41e-05
2.14e-06 1.74e-06 2.14e-06 2.10e-06 2.14e-06 1.45e-06 1.99e-06
3.80e-05 3.98e-05 3.80e-05 3.95e-05 3.80e-05 2.51e-05 3.55e-05
2.95e-06 2.82e-06 2.95e-06 3.12e-06 2.95e-06 2.14e-06 2.88e-06
3.55e-05 3.24e-05 3.55e-05 3.68e-05 3.35e-05 1.86e-05 3.47e-05
2.82e-07 2.57e-07 2.82e-07 3.82e-07 2.82e-07 2.63e-07 2.88e-07
154
S
Cl
Ar
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
1.62e-05 1.32e-05 1.62e-05 1.89e-05 2.14e-05 1.23e-05 1.55e-05
1.88e-07 3.16e-07 1.88e-07 1.93e-07 3.16e-07 1.32e-07 1.82e-07
3.63e-06 2.51e-06 4.47e-06 3.82e-06 2.51e-06 2.57e-06 3.55e-06
1.32e-07 1.07e-07 1.32e-07 1.39e-07 1.32e-07 0.00 1.29e-07
2.29e-06 2.19e-06 2.29e-06 2.25e-06 2.29e-06 1.58e-06 2.19e-06
1.26e-09 1.41e-09 1.48e-09 1.24e-09 1.48e-09 0.00 1.17e-09
9.77e-08 8.91e-08 1.05e-07 8.82e-08 1.05e-07 6.46e-08 8.32e-08
1.00e-08 8.51e-09 1.00e-08 1.08e-08 1.00e-08 0.00 1.00e-08
4.84e-07 4.37e-07 4.84e-07 4.93e-07 4.68e-07 3.24e-07 4.47e-07
2.45e-07 2.69e-07 2.45e-07 3.50e-07 2.45e-07 2.19e-07 3.16e-07
4.68e-05 3.16e-05 3.24e-05 3.31e-05 3.16e-05 2.69e-05 2.95e-05
8.60e-08 9.77e-08 8.60e-08 8.27e-08 8.32e-08 8.32e-08 8.13e-08
1.78e-06 1.66e-06 1.78e-06 1.81e-06 1.78e-06 1.12e-06 1.66e-06
1.62e-08 1.55e-08 1.62e-08 1.89e-08 1.62e-08 0.00 1.82e-08
3.98e-08 3.63e-08 3.98e-08 4.63e-08 3.98e-08 0.00 4.27e-08
5.8.2 cosmo: set the cosmology
Set the cosmology used (i.e.,
H
0
,
q
0
, and
Syntax: cosmo
0 0 where
H
0
is the Hubble constant in km s –1
Mpc
–1
,
q
0
is the deceleration parameter, and
XSPEC requires that the universe is flat. In this case the value of
XSPEC will assume that
0.73
matter
1
H
0
70 ,
q
0
0.0
, and
Examples:
XSPEC12>
cosmo 100
// Set
< H >= 100kms Mpc
XSPEC12>
cosmo ,0
-1
// Set
155
XSPEC12>
cosmo ,,0.7
// Set a flat universe with
.
5.8.3 method: change the fitting method
Set the minimization method.
Syntax:
method
<algorithm> [<# of trials/evaluations> [<critical delta>] [methodspecific options]] where
<algorithm>
is the method in use and the other arguments are control values for the minimization. Their meanings are explained under the individual methods. The migrad and
simplex methods are taken from the CERN Minuit2 package, with documentation located at
http://seal.web.cern.ch/seal/MathLibs/Minuit2/html/index.html
. If either of these are used, then the error command will use the Minuit2 minos method to find the confidence regions.
leven
method
leven
[<# of eval> [<crit delta>] [<crit beta>]] [delay | nodelay]
The default XSPEC minimization method using the modified Levenberg-Marquardt algorithm based on the CURFIT routine from Bevington.
<# of eval>
is the number of trial vectors before the user is prompted to say whether they want to continue fitting.
<crit delta>
is the convergence criterion, which is the (absolute, not fractional) difference in fit statistic between successive iterations, less than which the fit is determined to have converged.
<crit beta>
refers to the |beta|/N value reported during a fit. This is the norm of the vector of derivatives of the statistic with respect to the parameters divided by the number of parameters. At the best fit this should be zero, and so provides another measure of how well the fit is converging.
When this is set to a positive value, it will provide another fit stopping criterion in addition to that of the
<crit delta>
setting.
Including the string delay as an argument turns on delayed gratification. It is turned off by nodelay.
Delayed gratification modifies the way the damping parameter is set and has been shown in many cases to speed up convergence. The default is nodelay.
<# of eval>
,
<crit delta>
,
<crit beta>, delay, and
nodelay
may also be set through the fit command.
This method requires an estimate of the second derivative of the statistic with respect to the parameters. By default, XSPEC calculates these using an analytic expression which assumes that partial 2 nd
derivatives of the model with respect to its parameters may be ignored. This may be changed by setting the USE_NUMERICAL_DIFFERENTIATION flag to “true” in the user’s startup Xspec.init initialization file. XSPEC will then calculate all second derivatives numerically, which can be noticeably slower.
156
migrad
method
migrad
[<# of eval>]
The Minuit2 migrad method.
<# of eval>
is the number of function evaluations to perform before giving up. Migrad uses an internal convergence criterion.
The current version of Minuit2 included is that from ROOT v5.34. Documentation on
Minuit2 can be found at http://seal.web.cern.ch/seal/MathLibs/Minuit2/html/.
If migrad is not working well try experimenting with different hard and soft limits on parameters.
simplex
method simplex [< # of evaluations
>]
The Minuit2 simplex method. <
# of evaluations
> is the number of function evaluations to perform before giving up. Simplex uses an internal convergence criterion. This method is included for historical interest and is almost always outperformed by migrad.
5.8.4 statistic: change the objective function (statistic) for the fit
Change the fit or test statistic in use, for one or more spectra.
Syntax: statistic
[chi | cstat | lstat | pgstat | pstat | whittle[#]]
[<spectrum range>]
statistic test
[ad | chi| cvm | ks | pchi | runs] [<spectrum range>]
The fit statistic options are chi-squared (chi), C statistic (cstat), Loredo statistic (lstat), a statistic for Poisson data with assumed known background (pstat), a statistic for Poisson data with
Gaussian background (pgstat), and the Whittle statistic (whittle) for power density functions. If the statistic is given as whittle with a number appended (e.g. whittle5) then the statistic is appropriate for that number of power density functions averaged together. The test statistic options are
Anderson-Darling (ad), chi-squared (chi), Cramer-von Mises (cvm), Kolmogorov-Smirnov (ks),
Pearson chi-square (pchi) and Runs (runs). These statistics are described in the appendix on
Statistics in XSPEC. If a spectrum number or spectrum range is given, the chosen statistic will only apply to those spectra. It is therefore possible for a multi-spectrum fit to use more than one fit or test statistic. If no spectrum number or range is given, the chosen statistic will apply to all loaded spectra and will be the default statistic for any future loaded spectra.
Note that if the chosen statistic is not compatible with the currently used weight method, the
weight method will be changed to standard weighting until the conflict is removed.
Examples:
Assume 3 spectra are currently loaded, all using the chi-squared statistic, and that chi-squared is the default statistic.
XSPEC12>statistic cstat 2-3
// Spectrum 1 continues to use chi-sq, 2 and 3 use cstat.
XSPEC Models 157
XSPEC12>data 4 spec4.pha
// New spectrum 4 will use chi-sq.
XSPEC12>statistic cstat
// All 4 spectra now use cstat, cstat is the new default.
XSPEC12>data 5 spec5.pha
// New spectrum 5 will use cstat.
XSPEC12>statistic test ks
// All 4 spectra now use ks as the test statistic.
5.8.5 xsect: set the photoionization cross-sections
Change the photoelectric absorption cross-sections in use.
Syntax:
xsect
[bcmc|obcm|vern]
The three options are:
bcmc
, from Balucinska-Church & McCammon (1992; Ap.J.400,
699) with a new He cross-section based on (1998; Ap.J. 496, 1044); obcm
, as bcmc
but with the old
He cross-section, and, vern
, from Verneret. al. (1996 Ap.J.). This changes the cross-sections in use for all absorption models with the exception of
wabs
.
XSPEC Models 158
5.8.6 xset: set variables for XSPEC models.
Modify a number of XSPEC internal switches.
Syntax:
xset [abund | cosmo | delta | mdatadir | method | seed | statistic | weight | xsect | <string_name> ] [ <options> |
<string_value> ] xsect
The arguments abund, cosmo, method, statistic, weight, and
just run the appropriate XSPEC commands. mdatadir
changes the directory in which XSPEC searches for model data files. You probably don't want to change this.
The seed
option requires an integer argument, which will then be used to immediately re-seed and re-initialize XSPEC’s random-number generator.
The delta
option is for setting fit delta values (see the newpar command) which are proportional to the current parameter value rather than fixed. For example,
XSPEC12> xset delta .15 will set each parameter fit delta to .15 * parVal. To turn proportional deltas off and restore the original fixed deltas, set delta
to a negative value or 0.0. The current proportional delta setting can be seen with show control.
The
<string_name>
option can be used to pass string values to models.
XSPEC maintains a database of
<string_name>
,
<string_value>
pairs created using this command. Individual model functions can then access this database. Note that xset does no checking on whether the
<string_name>
is used by any model so spelling errors will not be trapped.
To access the
<string_name>
,
<string_value>
database from within a model function use the fortran function fgmstr
. This is defined as character*128
and takes a single argument, the string name as a character*128
. If the
<string_name> has not been set then a blank string will be returned.
The current
<string_name> options, models to which they apply and brief descriptions are given in the following table :
APECROOT apec, vapec, bapec, bvapec, equil, vequil, npshock, vnpshock, pshock, vpshock, sedov, vsedov, c6mekl, c6vmekl, c6pmekl, c6pvmekl, cemkl, cevmkl, mekal, vmekal, mkcflow, vmclow
Switch from default
APEC input files.
XSPEC Models 159
APECTHERMAL
APECVELOCITY
NEIAPECROOT
POW_EMIN, POW_EMAX gnei, nei, vgnei, nvei, equil, vequil, npshock, vnpshock, pshock, vpshock, sedov, vsedov
Switch from default
NEIAPEC input files. powerlaw, bknpower, bkn2pow, cutoffpl
Switch to normalize to a flux calculated over an energy range.
NEIVERS
CFLOW_VERSION
CFLOW_NTEMPS gnei, nei, vgnei, vnei, equil, vequil, npshock, vnpshock, pshock, vpshock, sedov, vsedov
Switch NEIAPEC version number. mkcflow, vmclow mkcflow, vmclow
Switch CFLOW version number.
Switch number of temperature bins used in
CFLOW model.
SUZPSF-IMAGE
SUZPSF-RA apec, vapec, bapec, bvapec, equil, vequil, npshock, vnpshock, pshock, vpshock, sedov, vsedov, c6mekl, c6vmekl, c6pmekl, c6pvmekl, cemkl, cevmkl, mekal, vmekal, mkcflow, vmclow
Thermally broaden emission lines in APEC input files. apec, vapec, bapec, bvapec, equil, vequil, npshock, vnpshock, pshock, vpshock, sedov, vsedov, c6mekl, c6vmekl, c6pmekl, c6pvmekl, cemkl, cevmkl, mekal, vmekal, mkcflow, vmclow
Velocity broaden emission lines in APEC input files. suzpsf suzpsf
Set image file to be used for surface brightness.
Set RA for center surface
XSPEC Models
SUZPSF-DEC suzpsf
SUZPSF-MIXFACT-IFILE# suzpsf
SUZSF-MIXFACT-OFILE# suzpsf
XMMPSF-IMAGE
XMMPSF-RA xmmpsf xmmpsf
XMMPSF-DEC xmmpsf
XMMPSF-MIXFACT-IFILE# xmmpsf
XMMPSF-MIXFACT-OFILE# xmmpsf
NSA_FILE
NSAGRAV_DIR
NSMAX_DIR
ZXIPCF_DIR nsa nsagrav nsmax zxipcf
160
brightness map which is taken from the WMAP.
Set Dec for center surface brightness map which is taken from the
WMAP.
Set filename to read mixing factors.
Set filename to write mixing factors.
Set image file to be used for surface brightness.
Set RA for center surface brightness map which is taken from the WMAP.
Set Dec for center surface brightness map which is taken from the
WMAP.
Set filename to read mixing factors.
Set filename to write mixing factors.
Change filename used for model data.
Change directory used for model data files.
Change directory used for model data files.
Change directory used
XSPEC Models 161
for model data files.
Examples:
XSPEC12>
xset neivers 2.0
// Set the NEIVERS variable to 2.0
XSPEC12>
xset
// List the current string variables
XSPEC12>
xset apecroot /foo/bar/apec_v1.01
// Set the APECROOT variable
XSPEC12> xset seed 1515151
// Re-initialize the pseudo random-number generator
// with the seed value 1515151
5.9 Tcl Scripts
The following Tcl scripts are auto-loaded when xspec starts up so can be used in the same ways as commands. Entering the name of the script without arguments will produce a short summary. The scripts themselves can be found in
$HEADAS/../spectral/scripts and can be used as the starting point for more complicated scripting of xspec.
5.9.1 lrt: likelihood ratio test between two models
Tcl script to perform a likelihood ratio test between two models.
Syntax: lrt
<niter> <model0_name> <model1_name> [<filename>]
Runs <niter>
simulations of datasets based on <model0_name>, calculates the likelihood ratio for <model1_name> relative to <model0_name> (calculated by the statistic for <model0_name> minus the statistic for <model1_name>), and outputs the fraction of iterations with the likelihood ratio smaller than that for the data. If the optional filename is given then the simulation results are written to the file. The first line of the file contains the results for the data, the other lines the simulations. Each line comprises the statistic values for <model0_name>, the statistic value for
<model1_name>, and the difference.
Before running this procedure you must have created command files called <model0_name>.xcm and <model1_name>.xcm which define the two models. A good way to do this is to set up the model then use save model to make the command file.
5.9.2 multifake: perform multiple fakeit iterations and save to file.
Tcl script to perform many iterations of fakeit and save the results in a FITS file.
Syntax:
multifake
<time> <niter> <outfile>
XSPEC Models 162
This script runs <niter> iterations of fakeit with an exposure of <time> and writes the results to
<outfile>. Before running this procedure you have read in one (and only one) dataset along with its response and optional background and arf files. You must also have defined the model.
The output file is a FITS binary table with the columns being the value fit for each parameter in each iteration. The final column is the statistic value for that iteration.
Note that if an error occurs during the fit of a faked spectrum then -999 is written for all parameters and the statistic value for that iteration.
5.9.3 rescalecov: rescale the covariance matrix.
Tcl script to rescale the entire covariance matrix used in the proposal chain command.
Syntax:
rescalecov
<scale>
Rescales the chain proposal distribution covariance matrix by the factor input as <scale>.
5.9.4 simftest: estimate the F-test probability for adding a component.
Tcl script to generate simulated datasets and use these to estimate the F-test probability for adding a model component.
Syntax: simftest
<model_comp> <niter> [<filename>]
This script runs <niter> sets of simulated datasets to estimate the F-test probability for adding the additional model component number <model_comp>. If <filename> is specified then passes this to lrt.tcl to save likelihood ratio simulation information. The first line of the file written contains the results for the data, the other lines for the simulations. Each line comprises the statistic value for the model without <model_comp>, that for the model with <model_comp>, and the difference.
Before running this script the model should be set up including the additional component to be tested. The script will create temporary files model_with_comp.xcm and model_without_comp.xcm.
5.9.5 writefits: write information about the current fit and errors to a FITS file.
Tcl script to dump a lot of useful information to a FITS file.
163
Syntax: writefits
<FITS filename>
This script writes filenames, free parameter values and errors to one row of a FITS file. The error command should have been run on all the free parameters before running this script. If the FITS file already exists then a new row is appended.
6. XSPEC V12 Models
6.1 Alphabetical Summary of Models
Model
Description absori
Ionized absorber.
Extra absorption due to contamination on the ACIS filters.
acisabs ascac
ASCA PSF mixing model.
apec, vapec, vvapec
APEC thermal plasma model.
atable
Additive table model.
bapec, bvapec, bvvapec bbody, zbbody bbodyrad bexrav bexriv bknpower bkn2pow bmc bremss, vbremss, zbremss c6mekl, c6pmkl, c6vmkl, c6vpmkl cabs cemekl, cevmkl cflow cflux compbb
Velocity broadened APEC thermal plasma model.
Blackbody spectrum, with redshift variant
Blackbody spectrum with norm proportional to surface area.
E-folded broken power-law reflected from neutral matter
E-folded broken power-law reflected from ionized matter
Broken powerlaw.
Three-segment broken powerlaw.
Comptonization by relativistically moving matter.
Thermal bremsstrahlung, with redshift variant.
6th-order Chebyshev polynomial DEM using mekal and variants
Compton scattering (non-relativistic)
Multi-temperature mekal.
Cooling flow model.
Calculate flux of other model components.
Comptonized blackbody spectrum after Nishimura et al. 1986.
164
Model
compLS compmag compPS compST comptb compTT constant cpflux cplinear cutoffpl cyclabs disk diskbb diskir diskline diskm disko diskpbb diskpn dust edge, zedge eplogpar eqpair, eqtherm,
165
Description
Comptonization spectrum after Lamb and Sanford 1979.
Thermal and bulk Comptonization for cylindrical accretion onto the polar cap of a magnetized neutron star.
Comptonization spectrum after Poutanen and Svenson 1986.
Comptonization spectrum after Sunyaev and Titarchuk 1980.
Thermal and bulk Comptonization of a seed blackbody-like spectrum.
Comptonization spectrum after Titarchuk 1994.
Energy-independent multiplicative factor.
Convolution model to calculate photon flux.
Non-physical model for low count background spectra.
Powerlaw with high energy exponential rolloff.
Cyclotron absorption line.
Disk model.
Multiple blackbody disk model.
Irradiated inner and outer disk.
Line emission from relativistic accretion disk.
Disk model with gas pressure viscosity.
Modified blackbody disk model.
Accretion disk with power-law T(r)
Accretion disk around a black hole.
Dust scattering out of the beam.
Absorption edge.
Log-parabolic blazar model with vFv normalization.
Paolo Coppi’s hybrid hot plasma emission models.
166
Model
compth equil, vequil etable expabs expdec expfac ezdiskbb gabs gadem, vgadem gauss, zgauss gnei, vgnei grad grbm gsmooth heilin highecut, zhighect hrefl ireflect kdblur kdblur2 kerrbb kerrconv kerrd
Description
Equilibrium ionization collisional plasma model from Borkowski.
Table model for exponential of -1 times the input.
Low-energy exponential rolloff.
Exponential decay
Exponential factor.
Multiple blackbody disk model with zero-torque inner boundary.
Gaussian absorption line.
Plasma emission, multi-temperature with gaussian distribution of emission measure.
Simple gaussian line profile.
Generalized single ionization NEI plasma model.
GR accretion disk around a black hole.
Gamma-ray burst model.
Gaussian smoothing with an energy dependent sigma.
Voigt absorption profiles for He I series.
High energy cutoff.
Simple reflection model good up to 15 keV.
Reflection from ionized material.
Convolve with the Laor model shape.
Convolve with the Laor2 model shape.
Multi-temperature blackbody model for thin accretion disk around a
Kerr black hole.
Accretion disk line shape with BH spin as free parameter.
Optically thick accretion disk around a Kerr black hole.
167 laor laor2 logpar
Model
kerrdisk
Description
Accretion disk line emission with BH spin as free parameter.
Line from accretion disk around a black hole.
Line from accretion disk with broken power-law emissivity around a black hole.
Log-parabolic blazar model.
Lorentzian line profile.
lorentz lsmooth lyman meka, vmeka mekal, vmekal
Lorentzian smoothing with an energy dependent sigma.
Voigt absorption profiles for H I or He II Lyman series.
Mewe-Gronenschild-Kaastra thermal plasma (1992).
Mewe-Kaastra-Liedahl thermal plasma (1995).
Cooling flow model based on mekal.
mkcflow, vmcflow mtable nei, vnei
Multiplicative table model.
Simple nonequilibrium ionization plasma model.
Notch line absorption.
notch npshock, vnpshock
Plane-parallel shock with ion and electron temperatures.
nsa
Neutron star with hydrogen atmosphere
nsagrav nsatmos nsmax nteea nthcomp optxagnf, optxagn partcov pcfabs, zpcfabs
Neutron star with hydrogen atmosphere for different g.
Neutron star H atmosphere with e- conduction and self-irradiation
Neutron star magnetic atmosphere.
Pair plasma model.
Thermally comptonized continuum.
Colour temperature corrected disc and energetically coupled
Comptonisation model for AGN.
Convert absorption model into a partial covering absorption.
Partial covering fraction absorption.
pegpwlw pexmon pexrav pexriv
Model
Description
Powerlaw with pegged normalization.
Neutral Compton reflection with self-consistent Fe and Ni lines.
Exponentially cut-off power-law reflected from neutral matter.
Exponentially cut-off power-law reflected from ionized matter.
phabs, vphabs, zphabs, zvphabs
Photo-electric absorption
pileup plabs
CCD pile-up model for Chandra
Absorption model with power-law dependence on energy.
plcabs
Cut-off powerlaw observed through dense, cold matter.
Positronium continuum.
posm powerlaw, zpowerlw
Simple photon power law.
projct pshock, vpshock
3-D to 2-D projection mixing model.
Constant temperature, plane-parallel shock plasma model.
Power-law distribution of neutral absorbers.
pwab raymond, vraymond
Raymond-Smith thermal plasma.
rdblur
Convolve with the diskline model shape.
recorn
Change correction norm for a spectrum (replaces old recornrm command).
redden redge reflect
IR/optical/UV extinction from Cardelli et al. (1989)
Recombination edge. reflection from neutral matter
refsch sedov, vsedov sirf simpl
E-folded power-law reflected from an ionized relativistic disk.
Sedov model with electron and ion temperatures.
Multi-blackbody self-irradiated funnel model.
Comptonization of a seed spectrum.
168
Model
smaug smedge spexpcut spline srcut sresc
SSSice step suzpsf swind1 tbabs, ztbabs, tbgrain, tbvarabs uvred varabs, zvarabs wabs, zwabs wndabs, zwndabs xion xmmpsf zashift zbabs zdust zigm zmshift zredden
169
Description
Model for an optically-thin, spherically-symmetric thermal plasma.
Smoothed absorption edge.
Super-exponential cutoff absorption.
Spline multiplicative factor.
Synchrotron radiation from cut-off electron distribution.
Synchrotron radiation from escape-limited electron distribution.
Einstein Observatory SSS ice absorption.
Step function convolved with gaussian.
Suzaku PSF mixing model.
Absorption by partially ionized material with large velocity shear.
Absorption due to the ISM including molecules and grains.
UV reddening.
Photoelectric absorption with variable abundances.
Photoelectric absorption (Morrison & McCammon).
Photoelectric absorption with low energy window.
The reflected spectrum from a photo-ionized accretion disk.
XMM PSF model
Redshift an additive model.
EUV ISM attenuation.
Extinction by dust grains (Pei, 1992).
UV/Optical attenuation by the intergalactic medium.
Redshift a multiplicative model.
Redshifted IR/optical/UV extinction from Cardelli et al. (1989)
170
Model
zsmdust zvfeabs zxipcf
Description
Extinction by dust grains in starburst galaxies.
Redshifted absorption with variable iron abundance.
Partial covering absorption by partially ionized material.
6.2 Additive Model Components (Sources)
This and the following sections contain information on specific, installed XSPEC models.
The parameters are given as par1, par2,, and norm, which is the normalization. Additive models represent sources of emission.
6.2.1 apec, vapec, vvapec: APEC emission spectrum
An emission spectrum from collisionally-ionized diffuse gas calculated using the ATOMDB code v2.0.2. More information can be found at
http://atomdb.org/
which should be consulted by anyone running this model. This default version number can be changed by modifiying the
ATOMDB_VERSION string in your Xspec.init file.
By default this model reads atomic physics continuum and line data from the files apec_v[version]_coco.fits and apec_v[version]_line.fits in the $HEADAS/../spectral/modelData directory. Different files can be specified by using the command xset APECROOT. There are three options. APECROOT can be set to a version number (eg 1.10, 1.2.0, 1.3.1, 2.0.1). In this case the value of APECROOT will be used to replace 2.0.2 in the name of the standard files and the resulting files will be assumed to be in the modelData directory. Alternatively, a filename root (eg apec_v1.2.0
) can be given. This root will be used as a prefix for the
_coco.fits
and
_line.fits files. Finally, if neither of these work then the model will assume that the
APECROOT value gives the complete directory path, e.g.
XSPEC12> xset APECROOT /foo/bar/apec_v1.2.0 will use the input files
/foo/bar/apec_v1.2.0_coco.fits
/foo/bar/apec_v1.2.0_line.fits
.
Thermal broadening of lines can be included by using: xset APECTHERMAL yes. This runs significantly slower than the option without thermal broadening so you should only use this when necessary. Velocity broadening of lines can be included by using: xset APECVELOCITY
<velocity>, where <velocity> is sigma in km/s. This is added in Gaussian quadrature with any thermal broadening in use.
171
The apec model uses abundances set by the abund command. The vapec and vvapec variants allow the user to set the abundance using additional parameters. For apec and vapec the abundances of the trace elements (ie Li, Be, B, F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, Zn) can be set using xset APEC_TRACE_ABUND. These trace element abundances can be set either to the abundance of one of the main elements or to a numerical value (relative to Solar). For instance,
XSPEC12> xset APEC_TRACE_ABUND Fe sets trace element abundances to that of iron while
XSPEC12> xset APEC_TRACE_ABUND 1.0 sets them to Solar. The default value for APEC_TRACE_ABUND is 1.0. Note that this means that the apec and vapec models will show emission lines even if the abundance parameters are set to zero.
For the apec model the parameters are: par1 plasma temperature, keV par2
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni.
Relative abundances are set by the abund command. The trace element abundances are from xset
APEC_TRACE_ABUND, the default is 1.0. norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
and
n
H
are the electron and H densities (cm
-3
)
For the vapec variant the parameters are as follows. par1 par2par14 plasma temperature, keV
Abundances for He, C, N, O, Ne, Mg,Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command). The trace element abundances are from xset APEC_TRACE_ABUND, the default is 1.0.
172
norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
and
n
H
are the electron and H densities (cm
-3
)
For the vvapec variant the parameters are as follows.
Par1 plasma temperature, keV par2par31
Abundances for H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al,
Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn wrt Solar (defined by the abund command) norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
densities (cm
-3
)
and
n
H
are the electron and H
6.2.2 atable: tabulated additive model
An additive table model component. The filename to be used must be given immediately after atable
in the model command. For example
model atable{mymod.mod} uses mymod.mod
as the input for the model. For specifications of the table model file, see the
OGIP memo 92-009 on the FITS file format for table model files (available on the WWW or by anonymous ftp from
ftp://legacy.gsfc.nasa.gov/caldb/docs/memos
. Example additive table model files are mekal.mod
and raysmith.mod in
$HEADAS/../spectral/modelData
and testpo.mod
in
$HEADAS/../spectral/session
.
Any number of tabulated model components (additive, multiplicative or exponential) may be used simultaneously.
173
6.2.3 bapec, bvapec, bvvapec: velocity broadened APEC thermal plasma model
A velocity- and thermally-broadened emission spectrum from collisionally-ionized diffuse gas calculated using the ATOMDB code v2.0.2. More information can be found at
http://atomdb.org/
which should be consulted by anyone running this model. This default version number can be changed by modifiying the ATOMDB_VERSION string in your Xspec.init file.
By default this model reads atomic physics continuum and line data from apec_v[version]_coco.fits and apec_v[version]_line.fits in the $HEADAS/../spectral/modelData directory. Different files can be specified by using the command xset APECROOT. There are three options. APECROOT can be set to a version number (eg 1.10, 1.2.0, 1.3.1, 2.0.1). In this case the value of APECROOT will be used to replace 2.0.2 in the name of the standard files and the resulting files will be assumed to be in the modelData directory. Alternatively, a filename root (eg apec_v1.2.0
) can be given. This root will be used as a prefix for the
_coco.fits
and
_line.fits files. Finally, if neither of these work then the model will assume that the
APECROOT value gives the complete directory path, e.g.
XSPEC12> xset APECROOT /foo/bar/apec_v1.2.0
will use the input files
/foo/bar/apec_v1.2.0_coco.fits
/foo/bar/apec_v1.2.0_line.fits
.
The bapec model uses abundances set by the abund command. The bvapec and bvvapec variants allow the user to set the abundance using additional parameters. For bapec and bvapec the abundances of the trace elements (ie Li, Be, B, F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, Zn) can be set using xset APEC_TRACE_ABUND. These trace element abundances can be set either to the abundance of one of the main elements or to a numerical value (relative to Solar). For instance,
XSPEC12> xset APEC_TRACE_ABUND Fe sets trace element abundances to that of iron while
XSPEC12> xset APEC_TRACE_ABUND 1.0 sets them to Solar.
For the vapec model the parameters are: par1 Plasma temperature, keV
par2
Metal abundances (He fixed at cosmic). The elements included are C,
N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Relative abundances are set by the abund command.
174
par4 Gaussian sigma for velocity broadening (km/s) norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
and
n
H
are the electron and H densities (cm
-3
)
For the bvapec variant the parameters are as follows. par1 plasma temperature, keV par2-par14
Abundances for He, C, N, O, Ne, Mg,Al, Si, S, Ar, Ca, Fe, Ni wrt
Solar (defined by the abund command) par16 Gaussian sigma for velocity broadening (km/s) norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
and
n
H
are the electron and H densities (cm
-3
)
For the bvvapec variant the parameters are as follows. par1 plasma temperature, keV par2-par31
Abundances for H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P,
S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn wrt Solar
(defined by the abund command)
Par33 Gaussian sigma for velocity broadening (km/s)
175
norm
4
10
14
D
A
(1
z
)
2
,where
D
A
is the angular diameter distance to the source (cm),
n e
and
n
H
are the electron and H densities (cm
-3
)
6.2.4 bbody, zbbody: blackbody
A blackbody spectrum.
K
8.0525
(
kT
) exp
1
where par1= kT temperature norm= K
L
39
D
2
10
, where L is the source luminosity in units of 10
D
10
is the distance to the source in units of 10 kpc
39
ergs
-1
,
The zbbody variant allows an additional (fixed) redshift parameter
A
(
E
)
( 1
8 .
z
)
0525
K kT
4
exp
E
( 1
E
( 1
z
)
2
z
)
dE kT
1
where par1= kT temperature
z
Fixed redshift norm= K
L
39
( 1
z
2
, where L is the source luminosity in units of 10
39
D
10
) ergs
-1
,
D
10
is the distance to the source in units of 10 kpc
6.2.5 bbodyrad: blackbody spectrum, area normalized
A blackbody spectrum with normalization proportional to the surface area.
K
exp
3
E dE
1
176
norm, K
R
2
km
D
2
10
, where
R km
is the source radius in km, and, distance to the source in units of 10 kpc
D
10
is the
6.2.6 bexrav: reflected e-folded broken power law, neutral medium
A broken power-law spectrum multiplied by exponential high-energy cutoff,
exp(-E/E c
), and reflected from neutral material. See Magdziarz & Zdziarski 1995, MNRAS, 273, 837 for details.
The output spectrum is the sum of an e-folded broken power law and the reflection component. The reflection component alone can be obtained for
rel
refl
0
Then the actual reflection normalization is |
rel
refl
|. Note that you need to change then the limits of
rel
refl
excluding zero (as then the direct component appears). If
E c
= 0, there is no cutoff in the power law. The metal and iron abundance are variable with respect to those set by the command abund. The opacities are those set by the command xsect. As expected in AGNs, H and He are assumed to be fully ionized.
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached.
The precision can be changed by setting BEXRAV_PRECISION eg xset
BEXRAV_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1
1
, first power law photon index par2 par3 par4
Ebreak, break energy (keV)
2
, second power law photon index
Ec, the e-folding energy in keV (if
E c
= 0 there is no cutoff)
par5
177
relrefl, reflection scaling factor (1 for isotropic source above disk) par7 par8 par9 norm abundance of elements heavier than He relative to the solar abundances iron abundance relative to the above cosine of inclination angle photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame.}
6.2.7 bexriv: reflected e-folded broken power law, ionized medium
Broken power-law spectrum multiplied by exponential high-energy cutoff,
exp(-E/E c
), and reflected from ionized material. See Magdziarz & Zdziarski 1995, MNRAS, 273, 837 for details. Ionization and opacities of the reflecting medium is computed as in the absori model. The output spectrum is the sum of an e-folded broken power law and the reflection component. The reflection component alone can be obtained for
rel
refl
0
rel
refl
0 that you need to change then the limits of
rel
refl
0 appears). If
E c
= 0, there is no cutoff in the power law. The metal and iron abundances are variable with respect to those set by the command abund.
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached. The precision can be changed by setting BEXRIV_PRECISION eg xset BEXRIV_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1
1
, first power law photon index par2 par3 par4 par5
E
break
, break energy (keV)
2
, second power law photon index
E
c
, the e-folding energy in keV (if
E c
= 0 there is no cutoff)
rel
refl
, reflection scaling factor (1 for isotropic source above disk) par7 abundance of elements heavier than He relative to the solar abundances
par8 par9 iron abundance relative to the above cosine of inclination angle
178
par11 norm disk ionization parameter,
n
, where F ion
is the 5eV–20 keV irradiating flux, n is the density of the reflector; see Done et al., 1992, ApJ,
395, 275}
ion photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame.}
6.2.8 bknpower: broken power law
A broken power law.
KE
1
E
E break
KE
break
1
(
E
1keV
)
2
E
E break where: par1 =
1 power law photon index for E < E break par2
=E
break par3=
2 break point for the energy in keV power law photon index for E > E break
-1
at 1 keV}
If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10
-12
ergs cm
-2
s
-1
over the energy range (POW_EMIN, POW_EMAX) keV unless POW_EMIN = POW_EMAX in which case the norm becomes the flux density in micro-
Jansky at POW_EMIN keV. In these cases it is important that POW_EMIN and POW_EMAX lie within the energy range on which the model is being evaluated.
6.2.9 bkn2pow: broken power law, 2 break energies
A three-segment broken power law (ie with two break energies).
( )
KE
1
E
E break,1
179
KE
break,1
1
(
E
1keV
)
2
KE
E
2 break,1 break,2
(
E
1keV
)
3
E
E
break,1 break,2
≤ E ≤ E
≤ E
where : par1
=
1 power law photon index for E < E break,1 par2
=E
break,1 first break point for the energy, keV par3
=
2 power law photon index for
E
break,1
< E < E break,2 par4
=E
break,2 second break point for the energy, keV break,2 par5 =
3 power law photon index for E > E
Norm =K photons keV
-1 cm
-2 s
-1
at 1 keV break,2
If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10
-12
ergs cm
-2
s
-1
over the energy range (POW_EMIN, POW_EMAX) keV unless POW_EMIN = POW_EMAX in which case the norm becomes the flux density in micro-
Jansky at POW_EMIN keV. In these cases it is important that POW_EMIN and POW_EMAX lie within the energy range on which the model is being evaluated.
6.2.10 bmc: Comptonization by relativistic matter
This is an analytic model describing Comptonization of soft photons by matter undergoing relativistic bulk-motion. The typical scenario involves thermal X-rays from the inner region of an accretion disk in a black-hole binary illuminating in-falling matter in close proximity to the blackhole event horizon. For a detailed description of the model, refer to Titarchuk, Mastichiadis &
Kylafis 1997, ApJ, 487, 834; Titarchuk & Zannias, 1998, ApJ, 493, 863; Laurent & Titarchuk
1999, ApJ, 511, 289; Zannias, Borozdin, Revnivtsev., Trudolyubov, Shrader, & Titarchuk, 1999,
ApJ, 517, 367; or Shrader & Titarchuk 1999, ApJ 521, L21. The model parameters are the characteristic black-body temperature of the soft photon source, a spectral (energy) index, and an illumination parameter characterizing the fractional illumination of the bulk-motion flow by the thermal photon source. It must be emphasized that this model is not an additive combination of power law and thermal sources, rather it represents a self-consistent convolution. The bulk-motion up-scattering and Compton recoil combine to produce the hard spectral tail, which combined with the thermal source results in the canonical high-soft-state spectrum of black hole accretion. The position of the sharp high energy cutoff (due to recoil) can be determined using the theta function
180
E
c
E
. The model can also be used for the general Comptonization case when the energy range is limited from above by the plasma temperature (see compTT and compST). par1 Temperature of thermal photon source in keV. par2 par3
Energy spectral index alpha.
Log of the A parameter. Note that f in Borozdin et al. 1999 and Shrader
& Titarchuk 1999 is 10 par3 norm
A
N
defined in Borozdin et al 1999 and Shrader & Titarchuk (1999)
6.2.11 bremss, vbremss, zbremss: thermal bremsstrahlung
A thermal bremsstrahlung spectrum based on the Kellogg, Baldwin & Koch (ApJ 199, 299) polynomial fits to the Karzas & Latter (ApJS 6, 167) numerical values. A routine from Kurucz
(private communication) is used in at low temperature end. The He abundance is assumed to be 8.5
% of H by number.
Choice of fixed redshift is allowed by using zbremss variant
Choice of Hydrogen to Helium abundance ratio is allowed by using the vbremss variant.
The parameter settings are thus:
For bremss: par1 plasma temperature in keV norm
15
4
D
2
, where D is the distance to the source (cm) and are the electron and ion densities (cm
-3
)
n
e
,
n
I
For zbremss: par1 par2 = z norm plasma temperature in keV redshift
4
D
2
15
, where D is the distance to the source (cm) and
n
e
,
n
I
181
are the electron and ion densities (cm
-3
)
For vbremss: par1 par2 norm plasma temperature in keV
n(He)/n(H) (note that the Solar ratio is 0.085)
15
4
D
2
, where D is the distance to the source (cm) and are the electron and ion densities (cm
-3
)
n
e
,
n
I
6.2.12 c6mekl, c6vmekl, c6pmekl, c6pvmkl: differential emission measure using Chebyshev representations with multi-temperature mekal
c6mekl is a multi-temperature mekal model using sixth-order Chebyshev polynomial for the differential emission measure. The DEM is not constrained to be positive.. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al. (1996, ApJ, 456,
766).
c6pmekl differs by using the exponential of the 6 th
order Chebyshev polynomial
c6mekl
and c6pmekl use abundances relative to the Solar abundances set by the abund command
The variants c6vmkl and c6pvmkl with polynomial and exponential polynomial respectively allow the user to specify 14 elemental abundance.
For c6mekl and c6pmkl the parameters are: par1-6 par7 par8
Chebyshev polynomial coefficients
H density (cm
-3
)
abundance wrt to Solar par10
0 calculate
1 interpolate
2 interpolate using APEC model norm Normalization
While for c6vmkl and
c6vpmkl
the parameters are: par1-6 par7 par8-21
Chebyshev polynomial coefficients
H density (cm
-3
)
Abundances of He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
182
par23
0 calculate
1 interpolate
2 interpolate using APEC model norm Normalization
6.2.13 cemekl, cevmkl: plasma emission, multi-temperature using mekal
A multi-temperature plasma emission model built from the mekal code. Emission measures follow a power-law in temperature (d
EM = (T/T
max
)
d
T/T max
).The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.
For the cemekl version, the abundance ratios are set by the abund command. The cevmkl variant allows the user to define the abundances.
The parameters for cemekl are: par1=
index for power-law emissivity function par2=
T max
par3 par4 maximum temperature
n
H
(cm
-3
) abundance relative to solar
par6
0 calculate
1 interpolate
2 interpolate using APEC model norm Normalization
For the cevmkl variant the parameters are: par1 index for power-law emissivity function par3 par4-17
n
H
(cm
-3
) abundance relative to solar Abundances for He, C, N, O, Ne, Na,
Mg, Al, Si, S,Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
183
par19
0 calculate
1 interpolate
2 interpolate using APEC model norm Normalization
6.2.14 cflow: cooling flow
A cooling flow model after Mushotzky & Szymkowiak ( Cooling Flows in Clusters and Galaxies, ed. Fabian, 1988). An index of zero for the power-law emissivity function corresponds to emission measure weighted by the inverse of the bolometric luminosity at that temperature. The model assumes
H
0
50 and
q
0
0 par1 par2 index for power-law emissivity function low temperature (keV)
184
par4 abundance relative Solar norm Mass accretion rate (solar mass/yr)
6.2.15 compbb: Comptonization, black body
Comptonized blackbody model by Nishimura, Mitsuda and Itoh, 1986, PASJ, 38, 819. The electron temperature should normally be kept fixed since the Compton y parameter is the product of the electron temperature and optical depth. par1 blackbody temperature (keV) electron temperature of the hot plasma (keV) par2 par3 norm optical depth of the plasma
L
39
D
10
2
, where
L
39
is the source luminosity in units of
10
39
ergs
-1
and
D
10
is the distance to the source in units of 10 kpc (the same definition used for the bbodyrad model)
6.2.16 compLS: Comptonization, Lamb & Sanford
A Comptonization spectrum after Lamb and Sanford, 1979, M.N.R.A.S, 288, 555. This model calculates the self-Comptonization of a bremsstrahlung emission from an optically thick spherical plasma cloud with a given optical depth and temperature. It was popular for Sco X-1. norm normalization
185
6.2.17 compmag: Thermal and bulk Comptonization for cylindrical accretion onto the polar cap of a magnetized neutron star
This model describes the spectral formation in the accretion column onto the polar cap of a magnetized neutron star, with both thermal and bulk Comptonization processes taken into account. The details for the method adopted for the numerical solution of the radiative transfer equation are reported in
Farinelli et al. (2012, A&A, 538, A67)
.
This model can be used for spectral fitting of both accreting X-ray pulsars and Supergiant
Fast X-ray Trasients. par1 kT bb
, temperature of the seed blackbody spectrum (keV). par2 kT e
, electron temperature of the accretion column (keV). par3 τ, vertical optical depth of the accretion column, with electron cross-section equal to 10 section.
-3
of the Thomson crosspar4 par5
η, index of the velocity profile when the accretion velocity increases towards the neutron star (valid when par8=1).
β
0
, terminal velocity of the accreting matter at the neutron star surface (valid when par8=1). par6 r
0
, radius of the accretion column in units of the neutron star
Schwarzschild radius. par7 A, albedo at the neutron star surface. par8 Flag for setting the velocity profile of the accretion column
if = 1 β(z)=A (Z s
/Z)
if = 2 β(τ)=-α τ
-η
, where A=β
0
(Z
0
/Z s
)
η norm R
2 km
/D
2
10
, where R km
and D
10
are the accretion column radius in km and the source distance in units of 10 kpc, respectively.
6.2.18 compPS: Comptonization, Poutanen & Svenson
Comptonization spectra computed for different geometries using exact numerical solution of the radiative transfer equation. The computational "iterative scattering method" is similar to the standard Lambda-iteration and is described in Poutanen J., Svensson R., 1996, ApJ, 470, 249
186
(PS96). The Compton scattering kernel is the exact one as derived by Jones F. C., 1968, Phys.
Rev., 167, 1159 (see PS96 for references).
Comptonization spectra depend on the geometry (slab, sphere, hemisphere, cylinder),
Thomson optical depth tau, parameters of the electron distribution, spectral distribution of soft seed photons, the way seed soft photons are injected to the electron cloud, and the inclination angle of the observer.
The resulting spectrum is reflected from the cool medium according to the computational method of Magdziarz & Zdziarski (1995) (see reflect, pexrav, pexriv models). rel_refl is the solid angle of the cold material visible from the Comptonizing source (in units 2 pi), other parameters determine the abundances and ionization state of reflecting material (Fe_ab_re, Me_ab, xi, Tdisk).
The reflected spectrum is smeared out by rotation of the disk due to special and general relativistic effects using "diskline"-type kernel (with parameters Betor10, Rin, Rout).
Electron distribution function can be Maxwellian, power-law, cutoff Maxwellian, or hybrid
(with low temperature Maxwellian plus a power-law tail).
Possible geometries include plane-parallel slab, cylinder (described by the height-to-radius ratio H/R), sphere, or hemisphere. By default the lower boundary of the "cloud" (not for spherical geometry) is fully absorbive (e.g. cold disk). However, by varying covering factor parameter cov_fac, it may be made transparent for radiation. In that case, photons from the "upper" cloud can also be upscattered in the "lower" cloud below the disk. This geometry is that for an accretion disk with cold cloudlets in the central plane (Zdziarski, Poutanen, et al. 1998, MNRAS, 301, 435). For cylinder and hemisphere geometries, an approximate solution is obtained by averaging specific intensities over horizontal layers (see PS96). For slab and sphere geometries, no approximation is made.
The seed photons can be injected to the electron cloud either isotropically and homogeneously through out the cloud, or at the bottom of the slab, cylinder, hemisphere or center of the sphere (or from the central plane of the slab if cov_frac ne 1). For the sphere, there exist a possibility (IGEOM=-5) for photon injection according to the eigenfunction of the diffusion equation sin (pi*tau'/tau)/(pi*tau'/tau), where tau' is the optical depth measured from the center (see
Sunyaev & Titarchuk 1980).
Seed photons can be black body (bbodyrad) for Tbb>0 or multicolor disk (diskbb) for
Tbb<0. The normalization of the model also follows those models: (1) Tbb>0, K = (RKM)**2
/(D10)**2, where D10 is the distance in units of 10 kpc and RKM is the source radius in km; (2)
Tbb<0 K = (RKM)**2 /(D10)**2 cos(theta), where theta is the inclination angle.
Thomson optical depth of the cloud is not always good parameter to fit. Instead the
Compton parameter y=4 * tau * Theta (where Theta= Te (keV) / 511 ) can be used. Parameter y is directly related to the spectral index and therefore is much more stable in fitting procedure. The fitting can be done taking 6th parameter negative, and optical depth then can be obtained via tau= y/(4* Te / 511).
The region of parameter space where the numerical method produces reasonable results is constrained as follows : 1) Electron temperature Te > 10 keV; 2) Thomson optical depth tau < 1.5 for slab geometry and tau < 3, for other geometries.
In versions 4.0 and above the Compton reflection is done by a call to the ireflct model code and the relativistic blurring by a call to rdblur. This does introduce some changes in the spectrum
187
from earlier versions. For the case of a neutral reflector (i.e. the ionization parameter is zero) more accurate opacities are calculated. For the case of an ionized reflector the old version assumed that for the purposes of calculating opacities the input spectrum was a power-law (with index based on the 2-10 keV spectrum). The new version uses the actual input spectrum, which is usually not a power law, giving different opacities for a given ionization parameter and disk temperature. The
Greens' function integration required for the Compton reflection calculation is performed to an accuracy of 0.01 (i.e. 1%). This can be changed using e.g. xset COMPPS_PRECISION 0.05.
The model parameters are as follows :
par1 = Te, electron temperature in keV
par2 = p, electron power-law index [ N(gamma)=gamma^-p ]
par3 = gmin, minimum Lorentz factor gamma
par4 = gmax, maximum Lorentz factor gamma
(a) if any of gmin or gmax < 1 then Maxwellian electron
distribution with parameter Te
(b) if Te=0. then power-law electrons with parameters p,
gmin, gmax
(c) if both gmin,gmax>=1 but gmax<gmin then cutoff Maxwellian
with Te, p, gmin (cutoff Lorentz factor) as parameters
(d) if Te.ne.0, gmin, gmax >=1 then hybrid electron distribution
with parameters Te, p, gmin, gmax
par5 = Tbb, temperature of soft photons
Tbb>0 blackbody
Tbb<0 multicolor disk with inner disk temperature Tbb
par6 = if > 0 : tau, vertical optical depth of the corona
if < 0 : y = 4*Theta*tau
limits: for the slab geometry - tau < 1
if say tau~2 increase MAXTAU to 50
for sphere - tau < 3
par7 = geom, 0 - approximate treatment of radiative transfer using
escape probability for a sphere (very fast method); 1 - slab;
2 - cylinder; 3 - hemisphere; 4,5 - sphere
input photons at the bottom of the slab, cylinder, hemisphere
or center of the sphere (or from the central plane of the slab
if cov_fact not 1). if < 0 then geometry defined by |geom| and
sources of incident photons are isotropic and homogeneous.
-5 - sphere with the source of photons distributed according to
the eigenfunction of the diffusion equation
f(tau')=sim(pi*tau'/tau)/(pi*tau'/tau) where tau' varies between
0 and tau.
par8 = H/R for cylinder geometry only
par9 = cosIncl, cosine of inclination angle
(if < 0 then only black body)
par10 = cov_fac, covering factor of cold clouds
if geom =+/- 4,5 then cov_fac is dummy
par11 = R, amount of reflection Omega/(2*pi)
(if R < 0 then only reflection component)
par12 = FeAb, iron abundance in units of solar
par13 = MeAb, abundance of heavy elements in units of solar
par14 = xi, disk ionization parameter L/(nR^2)
par15 = temp, disk temperature for reflection in K
par16 = beta, reflection emissivity law (r^beta)
if beta=-10 then non-rotating disk
if beta=10 then 1.-sqrt(6./rg))/rg**3
par17 = Rin/Rg, inner radius of the disk (Schwarzschild units)
par18 = Rout/Rg, outer radius of the disk
par19 = redshift
6.2.19 compST: Comptonization, Sunyaev & Titarchuk
A Comptonization spectrum after Sunyaev and Titarchuk 1980, A&A, 86, 121. This model is the
Comptonization of cool photons on hot electrons.
188
norm
Nf
4
d
2
, where N is the total number of photons from the source, d is the
189
(
3)
y z
distance to the source, and f is the factor
(2
z
z
. z is the spectral index, y is the injected photon energy in units of the temperature, and
is the incomplete gamma function.
190
6.2.20 comptb: Thermal and bulk Comptonization of a seed blackbody-like spectrum.
This model describes the Comptonization spectrum of soft photons off electrons which are either purely thermal or additionally subjected to an inward bulk motion. It consists of two components: one is the direct seed photon spectrum and the other one is the
Comptonizated spectrum. The latter is obtained as a self-consistent convolution of the seed photon spectrum with the system Green's function.
The model is not specific to bulk Comptonization but it includes in a coherent way different spectral shapes such as simple blackbody (i.e. neither thermal nor bulk
Comptonization), thermal Comptonization (equivalent to compTT) and thermal plus bulk
Comptonization. In the latter case, it can be considered a completion and update of the
BMC model, as it includes the cut-off term in the spectrum.
All mathematical details of the model and its validity limits for applications are reported in
Farinelli et al. (2008, ApJ, 680, 602)
. par1 kT s
, temperature of the seed photons (keV). par2 gamma, index of the seed photon spectrum (default gamma=3). par3 par4 alpha, energy index of the Comptonization spectrum. delta, bulk parameter, efficiency of bulk over thermal
Comptonization. par5 kT e
, temperature of the electrons (keV). par6 norm log(A), log of the illuminating factor parameter (A).
Normalization of the seed photon spectrum, defined in the same way as the bbody model.
6.2.21 compTT: Comptonization, Titarchuk
This is an analytic model describing Comptonization of soft photons in a hot plasma, developed by
L. Titarchuk (see ApJ, 434, 313). This replaces the Sunyaev-Titarchuk Comptonization model in the sense that the theory is extended to include relativistic effects. Also, the approximations used in the model work well for both the optically thin and thick regimes. The Comptonized spectrum is determined completely by the plasma temperature and the so-called
parameter which is independent of geometry. The optical depth is then determined as a function of
for a given
191
geometry. Thus par5 switches between spherical and disk geometries so that
is not a direct input here. This parameter MUST be frozen. If par5
0 using analytic approximation (e.g. Titarchuk 1994). If par5
< 0 and 0.1 <
< 10$, is obtained by interpolation from a set of accurately calculated pairs of
and from Sunyaev & Titarchuk
1985 (A&A 143, 374).
In this incarnation of the model, the soft photon input spectrum is a Wien law [
x e
x
photons] because this lends itself to a particularly simple analytical form of the model. For present
X-ray detectors this should be adequate. Note that in energy flux space the peak of the Wien law occurs at 3kT as opposed to 2.8kT for a blackbody. The plasma temperature may range from 2-500 keV, but the model is not valid for simultaneously low temperatures and low optical depth, or for high temperatures and high optical depth. The user is strongly urged to read the following references (esp. HT95 Fig 7) before and after using this model in order to fully understand and appreciate the physical assumptions made:
Titarchuk, L., 1994, ApJ, 434, 313; Hua, X-M., Titarchuk, L., 1995, ApJ, 449, 188;
Titarchuk, L., Lyubarskij, Y., 1995, ApJ, 450, 876. par2 par3 par4 par5
Input soft photon (Wien) temperature (keV)
Plasma temperature (keV)
Plasma optical depth par5
Geometry switch. (sign denotes approximation technique, magnitude determines geometry)
1 disk
>1 sphere
< 0 use analytic approx for
vs
vs. from interpolation norm normalization
6.2.22 cplinear: a non-physical piecewise-linear model for low count background spectra.
This is a simple non-physical model for low-count background spectra, used by fitting scripts in the
ACIS Extract (AE) package. Using this model outside the context of the AE package should be done with extreme caution since it requires a choice on vertex energies and number of segments.
AE places the first and last vertices at the lowest and highest energy of the background counts.
192
Intermediate vertices are placed at energies where a background count exists such that each segment covers a similar number of background counts. Any results using this model should cite
Broos et al. (2010).
Note that if all the rate parameters in use are thawed then the norm parameter is degenerate and must be frozen. Freezing one of the rate parameters will not work because if that vertex is driven to zero in the fit then the norm will be zero and the other rate parameters infinite. par1 par2 energy00 (keV) energy01 (keV) par3 par4 energy02 (keV) energy03 (keV) par5 par6 par7 par8 par9 par10 energy04 (keV) energy05 (keV) energy06 (keV) energy07 (keV) energy08 (keV) energy09 (keV) par11 log_rate00 par12 log_rate01 par13 log_rate02 par14 log_rate03 par15 log_rate04 par16 log_rate05 par17 log_rate06 par18 log_rate07 par19 log_rate08 par10 log_rate09
193
norm
6.2.23 cutoffpl: power law, high energy exponential cutoff
A power law with high energy exponential rolloff.
( )
KE
exp par1 =
power law photon index par2 =
e-folding energy of exponential rolloff (in keV) norm =
K
Photons keV
-1 cm
-2 s
-1
at 1 keV
If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10
-12
ergs cm
-2
s
-1
over the energy range (POW_EMIN, POW_EMAX) keV unless POW_EMIN = POW_EMAX in which case the norm becomes the flux density in micro-
Jansky at POW_EMIN keV. In these cases it is important that POW_EMIN and POW_EMAX lie within the energy range on which the model is being evaluated.
6.2.24 disk: accretion disk, black body
The spectrum from an accretion disk, where the opacities are dominated by free-free absorption, i.e., the so-called blackbody disk model. Not correct for a disk around a neutron star. par1 par2 par3 norm accretion rate in Eddington Luminosities central mass in solar mass units inner disk radius in gravitational (= 3 Schwarzschild radii)
2
where i is the inclination of the disk and d is the distance in units of 10 kpc
6.2.25 diskbb: accretion disk, multi-black body components
The spectrum from an accretion disk consisting of multiple blackbody components. For example, see Mitsuda et al., PASJ, 36, 741, (1984), Makishima et al., ApJ 308, 635, (1986).
194
norm
D
10
kpc
2 cos
, where
R
in
is “an apparent” inner disk radius,
D the distance to the source, and θ the angle of the disk (θ = 0 is face-on).
On the correction factor between the apparent inner disk radius and the realistic radius, see e.g., Kubota et al. 1998, PASJ, 50, 667.
6.2.26 Diskir: Irradiated inner and outer disk
The inner disk can be irradiated by the Compton tail. This can substantially change the inner disk temperature structure from that expected from an unilluminated disk in the limit where the ratio of luminosity in the tail to that in the disk, Lc/Ld>>1.
This is generally the case in the low/hard state of accreting black holes, and neglecting this effect leads to an underestimate of the inner disk radius (Gierlinski, Done & Page
2008a MNRAS, 388, 753).
The irradiated inner disk and Compton tail can illuminate the rest of the disk, and a fraction f_out of the bolometric flux is thermalized to the local blackbody temperature at each radius. This reprocessed flux generally dominates the optical and UV bandpass of
LMXBs (Gierlinski, Done & Page 2008b MNRAS, submitted). par1 = kT_disk, innermost temperature of the UNILLUMINATED disk par2 = Gamma, asymptotic power-law photon index par3 = kT_e, electon temperature (high energy rollover) par4 = Lc/Ld, ratio of luminosity in the Compton tail to that of the
UNILLUMINATED disk par5 = fin, fraction of luminosity in the Compton tail which is thermalized in the inner disk (generally fix at 0.1 as appropriate for an albedo of 0.3 and solid angle of 0.3) par6 = rirr, radius of the Compton illuminated disk in terms of the inner disk radius par7 = fout, fraction of bolometric flux which is thermalized in the outer disk par8 = logrout, log10 of the outer disk radius in terms of the inner disk radius
K = normalization, as in diskbb
6.2.27 diskline: accretion disk line emission, relativistic
A line emission from a relativistic accretion disk. See Fabian et al., MNRAS 238, 729.
Setting par2
to 10 is the special case of the accretion disk emissivity law
1
6 /
R
R
3
.
195
par2 par3 par4 power law dependence of emissivity. If this parameter is 10 or greater then the accretion disk emissivity law
1
6 /
R
R
3
is used. Otherwise the emissivity scales as Rpar2 inner radius (units of outer radius (units of norm photon cm-2 s-1 in the spectrum
6.2.28 diskm: accretion disk with gas pressure viscosity
A disk model with gas pressure viscosity. The spectrum from an accretion disk where the viscosity scales as the gas pressure. From Stella and Rosner 1984, ApJ, 277,
312. par1 par2 par3 accretion rate in Eddington Luminosities central mass in solar mass units inner disk radius in gravitational (= 3 Schwarzschild radii) par4 viscosity norm
2
where i is the inclination of the disk and d is the distance in units of 10 kpc
6.2.29 disko: accretion disk, inner, radiation pressure viscosity
A modified blackbody disk model. The spectrum from the inner region of an accretion disk where the viscosity is dominated by radiation pressure. par1 accretion rate in Eddington Luminosities
196
par2 par3 central mass in solar mass units inner disk radius in gravitational (= 3 Schwarzschild radii) par4 viscosity norm
2
where i is the inclination of the disk and d is the distance in units of 10 kpc
6.2.30 diskpbb: accretion disk, power-law dependence for T(r)
A multiple blackbody disk model where local disk temperature T(r) is proportional to r
-p where p is a free parameter. The standard disk model, diskbb, is recovered if p = 0.75. If
, radial advection is important then p < 0.75. See the discussion and examples in, e.g.,
Mineshige et al. 1994, ApJ, 426, 308, Hirano et al. 1995, ApJ, 446, 350, Watarai et al.
2000, PASJ, 52, 133, Kubota and Makishima 2004, ApJ, 601, 428, Kubota et al. 2005,
ApJ, 631, 1062 .
par1 Tin: temperature at inner disk radius (keV) par2 p: exponent of the radial dependence of the disk temperature norm
D
10
kpc
2
cos
, where
R
in
is “an apparent” inner disk radius, D the distance to the source, and θ the angle of the disk (θ =
0 is face-on). On the correction factor between the apparent inner disk radius and the realistic radius, see e.g., Kubota et al. 1998,
PASJ, 50, 667.
6.2.31 diskpn: accretion disk, black hole, black body
Blackbody spectrum of an accretion disk. This is an extension of the
diskbb
model, including corrections for temperature distribution near the black hole. The temperature distribution was calculated in Paczynski-Wiita pseudo-Newtonian potential.
An accretion rate can be computed from the maximum temperature found. For details see Gierlinski et al., 1999, MNRAS, 309, 496. Please note that the inner disk radius
( par2
) can be a free parameter only close to par2
= 6; otherwise par2
is strongly correlated with K. par1 maximum temperature in the disk (keV)
197
par2 inner disk radius in
R g
=
GM/c
2
units, 6
par2
1000 norm
M
2 cos
i
D
2
4
normalization, where M = central mass (solar masses), D distance to the source (kpc), i inclination of the disk, and
color/effective temperature ratio.
6.2.32 eplogpar: log-parabolic blazar model with
F
normalization
eplogpar is a power-law with an index which varies with energy as a log parabola.
( ) 10
(
E E p
)) )
/
E
2 par1 = Ep par2 =
The peak energy in
F
Curvature term norm=
K
The flux in
F
units at energy Ep keV
See for instance
Tramacere et al., 2007
and
Tramacere et al., 2009
.
6.2.33 Eqpair, eqtherm, compth: Paolo Coppi's hybrid
(thermal/non-thermal) hot plasma emission models.
These models are based on Paolo Coppi's hybrid thermal/non-thermal hot plasma emission model for X-ray binaries. The underlying physics and a detailed description of the code are included in the draft paper http://www.astro.yale.edu/coppi/eqpair/eqpap4.ps.
Do not use these models without reading and understanding this paper. Simplified models
eqtherm and compth are provided for cases where non-thermal processes are not important and photon-photon pair production can be ignored. These should only be used if l bb
<~ 10.
The temperature of the thermal component of the electron distribution and the total electron optical depth (for both ionization electrons and electron-positron pairs) are written out if the chatter level is set to 15. This information is important for checking self-consistency.
198
In versions 1.10 and above the Compton reflection is done by a call to the ireflct model code and the relativistic blurring by a call to rdblur. This does introduce some changes in the spectrum from earlier versions. For the case of a neutral reflector (i.e. the ionization parameter is zero) more accurate opacities are calculated. For the case of an ionized reflector the old version assumed that for the purposes of calculating opacities the input spectrum was a power-law (with index based on the 2-10 keV spectrum). The new version uses the actual input spectrum, which is usually not a power law, giving different opacities for a given ionization parameter and disk temperature. The Greens' function integration required for the Compton reflection calculation is performed to an accuracy of
0.01 (i.e. 1%). This can be changed using e.g. xset EQPAIR_PRECISION 0.05.
The parameters for all three models are: par1 l h
/l s
, ratio of the hard to soft compactnesses par2 l bb
, the soft photon compactness par3 kT bb
, if > 0 then temperature of the inner edge of the accretion disk for the diskbb model; if < 0 then abs(kT bb
) is the T parameter for the diskpn model max par4 par5 par6 l nt
/l h
, fraction of power supplied to energetic particles which goes into accelerating non-thermal particles
p
, the Thomson scattering depth radius, the size of the scattering region (cm) par7 g min
, minimum Lorentz factor of the pairs par8 g max
, maximum Lorentz factor of the pairs par9 par10
G inj
, if < 0 then non-thermal spectrum is assumed monoenergetic at g max
; if > 0 then a power-law from g min
to g max pairinj, if = 0 then accelerated particles are electrons from thermal pool; if = 1 then accelerated particles are electrons and positrons par11 par12 par13 par14 cosIncl, inclination of reflecting material wrt line-of-sight
Refl, fraction of scattering region's emission intercepted by reflecting material
Fe_abund, relative abundance of iron
Ab>He, relative abundance of other metals
par15 T disk
, temperature of reflecting disk par16
, ionization parameter of reflector par17
, power-law index with radius of disk reflection emissivity par18 R in
, inner radius of reflecting material (GM/c
2
) par19 R out
, outer radius of reflecting material (GM/c
2
)
199
norm
6.2.34 equil, vequil: collisional plasma, ionization equilibrium
Ionization equilibrium collisional plasma model. This is the equilibrium version of Kazik Borkowski's NEI models. Several versions are available. To switch between them use the xset
neivers
command. xset
neivers 1.0
gives the version from xspec v11.1, xset
neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset
neivers 2.0
uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.
The vequil variant allows the user to set the abundances for the model.
For the equil model the parameters are: par1 par2 plasma temperature (keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Abundances are defined by the abund command par3 redshift norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm),
n
e
is the electron density (cm
-3 and
n
H
is the hydrogen density (cm
-3
)
),
For the vequil model, the parameters are: par1 plasma temperature (keV) par2-par13 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
200
norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm),
n
e
is the electron density (cm
-3
), and
n
H
is the hydrogen density (cm
-3
)
The references for this model are as follows:
Borkowski, Lyerly & Reynolds, 2001, ApJ, 548, 820
Hamilton, A.J.S., Sarazin, C. L. & Chevalier, R. A. , 1983,ApJS, 51,115
Borkowski, K.J., Sarazin, C.L. & Blondin, J.M. 1994, ApJ, 429, 710
Liedahl, D.A., Osterheld, A.L. Goldstein, W.H. 1995, ApJ, 438, L11
6.2.35 expdec: exponential decay
An exponential decay.
KE
) where: par1 = K exponential factor
6.2.36 ezdiskbb: multiple blackbody disk model with zero-torque inner boundary
A multi-temperature blackbody model for a thin, steady-state, Newtonian accretion disk, assuming zero torque at the inner boundary for the disk at radius R_in.
The temperature of the disk as a function of radius is assumed to be T(r) = T_* r^(-3/4)
201
(1-r^(-1/2))^(1/4), where r = R/R_in and T_* = f(3 G M Mdot / 8 pi R_in^3 sigma)^(1/4).
The maximum temperature in the disk is given by T_max = 0.488 T_*.
This model is an alternative to diskbb, which assumes a non-zero torque at the inner edge and a temperature profile T(r) = T_* r^(-3/4), and it should be used to fit spectra of disks when the zero-torque inner boundary condition is appropriate. For details see Zimmerman et al. (2004) astro-ph/0408209.
par1 = maximum temperature in the disk (keV)
par2 = (1/f^4) (R_in/D)^2 cos i, where R_in is the inner radius of the disk in km,
D is the distance to the source in units of 10 kpc, i is the inclination, and f is the color to effective temperature ratio.
6.2.37 gadem, vgadem: plasma emission, multi-temperature with gaussian distribution of emission measure.
A multi-temperature plasma emission model built on top of the apec or mekal codes. The emission measure distribution is a gaussian with mean and sigma given by the first two model parameters. The switch parameter determines whether the apec or mekal codes will be used. For the mekal code there are also the options to run the code for each temperature or interpolate from a pre-calculated table. The former is slower but more accurate. See the documentation on the apec model for additional information on using different AtomDB versions or applying thermal or velocity broadening.
For the gadem version, the abundance ratios are set by the abund command. The
vgadem variant allows the user to define the abundances. See the documentation on the
apec model for information on using additional elements included in AtomDB v2.
The parameters for gadem are: par1 mean temperature for gaussian emission measure distribution par2 sigma temperature for gaussian emission measure distribution par3
n
H
(cm
-3
) par4 abundance relative to solar par6
0 calculate using MEKAL model
1 interpolate using MEKAL model
2 interpolate using APEC model norm Normalization
For the vgadem variant the parameters are: par1 mean temperature for gaussian emission measure distribution par2 sigma temperature for gaussian emission measure distribution par3
n
H
(cm
-3
) par4-
17 abundance relative to solar Abundances for He, C, N, O, Ne, Na, Mg,
Al, Si, S,Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
202
0 calculate using MEKAL model par19
1 interpolate using APEC model
2 interpolate using APEC model norm Normalization
6.2.38 gauss, zgauss: gaussian line profile
zgauss variant computes a redshifted gaussian.
( )
K
1
2
exp
( where:
l
)
2
2
2 par1 =
E
par2 =
Norm =
l
K line energy in keV line width in keV total photons cm
-2 s
-1
in the line
For zgauss the corresponding formula is:
A
(
E
)
2
K
2
( 1
z
) exp
1
2
(
E
( 1
z
)
E
L
)
2
and parameter settings are:
203
par1
E
L line energy in keV par2 line width in keV par3
z
redshift norm
K
total photons cm
–2 s
–1
in the line
6.2.39 gnei, vgnei: collisional plasma, non-equilibrium, temperature evolution
Non-equilibrium ionization collisional plasma model. This is a generalization of the nei model where the temperature is allowed to have been different in the past i.e. the ionization timescale averaged temperature is not necessarily equal to the current temperature. For example, in a standard Sedov model with equal electron and ion temperatures, the ionization timescale averaged temperature is always higher than the current temperature for each fluid element. The references for this model can be found under the description of the equil model. Several versions are available.
To switch between them use the xset
neivers
command. xset
neivers 1.0
gives the version from xspec v11.1, xset
neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset
neivers 2.0
uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.
The vgnei variant allows the user to set the abundances of the model.
For the gnei model the parameters are: par1 par2 par3 plasma temperature (keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni.
Abundances are defined by the abund command
Ionization timescale in units of s cm
–3
. norm
4
10
14
D
A
(1
z
)
2
H
where
D
A
is the angular diameter
distance to the source (cm),
n
e and
n
H
(cm
-3 and hydrogen densities respectively.
) are the electron
For vgnei the parameters are: par1 plasma temperature (keV) par2-par13 (Fixed) Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca,
Fe, Ni wrt Solar (defined by the abund command) par14 Ionization timescale in units of s cm
–3
.
204
norm
4
10
14
D
A
(1
z
)
2
H
where
D
A
is the angular diameter distance to the source (cm), and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
6.2.40 grad: accretion disk, Schwarzschild black hole
General Relativistic Accretion Disk model around a Schwarzschild black hole. Inner radius is fixed to be 3 Schwarzschild radii, thus the energy conversion efficiency is 0.057. See Hanawa,
T., 1989, ApJ, 341, 948 and Ebisawa, K. Mitsuda, K. and Hanawa, T. 1991, ApJ, 367, 213. Several bugs were found in the old GRAD model which was included in xspec 11.0.1ae and before. Due to these bugs, it turned out that the mass obtained by fitting the old GRAD model to the observation was 1.4 times over-estimated. These bugs were fixed, and a new parameter (par6) was added to make the distinction between the old and new codes clear. par2 par3 par4 par5 disk inclination angle (deg; 0 for face-on) mass of the central object (solar units) mass accretion rate 10
18
gs
-1 spectral hardening factor,
T
col
/T eff
. Should be greater than 1.0, and considered to be 1.5–1.9 for accretion disks around a stellar-mass black hole. See, e.g.,
Shimura and Takahara, 1995, ApJ, 445, 780
205
par6 A flag to switch on/off the relativistic effects (never allowed to be free). If positive, relativistic calculation; if negative or zero, Newtonian calculation
(the inner radius is still fixed at 3 Schwarzschild radii, and the efficiency is
1/12).
Should be fixed to 1. norm
6.2.41 grbm: gamma-ray burst continuum
A model for gamma-ray burst continuum spectra developed by D. Band, et. al., 1993 (ApJ
413, 281).
A
(E )
K
(
100.
1 exp(
E E c
)
2
)
E c
100.
(
2
)
E
100.
2
)
E
(
1
2
)
E c
E
(
1
2
)
E c
where E is in units of keV. par1
1 first power law index par2
2 second power law index par3
E c
characteristic energy in keV norm
K
6.2.42 kerrbb: multi-temperature blackbody model for thin accretion disk around a Kerr black hole
A multi-temperature blackbody model for a thin, steady state, general relativistic accretion disk around a Kerr black hole. The effect of self-irradiation of the disk is considered, and the torque at the inner boundary of the disk is allowed to be non-zero.
This model is intended as an extension to grad, which assumes that the black hole is nonrotating. For details see Li et al., ApJSuppl, 157, 335, 2005.
par1 = eta, ratio of the disk power produced by a torque at the disk inner boundary to the disk power arising from accretion. It must be >= 0 and
206
<=1. When eta = 0, the solution corresponds to that of a standard
Keplerian disk with zero torque at the inner boundary.
par2 = specific angular momentum of the black hole in units of the black hole mass M (geometrized units G=c=1). Should be >= -1 and < 1.
par3 = disk's inclination angle (the angle between the axis of the disk and the line of sight). It is expressed in degrees. i=0 is for a "face-on" accretion disk. i should be <= 85 degree.
par4 = the mass of the black hole in units of the solar mass.
par5 = the "effective" mass accretion rate of the disk in units of 10^18 g/sec.
When eta = 0 (zero torque at the inner boundary), this is just the mass accretion rate of the disk. When eta is nonzero, the effective mass accretion rate = (1+eta) times the true mass accretion rate of the disk.
The total disk luminosity is then "epsilon" times "the effective mass accretion rate" times "c^2", where epsilon is the radiation efficiency of a standard accretion disk around the Kerr black hole
par6 = the distance from the observer to the black hole in units of kpc.
par7 = spectral hardening factor, T_col/T_eff. It should be greater than 1.0, and considered to be 1.5-1.9 for accretion disks around a stellar-mass black hole. See, e.g., Shimura and Takahara 1995, ApJ, 445, 780
par8 = a flag to switch on/off the effect of self-irradiation (never allowed to be free). Self-irradiation is included when > 0. Self-irradiation is not included when <= 0.
par9 = a flag to switch on/off the effect of limb-darkening (never allowed to be free). The disk emission is assumed to be limb-darkened when > 0. The disk emission is assumed to be isotropic when lflag is <= 0.
K = normalization. Should be set to 1 if the inclination, mass and distance are frozen.
6.2.43 kerrd: optically thick accretion disk around a Kerr black hole
Optically thick extreme-Kerr disk model based on the same tranfer-function used in the
"laor" Kerr disk-line model. Local emission is simply assumed to be the diluted blackbody. See
Laor 1991, ApJ, 376, L90 for explanation of the transfer function. See Ebisawa et al. 2003, ApJ,
597, 780 for examples of using this model.
par1 = distance (kpc)
par2 = spectral hardening factor, Tcol/Teff. Should be
greater than 1.0, and considered to be 1.5-1.9
207
for accretion disks around a stellar-mass black hole.
See, e.g., Shimura and Takahara, 1995, ApJ, 445, 780
par3 = mass of the central object (solar unit)
par4 = mass accretion rate (1e18 g/s)
par5 = disk inclination angle (deg; 0 for face-on)
par6 = inner radius (units of GM/c**2). 1.235 is the
last stable orbit.
par7 = outer radius (units of GM/c**2)
K = normalization factor. should be fixed to 1.
6.2.44 kerrdisk: accretion disk line emission with BH spin as free parameter
Model for an accretion disk broad emission line with the black hole spin allowed to be a free parameter. A detailed description can be found in Brenneman & Reynolds
(2006ApJ...652.1028B).
This model is quite slow so is best used after models such as laor or diskline have been employed to get an estimate of the best-fit parameters.
par1 = rest frame line energy (keV)
par2 = emissivity index for the inner disk
par3 = emissivity index for the outer disk
par4 = break radius separating the inner and outer portions of the disk (gravitational radii)
par5 = dimensionless black hole spin
par6 = disk inclination angle to the line of sight (degrees)
par7 = inner radius of the disk in units of the radius of marginal stability
par8 = outer radius of the disk in units of the radius of marginal stability
par9 = redshift z
K = flux in line (photons/cm
2
/s)
6.2.45 laor: accretion disk, black hole emission line
An emission line from an accreti on disk around a black hole. Ari Laor's calculation including GR effects (ApJ 376, 90). par1 Line energy in keV
par2=
par3 par4 power law dependence of emissivity (scales as
R
–
) inner radius (units of
GM c
2
) outer radius (units of
GM c
2
)
6.2.46 laor2: accretion disk with broken-power law emissivity profile, black hole emission line
An emission line from an accreti on disk with a broken power-law emissivity profile around a black hole. Uses Ari Laor's calculation including GR effects (ApJ 376,
90). Modified from laor model by Andy Fabian. par1 par2
Line energy in keV
Index: power law dependence of emissivity (scales as
R
–Index
) par3 inner radius (units of
GM c
2
) par4 outer radius (units of
GM c
2
) par6 par7 radius at which emissivity power-law index changes
Emissivity power-law index for radii > par6
6.2.47 logpar: log-parabolic blazar model
logpar is a power-law with an index which varies with energy as a log parabola.
E pivotE
)
( log(
E pivotE
)) par1 =
par2 =
Slope at the pivot energy
Curvature term
208
209
par3 = pivotE norm=
K
Fixed pivot energy (best near low end of energy range).
See for instance
Massaro et al., 2004.
6.2.48 lorentz: lorentz line profile
A Lorentzian line profile.
( )
K
(
L
)
2
(
2)
2 where: par1
E
L
line energy in keV par2 norm
K
cm
-2 s
-1
in the line
6.2.49 meka, vmeka: emission, hot diffuse gas (Mewe-
Gronenschild)
An emission spectrum from hot diffuse gas based on the model calculations of Mewe and
Gronenschild (as amended by Kaastra). The model includes line emissions from several elements. Abundances are the number of nuclei per Hydrogen nucleus relative to the
Solar abundances set by the abund command.
The vmeka variant allows the user to set the abundances for the model.
Parameters for the meka model are: par1 par2
plasma temperature in keV
H density (cm
–3
) par3 Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni.
210
norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), , and
n
e ,
n
H
(cm
-3 electron and hydrogen densities respectively.
) are the
Parameters for the vmeka model are: par1 par2
plasma temperature in keV
H density (cm
–3
) par3-par14 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (given by the Anders & Grevesse mixture) norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
The references for the MEKA model are as follows :
Mewe, R., Gronenschild, E.H.B.M., and van den Oord, G.H.J. 1985 A &AS, 62, 197
Mewe, R., Lemen, J.R., and van den Oord, G.H.J. 1986, A &AS, 65, 511
Kaastra, J.S. 1992, An X-Ray Spectral Code for Optically Thin Plasmas (Internal SRON-
Leiden Report, updated version 2.0)
Similar credit may also be given for the adopted ionization balance:
Arnaud, M., and Rothenflug, M. 1985, A & AS, 60, 425
Arnaud, M., and Raymond, J. 1992, ApJ, 398, 394
6.2.50
Liedahl) mekal, vmekal: emission, hot diffuse gas (Mewe-Kaastra-
An emission spectrum from hot diffuse gas based on the model calculations of
Mewe and Kaastra with Fe L calculations by Liedahl. The model includes line emissions from several elements. The switch parameter determines whether the mekal code will be
211
run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.
Relative abundances are set by the abund command for the mekal model. The vmekal variant allows the user to set the individual abundances for the model. par1 par2 par3
plasma temperature in keV
H density (cm
-3
)
Metal abundance (He fixed at cosmic). The elements included are C,
N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni. par4 (fixed) redshift
Par5
0 calculate
1 interpolate
2 interpolate using APEC model norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e , densities respectively.
n
H
(cm
-3
) are the electron and hydrogen
Parameters for the vmekal variant are: par1 par2
plasma temperature in keV
H density (cm
-3
) par3-par16 Abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt
Solar (given by the Anders & Grevesse mixture) par17 (fixed) redshift par18
0 calculate
1 interpolate
2 interpolate using APEC model
212
norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e , densities respectively.
n
H
(cm
-3
) are the electron and hydrogen
The references for the MEKAL model are as follows :
Mewe, R., Gronenschild, E.H.B.M., and van den Oord, G.H.J. 1985,A&AS, 62, 197
Mewe, R., Lemen, J.R., and van den Oord, G.H.J. 1986, A&AS}, 65, 511
Kaastra, J.S. 1992, An X-Ray Spectral Code for Optically Thin Plasmas (Internal SRON-
Leiden Report, updated version 2.0)
Liedahl, D.A., Osterheld, A.L., and Goldstein, W.H. 1995, ApJL, 438, 115
Similar acknowledgement may also be given for the adopted ionization balance:
Arnaud, M., and Rothenflug, M. 1985, A&AS, 60, 425
Arnaud, M., and Raymond, J. 1992, ApJ, 398, 394
6.2.51 mkcflow, vmcflow: cooling flow, mekal
A cooling flow model after Mushotzky & Szymkowiak (
Cooling Flows in
Clusters and Galaxies ed. A. C. Fabian, 1988). This one uses the mekal (or vmekal) model for the individual temperature components and differs from cflow in setting the emissivity function to be the inverse of the bolometric luminosity. The model assumes
H
= 50 and
q
0 determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated
0
= 0. Abundance ratios are set by the abund command. The switch parameter table. The former is slower but more accurate.
For the mkcflow model the parameters are: par1 low temperature (keV) par3 abundance relative to Solar
par5
0
calculate
1
interpolate
2
interpolate using APEC model
Mass accretion rate (solar mass/yr) norm
While for the vmcflow variant the parameters are: par1 low temperature (keV)
213
par3par16
Abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (given by the Anders & Grevesse mixture) par17 Redshift
0
calculate par18 1
interpolate
2
interpolate using APEC model norm Mass accretion rate (solar mass/yr)
6.2.52 nei, vnei: collisional plasma, non-equilibrium, constant temperature
Non-equilibrium ionization collisional plasma model. This assumes a constant temperature and single ionization parameter. It provides a characterization of the spectrum but is not a physical model. The references for this model can be found under the description of the equil model. The references for this model can be found under the description of the equil model. Several versions are available. To switch between them use the xset
neivers
command. xset
neivers 1.0
gives the version from xspec v11.1, xset
neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset
neivers 2.0
uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.
The vnei variant allows the user to set the abundance vector.
For the nei version the parameters are par1 par2 par3 plasma temperature (keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Relative abundances are defined by the abund command.
Ionization timescale in units of s cm
–3
.
214
norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
For the vnei variant the parameters are: par1 par2 plasma temperature (keV)
H density in cm
-3 par3-par14 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) par15 Ionization timescale in units of s cm
–3
. norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
215
6.2.53 npshock, vnpshock: shocked plasma, plane parallel, separate ion, electron temperatures.
Plane-parallel shock plasma model with separate ion and electron temperatures. This model is slow. par1
provides a measure of the average energy per particle
(ions+electrons) and is constant throughout the postshock flow in plane shock models
(Borkowski et al., 2001, ApJ, 548, 820). par2
should always be less than
par1
. If par2 exceeds par1
then their interpretations are switched (ie the larger of
par1
and par2
is always the mean temperature). Additional references can be found under the help for the equil model. Several versions are available. To switch between them use the xset neivers
command. xset
neivers 1.0
gives the version from xspec v11.1, xset neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset
neivers 2.0
uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.
The npshock version uses relative abundances from the Anders & Grevesse (1993) mix, while the vpnshock version allows the user to set the abundances.
Parameters for npshock are: par1 Mean shock temperature (keV) par2 par3 par4 par5 electron temperature immediately behind the shock front
(keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni.
Abundances are given by the Anders & Grevesse mixture.
Lower limit on ionization timescale in units of s cm
–3
.
Upper limit on ionization timescale in units of s cm
–3
. norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
For vnpshock the parameters are:
par1 par2
Mean shock temperature (keV) electron temperature immediately behind the shock front
(keV)
H density in cm
-3 par3 par4-par15 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (given by the Anders & Grevesse mixture) par16 Lower limit on ionization timescale in units of s cm
–3
. par17 Upper limit on ionization timescale in units of s cm
–3
.
216
norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e ,
n
H
(cm
-3 electron and hydrogen densities respectively.
) are the
6.2.54 nsa: neutron star atmosphere
This model provides the spectra in the X-ray range (0.05-10 keV) emitted from a hydrogen atmosphere of a neutron star. There are three options : nonmagnetized (B < 10
8
- 10
9
G) with a uniform surface (effective) temperature in the range of log
T eff
K
; a field B = 10
12
G with a uniform surface (effective) temperature in the range of log
T eff
( ) 5.5 6.8
; a field B = 10
13
G with a uniform surface
(effective) temperature in the range of log
T eff
( ) 5.5 6.8
. The atmosphere is in radiative and hydrostatic equilibrium; sources of heat are well below the atmosphere. The
Comptonization effects (significant at
T eff
6
K
) are taken into account. The model spectra are provided as seen by a distant observer, with allowance for the GR effects. The user is advised to keep
M ns
and
R ns
fixed and fit the temperature and the normalization.
MagField must be fixed at one of 0, 10
12
, or 10
13
.
The values of the effective temperature and radius as measured by a distant observer
(``values at infinity'') are :
217
T
eff
T g r
R
ns
R ns
/
g r
where
M ns
R ns
1/2 is the gravitational redshift parameter.
Please send your comments/questions to Slava Zavlin
([email protected]) and/or George Pavlov
([email protected]). If you publish results obtained using these models, please reference Zavlin, V.E., Pavlov, G.G., & Shibanov, Yu.A. 1996, A&A, 315, 141 for nonmagnetic models, and Pavlov, G.G., Shibanov, Yu.A., Zavlin, V.E., & Meyer, R.D.
1995, in “The Lives of the Neutron Stars,” ed. M.A. Alpar, U. Kiziloglu, & J. van
Paradijs (NATO ASI Ser. C, 450; Dordrecht: Kluwer), p. 71 for magnetic models. par1 log
T eff
, (unredshifted) effective temperature par2
M ns
, neutron star gravitational mass (in units of solar mass) par3
R ns
, neutron star radius (in km) par4 neutron star magnetic field strength (0, 1e12, or 1e13 G)
K 1/
D
2
, where D is the distance of the object in pc.
6.2.55 nsagrav: NS H atmosphere model for different g
This model provides the spectra emitted from a nonmagnetic hydrogen atmosphere of a neutron star with surface gravitational acceleration g ranging from 1e13 to 1e15 cm/s
2
, allowed by equations of state for the neutron star matter (the nsa model gives the spectra calculated for g=2.43e14 cm/s
2
). The uniform surface (effective) temperature is in the range of Log T eff
(K) = 5.5 - 6.5. The atmosphere is in radiative and hydrostatic equilibrium; sources of heat are well below the atmosphere. The radiative force and electron heat conduction are included in the models, but they are of no importance in the specified ranges of T eff
and g. The model spectra are provided as seen by a distant observer, with allowance for the GR effects.
The neutron star mass M and radius R determine the redshift parameter,
g r
=[1-2.952*M/R]
0.5
,
218
and the gravitational acceleration at the surface,
g=1.33e16*M/R
2
/g r
cm/s
2
, where M is in units of solar mass, and R is in km. The allowed domain in the M-R plane corresponds to g r
2
> 1/3 and 1e13 < g < 1e15 cm/s
2
. (This domain is restricted by the solid curves in the figure). If chosen M and R values correspond to g r
or/and g values outside the allowed domain, then the code sets the latter to be the closest limiting values
(e.g., if one chooses M=2, R=8, then the code will use g r
=3
-1/2
=0.578 instead of g r
=0.512 corresponding to the M and R chosen), which would lead to unphysical results.
The values of the effective temperature and radius as measured by a distant observer ("values at infinity") are:
T
g T
,
R
/
r
The nsagrav model may be useful for putting constraints on M and R from spectral fits to thermal emission detected from neutron stars, provided the quality of the observational data are good enough to warrant a detailed analysis. The parameters M and
R can be fixed at specific values or allowed to vary within a reasonable range (see the note above). For example, one can run spectral fits on a M-R grid (using the steppar command) within the allowed parameter domain (see above).
Please send your comments/questions (if any) to Slava Zavlin
([email protected]) and/or George Pavlov ([email protected]). If you publish results obtained using this model please reference Zavlin et al. (1996, A&A
315, 141).
par2 M ns
: neutron star gravitational mass (in units of Solar mass) par3 R ns
: “true” neutron star radius (km)
K 1/D
2
where D is the distance to the object in pc
6.2.56 nsatmos: NS Hydrogen Atmosphere model with electron conduction and self-irradiation
This model interpolates from a grid of NS atmosphere calculations provided by George
Rybicki and Ramesh Narayan to output a NS atmosphere spectrum. The model grids cover a wide range of surface gravity and effective temperature, and incorporate thermal electron conduction and self-irradiation by photons from the compact object. This code assumes negligible (less than 10^9 G) magnetic fields and a pure hydrogen atmosphere.
A detailed description of the model is given in Heinke et al. (2006), ApJ in press, astroph/0506563 (see also McClintock et al. 2004, ApJ, 615, 402).
219
par2 M ns
: neutron star gravitational mass (in units of Solar mass) par3 R ns
: “true” neutron star radius (km) par4
K dist : distance to the neutron star (in kpc) fraction of the neutron star surface emitting
6.2.57 nsmax: Neutron Star Magnetic Atmosphere
This model interpolates from a grid of neutron star (NS) atmosphere spectra to produce a final spectrum that depends on the parameters listed below. The atmosphere spectra are obtained using the latest equation of state and opacity results for a partially ionized, strongly magnetized hydrogen or mid-Z element plasma. The models are constructed by solving the coupled radiative transfer equations for the two photon polarization modes in a magnetized medium, and the atmosphere is in radiative and hydrostatic equilibrium. The atmosphere models mainly depend on the surface effective temperature T eff and magnetic field strength B and inclination Θ
B dependence on the surface gravity g=(1+z g
)GM/R
2
, where 1+z g
; there is also a
=(1-2GM/R) gravitational redshift and M and R are the NS mass and radius, respectively.
-1/2
is the
Two sets of models are given: one set with a single surface B and T eff and a set which is constructed with B and T eff varying across the surface according to the magnetic dipole model (for the latter, θ m
is the angle between the direction to the observer and the magnetic axis). The effective temperatures span the range log T and log T eff eff
=5.5-6.8 for hydrogen
.=5.8-6.9 for mid-Z elements(note: for the latter, change temperature range in nsmax_lmodel.dat) The models with single (B,T eff
) cover the energy range 0.05-10 keV, while the models with (B,T eff
)-distributions cover the range 0.09-5 keV. par1 = logTeff, surface (unredshifted) effective temperature
1+z g
, gravitational redshift par3 = switch indicating model to use (see nsmax.dat or
model list
)
A = /d)
2
, normalization, where R em
is the size (in km) of the emission region and d is the distance (kpc) to the object Note: A is added automatically by XSPEC.
Please send your comments/questions to Wynn Ho
(
). If you publish results obtained using NSMAX, please reference
Ho, W.C.G., Potekhin, A.Y., & Chabrier, G. (2008, ApJS, 178, 102)
and also
Mori, K. & Ho, W.C.G. (2007, MNRAS, 377, 905)
if using the mid-Z models.
220
6.2.58 nteea: non-thermal pair plasma
A nonthermal pair plasma model based on that of Lightman & Zdziarski (1987, ApJ 319,
643) from Magdziarz and Zdziarski. It includes angle-dependent reflection from
Magdziarz & Zdziarski (1995, MNRAS 273, 837). In versions 1.1 and above the
Compton reflection is done through an internal call to the reflct model. The Greens' function integration required for the Compton reflection calculation is performed to an accuracy of 0.01 (i.e. 1%). This can be changed using e.g. xset NTEEA_PRECISION
0.05.The abundances are set up by the command
abund
. Send questions or comments to
par1 nonthermal electron compactness par3 par4 par5 par6 par7 par8 par9 par10 par11 par12 par13 par14 norm scaling factor for reflection (1 for isotropic source above disk) blackbody temperature in eV the maximum Lorentz factor thermal compactness (0 for pure nonthermal plasma)
Thomson optical depth of ionization electrons ( e.g., 0) electron injection index (0 for monoenergetic injection) minimum Lorentz factor of the power law injection (not used for monoenergetic injection)
minimum Lorentz factor for nonthermal reprocessing
1
par10 par9
radius in cm (for Coulomb/bremsstrahlung only)
pair escape rate in c (0-1, see Zdziarski 1985, ApJ, 289, 514)
cosine of inclination angle
iron abundance relative to that defined by abund photon flux of the direct component (w/o reflection) at 1~keV in the observer's frame.
221
6.2.59 Nthcomp: Thermally comptonized continuum
Nthcomp is a *much* better description of the continuum shape from thermal comptonisation than an exponentially cutoff power law, but is not that much more complicated in terms of parameters. The high energy cutoff is sharper than an exponential, and is parameterized by the electron temperature (kT_e). VERY roughly, an exponential rollover energy E_c=2-3kT_e but the shape is very different, so it impacts on the reflected fraction as well. Another major effect (especially for X-ray binaries) is that it incorporates the low energy rollover. The hot electrons Compton UPscatter seed photons so there are few photons in the scattered spectrum at energies below the typical seed photon energies, making it significantly different to a power law below this energy.
Typically the physical picture is that these seed photons are (quasi)blackbody (eg neutron star boundary layer) or disk blackbody in shape. Either of these shapes can be selected
(input type), both being parameterized by a seed photon temperature (kT_bb). Between the low and high energy rollovers the shape of the spectrum is set by the combination of electron scattering optical depth and electron temperature. It is not necessarily a power law, but can be parameterized by an asymptotic power law index (Gamma). Details of this are given in Zycki, Done & Smith (1999), including a self-consistent reflection component which is NOT released here as it was written using non-FITS standard files so has significant issues with portability.
This is the thermally comptonized continuum model of Zdziarski, Johnson &
Magdziarz 1996, MNRAS, 283, 193, as extended by Zycki, Done & Smith 1999,
MNRAS 309, 561. Please reference these papers if you use it. par1 = Gamma, asymptotic power-law photon index. par2 = kT_e, electron temperature (high energy rollover) par3 = kT_bb, seed photon temperature (low energy rollover) par4 = inp_type, 0 or 1 for blackbody or disk-blackbody seed photons, respectively par5 = redshift
K = normalization, unity at 1 keV for a norm of 1.
222
6.2.60 Optxagnf, optxagn: Colour temperature corrected disc and energetically coupled Comptonisation model for AGN.
AGN spectral energy distributions are complex, but can be phenomenologically fit by a disc, optically thick, low temperature thermal Comptonisation (to produce the soft X-ray excess) and an optically thin, high temperature themal Comptonisation (to produce the power law emission which dominates above 2 keV). Here we combine these three components together assuming that they are all ultimately powered by gravitational energy released in accretion. We assume that the gravitational energy released in the disc at each radius is emitted as a (colour temperature corrected) blackbody only down to a given radius, R corona
. Below this radius, we further assume that the energy can no longer completely thermalise, and is distributed between powering the soft excess component and the high energy tail. This imposes an important energetic self consistency on the model. The key aspect of this model is that the optical luminosity constrains the mass accretion rate through the outer disc, Mdot, provided there is an independent estimate of the black hole mass (from e.g. the Hβ emission line profile). The total luminosity available to power the entire SED is L tot
=eff Mdot c
2
, where the efficiency is set by black hole spin assuming Novikov-Thorne emissivity.
There are two versions of the model. Optxagnf is the one recommended for most purposes, and has the colour temperature correction calculated for each temperature from the approximations given in
Done et al. (2011)
. Optxagn instead allows the user to define their own colour temperature correction, fcol, which is then applied to annuli with effective temperature > T scatt
. In both models the flux is set by the physical parameters of mass, L/L
Edd
, spin and distance, hence the model normalisations MUST be frozen at unity.
Parameters in Optxagnf: par1 = mass Black hole mass in solar masses par2 = dist Comoving (proper) distance in Mpc par3 = logL/Ledd Eddington ratio par4 = astar Dimensionless black hole spin par5 = rcor par6 = logrout
Coronal radius in R g
=GM/c
2
marking the transition from (colour temperature corrected) blackbody emission to a Comptonised spectrum. If this parameter is negative then only the blackbody component is used.
Log of the outer radius of the disc in units of R g is -ve the code will use the self gravity radius as
; if this calculated from
Laor & Netzer (1989)
par7 = kT_e par8 = tau
Electron temperature for the soft Comptonisation component (soft excess) in keV
Optical depth of the soft Comptonisation component. If this parameter is negative then only the soft Compton component is used. par9 = Gamma Spectral index of the hard Comptonisation component
('power law') which has temperature fixed to 100 keV. par10 = fpl Fraction of the power below rcor which is emitted in the hard comptonisation component. If this parameter is negative then only the hard Compton component is used. par11 = Redshift norm=
K
Must be frozen
Parameters in Optxagn: par1 = mass par2 = dist
Black hole mass in solar masses
Comoving (proper) distance in Mpc par3 = logL/Ledd Eddington ratio par4 = astar par5 = rcor par6 = logrout
Dimensionless black hole spin
Coronal radius in R g
=GM/c
2
marking the transition from (colour temperature corrected) blackbody emission to a Comptonised spectrum. If this parameter is negative then only the blackbody component is used.
Log of the outer radius of the disc in units of R g is -ve the code will use the self gravity radius as
; if this calculated from
Laor & Netzer (1989)
par7 = kT_e par8 = tau
Electron temperature for the soft Comptonisation component (soft excess) in keV
Optical depth of the soft Comptonisation component. If this parameter is negative then only the soft Compton component is used.
223
224
par9 = Gamma Spectral index of the hard Comptonisation component
('power law') which has temperature fixed to 100 keV. par10 = fpl Fraction of the power below rcor which is emitted in the hard comptonisation component. If this parameter is negative then only the hard Compton component is used. par11 = fcol Colour temperature correction to apply to the disc blackbody emission for radii below rcor with effective temperature > Tscatt par12 = Tscatt par13 = Redshift
Effective temperature criterion used as described above
(in K). norm=
K
Must be frozen
6.2.61 pegpwrlw: power law, pegged normalization
A power law with pegged normalization.
KE
where : par1
photon index of power law (dimensionless) par2 par3 norm lower peg energy range upper peg energy range flux (in units of 10
–12
erg cm
–2 s
-1
over the energy par2
– par3
).
If .
par2
= par3
, it is the flux in micro-Jy at par2
6.2.62 pexmon: neutral Compton reflection with self-consistent
Fe and Ni lines.
This model from Nandra et al. (2007; MNRAS 382, 194) combines pexrav with selfconsistently generated Fe Kα, Fe Kβ, Ni Kα and the Fe Kα Compton shoulder. Line strengths are based on Monte Carlo calculations by George and Fabian (1991; MNRAS
249, 352) which are parametrized for 1.1 < γ < 2.5 by :
EW = 9.66 EW
0
(γ
-2.8
- 0.56) with inclination dependence for for i < 85 degrees :
EW = EW
0
(2.20 cos i - 1.749 (cos i)
2
+ 0.541(cos i)
3
)
225
and abundance dependence : log EW = log EW
0
(0.0641 log A
Fe
- 0.172 (log A
Fe
)
2
)
The Fe Kβ and Ni Kα line fluxes are 11.3% and 5% respectively of that for Fe Kα. The
Fe Kα Compton shoulder is approximated as a gaussian with E = 6.315 keV and σ =
0.035 keV. The inclination dependence is taken from Matt (2002; MNRAS 337, 147) such that :
EW shoulder
= EW
Fe Kα
(0.1 + 0.1 cos i)
The model parameters are : par1= γ power-law photon index, N
E
E -γ
. par2 = E c cutoff energy in keV (if E c
= 0 there is no cutoff). par3 = scale the scaling factor for reflection;
< 0 => no direct component,
=1 => isotropic source above the disk par4 = z redshift par5 = A abundance of elements heavier than He relative to Solar. par6 = A fe
iron abundance relative to Solar. par7 = cos i cosine of the inclination angle.
K normalization is the photon flux at 1 keV (photons/keV/cm
2
/s) of the cutoff
power law only (without reflection) and in the Earth frame.
6.2.63 pexrav: reflected powerlaw, neutral medium
Exponentially cut off power law spectrum reflected from neutral material (Magdziarz &
Zdziarski 1995, MNRAS, 273, 837). The output spectrum is the sum of the cut-off power law and the reflection component. The reflection component alone can be obtained for
rel
refl
0
. Then the actual reflection normalization is
rel
refl
. Note that you need to change then the limits of refl
E
c
= 0 there is no cutoff in the power law. The metal and iron abundance are variable with respect to those defined by the command abund. The opacities are those set by the command xsect. As expected in AGNs, H and He are assumed to be fully ionized
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached.
The precision can be changed by setting PEXRAV_PRECISION eg xset
PEXRAV_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1
, first power law photon index,
N
E
E
par2 par3
226
E
c
, cutoff energy (keV) (if
E
c
= 0 there is no cutoff)
rel
refl
, reflection scaling factor (0, no reflected component <
rel
refl
< 1 for isotropic source above disk) par5 par6 par7 norm abundance of elements heavier than He relative to the solar abundances iron abundance relative to that defined by abund cosine of inclination angle photon flux at 1 keV (photons keV
–1 cm
-2 s
-1
) of the cutoff broken power-law only (no reflection) in the observed frame.
6.2.64 pexriv: reflected powerlaw, ionized medium
Exponentially cut off power law spectrum reflected from ionized material (Magdziarz &
Zdziarski MNRAS, 273, 837; 1995). Ionization and opacities of the reflecting medium is computed as in the absori model. The output spectrum is the sum of the cutoff power law and the reflection component. The reflection component alone can be obtained for
rel
refl
0
. Then the actual reflection normalization is
rel
refl
. Note that you need to change then the limits of refl
E
c
= 0 there is no cutoff in the power law. The metal and iron abundances are variable with respect to those defined by the command abund.
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached.
The precision can be changed by setting PEXRIV_PRECISION eg xset
PEXRIV_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1
, first power law photon index,
N
E
E par2 par3
E
c
, cutoff energy (keV) (if
E
c
= 0 there is no cutoff)
rel
refl
, reflection scaling factor (0, no reflected component <
rel
refl
< 1 for isotropic source above disk) par5 par6 abundance of elements heavier than He relative to the solar abundances iron abundance relative to that defined by abund
par7
227
cosine of inclination angle par9 norm disk ionization parameter,
4
F ion n
, where
F
ion
is the 5eV – 20keV irradiating flux, n is the density of the reflector; see Done et al., 1992, ApJ,
395, 275. photon flux at 1 keV (photons keV
–1 cm
-2 s
-1
) of the cutoff broken power-law only (no reflection) in the observed frame.
6.2.65 plcabs: powerlaw observed through dense, cold matter
This model describes X-ray transmission of an isotropic source of photons located at the center of a uniform, spherical distribution of matter, correctly taking into account
Compton scattering. The model can be used for radial column densities up to
5
10
24 cm
-2
. The valid energy range for which data can be modeled is between 10 and
18.5 keV, depending on the column density. Details of the physics of the model, the approximations used and further details on the regimes of validity can be found in
Yaqoob (1997; ApJ, 479, 184). In this particular incarnation, the initial spectrum is a power law modified by a high-energy exponential cut-off above a certain threshold energy.
Also, to improve the speed, a FAST option is available in which a full integration over the input spectrum is replaced by a simple mean energy shift for each bin. This option is obtained by setting parameter 9 to a value of 1 or greater and cannot be made variable. Further, for single-scattering albedos less than ACRIT ( i.e. par8
) energy shifts are neglected altogether. The recommended value is ACRIT=0.1 which corresponds to about 4 keV for cosmic abundances and is more than adequate for ASCA data.
Note that for column densities in the range 10
23
– 10
24
cm
-2
, the maximum number of scatterings which need be considered for convergence of the spectrum of better than 1% is between 1 and 5. For column densities as high as
5
10
24 cm
-2 maximum number of scatterings which need be considered for the same level of convergence is 12. This parameter cannot be made variable.
, the par1 Column density in units 10
22
cm
–2 par2 Maximum number of scatterings to consider. par4 Iron K edge energy.
par5 par6 par7 par8 par9
Power-law photon index.
High-energy cut-off threshold energy.
High-energy cut-off e-folding energy.
Critical albedo for switching to elastic scattering.
If par9
> 1, function uses mean energy shift, not integration.
228
6.2.66 posm: positronium continuum
Positronium continuum (Brown & Leventhal 1987 ApJ 319, 637)
K
(
2
2
9)
E
C
A
(E )
E
(2
(
E
C
E
C
-
-E
)
E
)
2
2
E
C
(
E
C
E
2
-
E
) log
E
C
-
E
C
E
-
2
E
C
(
E
(2
E
C
C
-
-
E)
E
)
2
3 log
E
C
E
C
-
E
2
E
C
E
-
E
for E < Ec = 511 keV, where: norm = K normalization.
6.2.67 powerlaw, zpowerlw: power law photon spectrum
powerlaw is a simple photon power law. The zpowerlw variant computes a redshifted spectrum.
KE
par1 =
norm=
K
photon index of power law (dimensionless) photons keV
–1 cm
–2 s
–1
at 1 keV
229
For zpowerlw the formula and corresponding parameters are:
A
(
E
)
K
E
( 1
z
)
1
z
where : par1=
photon index of power law (dimensionless) par2=
z
Redshift norm=
K
photons keV
–1 cm
–2 s
–1
at 1 keV
If POW_EMIN and POW_EMAX have been defined by the xset command then the norm becomes the flux in units of 10
-12
ergs cm
-2
s
-1
over the energy range (POW_EMIN,
POW_EMAX) keV unless POW_EMIN = POW_EMAX in which case the norm becomes the flux density in micro-Jansky at POW_EMIN keV. In these cases it is important that POW_EMIN and POW_EMAX lie within the energy range on which the model is being evaluated.
6.2.68 pshock, vpshock: plane-parallel shocked plasma, constant temperature
Constant temperature, plane-parallel shock plasma model. The references for this model can be found under the description of the equil model. Several versions are available. To switch between them use the xset
neivers
command. xset
neivers 1.0
gives the version from xspec v11.1, xset
neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset neivers 2.0
uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1. ]
The pshock version has abundances given by the Anders & Grevesse (1993) mixture, while the vpshock variant allows the user to set the abundance vector.
Parameters for the pshock version are: par1 plasma temperature (keV) par2 Metal abundances (He fixed at cosmic). The elements included are
C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni in ratios set by the abund command.
par3 par4
Lower limit on ionization timescale in units of s cm
–3
.
Upper limit on ionization timescale in units of s cm
–3
.
230
norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e , densities respectively.
n
H
(cm
-3
) are the electron and hydrogen
Parameters for vpshock are: par1 par2 plasma temperature (keV)
H density in cm
-3 par3-par14 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt the solar as defined by the abund command. par15 par16
Lower limit on ionization timescale in units of s cm
–3
.
Upper limit on ionization timescale in units of s cm
–3
. norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e , densities respectively.
n
H
(cm
-3
) are the electron and hydrogen
6.2.69 raymond, vraymond: emission, hot diffuse gas,
Raymond-Smith
An emission spectrum from hot, diffuse gas based on the model calculations of Raymond and Smith (ApJS 35, 419 and additions) including line emissions from several elements.
This model interpolates on a grid of spectra for different temperatures. The grid is logarithmically spaced with 80 temperatures ranging from 0.008 to 80 keV.
The vraymond variant allows independent parameters to set the abundances.
Abundances are the number of nuclei per Hydrogen nucleus relative to the Solar abundances as set by the abund command.
For raymond the parameters are: par1 par2 plasma temperature (keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni.
Abundances are given by the Anders & Grevesse mixture.
231
norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e ,
n
H
(cm
-3 and hydrogen densities respectively.
) are the electron
For vraymond the parameters are: par1 plasma temperature (keV) par2-par13 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm), and
n
e ,
n
H
(cm
-3 and hydrogen densities respectively.
) are the electron
6.2.70 redge: emission, recombination edge
Recombination edge emission.
0
A
(E )
E
E
c
232
K T p
) exp
(
c
T
P
)
where: par1= E
Threshold energy par2=
T
p
Plasma temperature (keV) norm= K Photons s
–1
in the line
E
E
c
6.2.71 refsch: reflected power law from ionized accretion disk
Exponentially cut-off power-law spectrum reflected from an ionized relativistic accretion disk. In this model, spectrum of
pexriv
is convolved with a relativistic disk line profile diskline
. See Magdziarz & Zdziarski 1995 MNRAS, 273, 837 for details of Compton reflection. See Fabian et al. 1989, MNRAS, 238, 729 for details of the disk line profile. par1 par2
, power law photon index,
N
E
E
E
c
, cutoff energy (keV) (if 0 par3
rel
refl
, reflection scaling factor (0, no direct component <
rel
refl
< 1 for isotropic source above disk) par5 par6 par7 abundance of elements heavier than He relative to the solar abundances iron abundance relative to that defined by abund inclination angle (degrees) par9 par10 =
disk ionization parameter,
4
F ion
, where
F
ion
is the 5eV – 20keV
n
irradiating flux, n is the density of the reflector; see Done et al., 1992, ApJ,
395, 275. power law dependence of emissivity. the emissivity
R
233
par11 inner radius (units of par12 outer radius (units of par13 norm internal model accuracy - points of spectrum per energy decade photon flux at 1 keV (photons keV
–1 cm
-2 s
-1
) of the cutoff broken power-law only (no reflection) in the observed frame.
6.2.72 sedov, vsedov: sedov model, separate ion/electron temperature
Sedov model with separate ion and electron temperatures. This model is slow. par1 provides a measure of the average energy per particle (ions+electrons) and is constant throughout the postshock flow in plane shock models (Borkowski et al., 2001, ApJ, 548,
820). par2
should always be less than
par1
. If par2
exceeds
par1
then their interpretations are switched (ie the larger of
par1
and
par2
is always the mean temperature). Additional references can be found under the help for the equil model.
Several versions are available. To switch between them use the xset
neivers command. xset
neivers 1.0
gives the version from xspec v11.1, xset
neivers 1.1
uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset
neivers 2.0
uses the same ionization fractions as
1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.
The sedov model has relative abundances determined by the solar Anders and Grevesse mixture, while the vsedov variant allows the user to set the abundances.
Parameters for sedov are: par2 par3 par4 electron temperature immediately behind the shock front
(keV)
Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Relative abundances are defined by the abund command ionization age (s cm
–3
) of the remnant (= electron density immediately behind the shock front multiplied by the age of
the remnant) norm
4
10
14
D
A
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
For vsedov the parameters are: par2 par3 electron temperature immediately behind the shock front
(keV)
H density in cm
-3 par4-par15 Abundances for He, C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command) par4 ionization age (s cm
–3
) of the remnant (= electron density immediately behind the shock front multiplied by the age of the remnant)
234
norm
4
10
D
A
14
(1
z
)
2
where
D
A
is the angular diameter distance to the source (cm) , and
n
e ,
n
H
(cm
-3
) are the electron and hydrogen densities respectively.
6.2.73 sirf: self-irradiated funnel
The multi-blackbody "Self-IrRadiated Funnel" model is designed to model opticallythick outflow-dominated accretion. The basic idea is simple: you just assume a lot of matter, angular momentum and energy emerges in a limited volume. Momentum conservation leads to non-sphericity of the flow that has subsequently conical (funnellike) shape. The model calculates temperature distribution at the funnel walls (taking into account irradiation by iterative process) and the outer photosphere. We also assume that inside the cone there is a deep pseudo-photosphere. Relativistic boosts are taken into
235
account for high velocities. For a comprehensive description of the physical model, see:
Abolmasov, P., Karpov, S. and Kotani, T. PASJ, 61, 2, 213
. par1 par2 tin, inner temperature (at the inner, inside-the-funnel photosphere). par3 par4 rin, inner (inside-the-funnel photosphere) radius in "spherisation radius" units
(the latter is defined as 3 Κ Mdot / Ω f
c). rout, outer photosphere radius in "spherisation radius" units. theta, half-opening angle of the cone. par5 par6 par7 incl, inclination angle of the funnel. Affects mainly self-occultation and relativistic boost effects. valpha, velocity law exponent, v goes as r valpha
. gamma, adiabatic index. It affects the inner, hotter parts of the flow, therefore we set is to 4/3 by default. par8 mdot, mass ejection rate in Eddington (critical) units. par9 irrad, number of iterations for irradiation. norm
6.2.74 plasma. smaug: optically-thin, spherically-symmetric thermal
This model performs an analytical deprojection of an extended, optically-thin and spherically-symmetric source. A thorough description of the model is given in Pizzolato et al. (ApJ 592, 62, 2003). In this model the 3D distributions of hydrogen, metals and temperature throughout the source are given specific functional forms dependent on a number of parameters, whose values are determined by the fitting procedure. The user has to extract the spectra in annular sectors, concentric about the emission peak. The inner boundary (in arcmin), the outer by the fitting procedure. The user has to extract the spectra in annular sectors, concentric about the emission peak. The inner boundary (in arcmin), the outer boundary (also in arcmin), and the width (in degrees) of each annular sector are specified (respectively) by the three additional keywords XFLT0001,
XFLT0002, and XFLT0003, to be added to the spectrum extension in each input file (e.g. with the ftool FKEYPAR). Some parameters of smaug define the redshift and other options (see below). The other, 'relevant' ones define the 3D distributions of hydrogen density, temperature and metal abundance, determined by a simultaneous fit of the spectra. The cosmological parameters can be set using the cosmo
command.
par15 par16 par17 par18 par11 par12 par13 par14 par19 par20 par5 par6 par7 par8 par1 par2 par3 par4 par9 par10 par21 central temperature [keV] max difference of temperature [keV] exponent of the inner temperature radius of the inner temperature [Mpc] exponent of the middle temperature radius of the middle temperature [Mpc] exponent of the outer temperature radius of the outer temperature [Mpc] central hydrogen density [cm**-3] fraction of nH.cc relative to the 1st beta component exponent of the first beta component radius of the 1st beta component [Mpc] exponent of the 2nd beta component radius of the 2nd beta component [Mpc] central metallicity [solar units] exponent of the metal distribution radius of the metal distribution [Mpc] redshift of the source number of mesh-points of the dem summation grid cutoff radius for the calculation [Mpc] mode of spectral evaluation: 0 = calculate, 1 = interpolate, 2 = APEC interpolate
236
237
par22 type of plasma emission code, 1 = Raymond-Smith, 2 = Mekal, 3 = Meka,
4 = APEC
K
H
0 model normalisation (nH.cc squared [cm**-6] )
Note that if the interactive chattiness level in XSPEC is set to a value > 10, smaug also prints on screen the following quantities:
Hubble constant [km/s/Mpc] q
0
L
0 deceleration parameter cosmological constant
DA
DSET source angular distance [Mpc] dataset no. to which the quantities listed below are
IN
OUT inner rim of the projected annular sector [Mpc] outer rim of the projected annular sector [Mpc]
WID
EVOL
EINT width of the projected annular sector [deg] emitting volume within the integration radius cutoff [Mpc
3
] emission integral within the integration radius cutoff [ Mpc
3 cm
-
6]. If nH.cc is frozen to 1, the actual EI is obtaned by multiplying this figure by the square root of the model normalisation
6.2.75 srcut: synchrotron spectrum, cutoff power law
srcut
describes the synchrotron spectrum from an exponentially cut off power-law distribution of electrons in a homogeneous magnetic field. This spectrum is itself a power-law, rolling off more slowly than exponential in photon energies. Though more realistic than a power-law, it is highly oversimplified, but does give the maximally curved physically plausible spectrum and can be used to set limits on maximum accelerated-electron energies even in remnants whose X-rays are thermal. See Reynolds,
S.P. & Keohane, J.W. 1999, ApJ, 525, 368 and Reynolds, S.P., 1998 ApJ 493, 357. Note that the radio spectral index and flux can be obtained from Green's Catalogue at
http://www.mrao.cam.ac.uk/surveys/snrs
for galactic SNRs.
238
par1 par2 alpha: radio spectral index break Hz: approximately the frequency at which the flux has dropped by a factor of 10 from a straight power law.
1 GHz flux (Jy) norm
6.2.76 sresc: synchrotron spectrum, cut off by particle escape
The synchrotron spectrum from an electron distribution limited by particle escape above some energy. The electrons are shock-accelerated in a Sedov blast wave encountering a constant-density medium containing a uniform magnetic field. The model includes variations in electron acceleration efficiency with shock obliquity, and post-shock radiative and adiabatic losses, as described in Reynolds, S.P., ApJ 493, 357 1998. This is a highly specific, detailed model for a fairly narrow set of conditions. See also Reynolds,
S.P., ApJL 459, L13 1996. Note that the radio spectral index and flux can be obtained from Green's Catalogue at
http://www.mrao.cam.ac.uk/surveys/snrs
for galactic
SNRs. par1 alpha: radio spectral index (flux proportional to frequency
f
) par2 norm break Hz: approximately the frequency at which the flux has dropped by a factor of 6 below a straight power law extrapolation from radio frequencies. This frequency is 5.3 times the peak frequency radiated by electrons with energy
E
m3
in a magnetic field of 4
B
1
, in the notation of Reynolds (1998), Eq. (19).
1 GHz flux (Jy)
6.2.77 step: step function convolved with gaussian
A step function convolved with a gaussian.
A
(
E
)
K
2
1
erf
E
2
E
S
par1=
E start energy (keV) par2=
gaussian sigma (keV) norm= K step
239
6.3 Multiplicative Model Components
6.3.1 absori: ionized absorber
An ionized absorber based on that of Done et al. (1992, ApJ 395, 275) and developed by Magdziarz & Zdziarski. See also Zdziarski et al. (1995, ApJ 438, L63).
Photoionization rates are from Reilman & Manson (1979, ApJS 40, 815), who employ the Hartree-Slater approximation (accurate to about 5%), and recombination rates are from Shull & Steenburg (1982, ApJS 48, 95). The cross sections are extrapolated with
E
–
3
above 5 keV. The abundances are set up by the command abund. Send questions or comments to
par1 power-law photon index. par2 par6
Hydrogen column in units of 1022cm–2 par3 Absorber temperature in K. par4 Absorber ionization state (L/nR2), see Done et al. (1992) par5
z
redshift.
Iron abundance relative to that defined by the command abund
6.3.2 acisabs: Chandra ACIS q.e. decay
This model accounts for the decay in the ACIS quantum efficiency most likely caused by molecular contamination of the ACIS filters. The user needs to supply the number of days between Chandra launch and observation. The acisabs
parameters related to the composition of the hydrocarbon and the rate of decay should be frozen and not modified.
The present version of acisabs
is to be used for the analysis of bare ACIS I and ACIS S data. For the present version of acisabs
one must use the standard qe file vN0003 instead of the optional vN0004 file.
Because of the present large uncertainty in the ACIS gain at energies below
350eV we recommend that events in the 0—350eV range be ignored in the spectral analysis until the gain issue is resolved. acisabs calculates the mass absorption coefficients of the contaminant from atomic scattering factor files provided at
http://henke.lbl.gov/optical_constants/asf.html
.
240
par1 par2 par3 par4 par5 par6 par7
Days between Chandra launch and ACIS observation
Slope of linear quantum efficiency decay
Offset of linear quantum efficiency decay
Number of carbon atoms in hydrocarbon
Number of hydrogen atoms in hydrocarbon
Number of oxygen atoms in hydrocarbon
Number of nitrogen atoms in hydrocarbon
6.3.3 cabs: Optically-thin Compton scattering.
Optically-thin Compton scattering.
M
(
E
)
exp
n
H
T
(
E
)
where
T
(
E
) is the Thomson cross-section with Klein-Nishina corrections at high energies. Note that this model does not do frequency downshifting so is only valid for scattering out of the beam. par1=
n hydrogen column (in units of 10
22
atoms cm
–2
)
6.3.4 constant: energy-independent factor
An energy-independent multiplicative factor. par1= factor
6.3.5 cyclabs: absorption line, cyclotron
A cyclotron absorption line as used in pulsar spectra. See Mihara et al., Nature, 1990 or
Makishima et al. PASJ, 1990.
D
f
(
cycl
)
2 cycl
2
W
f
2
D
2h
h
2
(
E
2
E
cycl
)
2 cycl
2
W
2h
2
par1=
D
f depth of the fundamental
241
par2=
E
cycl
cyclotron par3=
W
f width of the fundamental par4=
D
2h depth 2nd harmonic par5=
W
2h width of the 2nd harmonic
6.3.6 dust: dust scattering
A modification of a spectrum due to scattering off dust on the line-of-sight. The model assumes that the scattered flux goes into a uniform disk whose size has a 1/E dependence and whose total flux has a 1/E
2
dependence. par1 par2 scattering fraction at 1 keV size of halo at 1 keV in units of the detector beamsize
6.3.7 edge, zedge: absorption edge
The edge model is absorption edge, given by.
M
(E )
1
E
E
c exp
D
E E c
3
E
E c
where: par1= E threshold energy par2
D
absorption depth at the threshold
The zedge model given by
M
(E )
1
E < E
c exp
D
E
( 1
z
) /
E c
3
E > E
c allows a redshift z where: par1 =
E
c
242
par2= D absorption depth at threshold par3= z redshift
6.3.8 etable: exponential tabular model
An exponential table model. The filename to be used should be given immediately after etable in the model command. For example:
XSPEC12>
model
etable{mymod.mod} uses mymod.mod as the input for the model. XSPEC will multiply the contents of the model by –1 then take the exponential i.e. this model is for calculating absorption functions. For specifications of the table model file, see the OGIP memo 92-009 on the
FITS file format for table model files (available on the WWW or by anonymous ftp from
ftp://legacy.gsfc.nasa.gov/caldb/docs/memos
.).
6.3.9 expabs: exponential roll-off at low E
A low-energy exponential rolloff.
M
(
E
)
exp(
E c
where: par1= E
c
e-folding energy for the absorption
E
)
6.3.10 expfac: exponential modification
An exponential modification of a spectrum.
1
A
exp(
fE
)
E
E c
M
(E )
1
E
E c
where: par1= A amplitude of effect par2= f exponential par3=
E c
start
6.3.11 gabs: gaussian absorption line
par
3
2
par
2 exp
.5
par
2
2
where :
par1 = line energy in keV.
par2 = line width (sigma) in keV.
par3 = line depth. The optical depth at line center is par3/par2/√(2π).
6.3.12 heilin: Voigt absorption profiles for He I series
This model calculate the Voigt absorption profiles for the He I series. par1 nHeI: He I column density (10
22
atoms/cm
2
)
par2
par3 b: b value (km/s) z: Redshift
243
6.3.13 highecut, zhighect: high-energy cutoff
A high energy cutoff. exp
E c
E
E f
E
E c
M
( E )
1.0
E
E c
where par1=
E c
cutoff energy in keV par2=
E f
e-folding energy in keV
The redshifted version zhighect has.
M
( E )
exp
E c
E
1
z
E s
E
E c
244
1.0 where : par1=
E c
par2=
E f
par3 = z cutoff energy in keV e-folding energy in keV redshift
E
E c
6.3.14 hrefl: reflection model
A simple multiplicative reflection model due to Tahir Yaqoob. This model gives the reflected X-ray spectrum from a cold, optically thick, circular slab with inner and outer radii (
R
i
&
R
o
, respectively) illuminated by a point source a height H above the center of the slab. The main difference between this model and other reflection models is that analytic approximations are used for the Chandrasekar H functions (and their integrals) and ELASTIC SCATTERING is assumed (see Basko 1978, ApJ, 223, 268). The elasticscattering approximation means that the model is ONLY VALID UP TO 15 keV in the source frame. Future enhancements will include fudge factors that will allow extension up to 100 keV. The fact that no integration is involved at any point makes the routine very fast and particularly suitable for generating error contours, especially when fitting a large number of data channels. The model is multiplicative, and so can be used with
ANY incident continuum.
Parameters are as follows: par1 minimum angle (degrees) between source photons incident on the slab and the slab normal
tan
1
par2 maximum angle (degrees) between source photons incident on the slab and the slab normal
tan
1
par3 par4
Angle (degrees) between the observer's line of sight and the slab normal.
Iron abundance relative to Solar par5 Iron energy par6 par7
Fraction of the direct flux seen by the observer
Normalization of the reflected continuum
245
par8 redshift
Suppose the incident photon spectrum is N(E) photons cm
–2 s
–1 keV
–1
and that the incident continuum is steady in time, and suppose further that the reflected continuum from the slab is R(E). When you multiply the incident spectrum with hrefl
, what you actually get is the following:
par6
par7
Thus, the actual physical situation described above corresponds to par6
=1.0 par7
=1.0.
You may decide to float par6 and/or par7. In that case, you must decide what the bestfitting values of these parameters mean physically for your case. It may imply time-lags between the direct and reflected components, different source and/or disk geometries to those assumed, or something else.
6.3.15 series lyman: Voigt absorption profiles for H I or He II Lyman
This model calculate the Voigt absorption profiles for the H I and He II Lyman series. par1 n: H I or He II column density (10
22
atoms/cm
2
)
par2 b: b value (km/s) z: Redshift
par3 par4
ZA: Atomic number of species being calculated
6.3.16 mtable: multiplicative tabular model
A multiplicative table model. The filename to be used should be given immediately after mtable
in the model command. For example:
XSPEC12>
model
mtable{mymod.mod} uses mymod.mod
as the input for the model. For specifications of the table model file, see the OGIP memo 92-009 on the FITS file format for table model files (available on the
WWW or by anonymous ftp from
ftp://legacy.gsfc.nasa.gov/caldb/docs/memos
. A sample multiplicative table model file is testpcfabs.mod
in
$HEADAS/../spectral/session.
246
6.3.17 notch: absorption line, notch
A notch line absorption. This is model is equivalent to a very saturated absorption line.
(1
f E
W
L
W
/ 2
( )
1 elsewhere where par1=
E
L line energy (keV) par2= W line width (keV) par3= f covering
6.3.18 pcfabs, zpcfabs: partial covering fraction absorption
A partial covering fraction absorption. The relative abundances are set by the abund command.
( )
f
exp
n
H
( )
f
) where
(E) is the photo-electric cross-section (NOT including Thomson scattering) (see phabs
) and: par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2= f covering fraction 0
par2
1 (dimensionless)
The redshifted variant zpcfabs is given by:
( )
f
exp
n
H
E
1
z
1
f
where
(E) is the photo-electric cross-section (NOT including Thomson scattering) (see phabs
). Relative abundances are as for pcfabs. Parameters are: par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2= f dimensionless covering fraction
0
f
par3= z redshift
247
6.3.19 phabs, vphabs, zphabs, zvphabs: photoelectric absorption
A photoelectric absorption using cross-sections set by the xsect command. The relative abundances are set by the abund command.
n
H
( )
where
(E) is the photo-electric cross-section (NOT including Thomson scattering). Note that the default He cross-section changed in v11. The old version can be recovered using the command
xsect obcm par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
)
The redshifted variant, zphabs, uses the formula
n
H
E
1
z
and has parameters par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2= z Redshift
The variants vphabs, zvphabs allow the user to set fixed abundance parameters with respect to the solar composition, as defined by the abund command. For vphabs (restframe) the parameters are par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2–par18 abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr,
Fe, Co, Ni wrt to Solar
While the corresponding redshifted variant zvphabs has parameters par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2-par18 abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr,
Fe, Co, Ni wrt to Solar (defined by the abund command) par19= z redshift
6.3.20 plabs: power law absorption
Absorption as a power-law in energy. Useful for things like dust.
248
( )
KE
par1=
index par2= K coefficient
6.3.21 pwab: power-law distribution of neutral absorbers
An extension of partial covering fraction absorption into a power-law distribution of covering fraction as a function of column density, built from the wabs code. See Done
& Magdziarz 1998 (MNRAS 298, 737) for details.
par1 = minimum equivalent hydrogen column (in units of 10**22 atoms/cm**2)
par2 = maximum equivalent hydrogen column (in units of 10**22 atoms/cm**2)
par3 = power law index for covering fraction.
6.3.22 recorn: change correction norm for a spectrum
This model is a replacement for and improvement on the old xspec command recornrm.
If a correction file is in use for a spectrum then its normalization can be fitted for using this model. The first parameter, which is not variable, is the spectrum number and the second the correction file normalization. The starting value of the second parameter should be set to the current value of the correction file norm (this can be independently set using the cornorm command).
Note that in order to fit the cornorm parameter, the
USE_NUMERICAL_DIFFERENTIATION setting in the user’s Xspec.init start-up file must be set to true. This causes XSPEC to use a slower full numerical differentiation algorithm when calculating parameter derivatives during a fit, and therefore is not recommended for general usage. par1 par2 specnum: spectrum number cornorm: correction file normalization
6.3.23 redden: interstellar extinction
IR/optical/UV extinction from Cardelli et al. (1989, ApJ, 345, 245). The transmission is set to unity shortward of the Lyman limit. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs.
249
par1
E(B-V)
6.3.24 smedge: smeared edge
A smeared edge (Ebisawa PhD thesis, implemented by Frank Marshall).
1
E < E c
M E
exp
f E E c
)
E c
/
c
where: par1=
E c
the threshold energy (keV) par2= f par3=
the maximum absorption factor at threshold index for photo-electric cross-section (normally –2.67) par4= W smearing width (keV)
6.3.25 spexpcut: super-exponential cutoff absorption
A high-energy super-exponential roll-off.
E
E
C
useful for fitting gamma-ray spectra of pulsars (see eg Nel & de Jager 1995), where: par1= E
c
e-folding energy for the absorption par2 = α exponent index
Caveat : the absorption for an energy bin is calculated as the arithmetic mean of the function value at the start and end energies of the bin. If the energy bins are large this can be inaccurate and the energies command should be used to define a finer energy grid on which to calculate the model.
6.3.26 spline: spline modification
A cubic spline modification.
250
6.3.27 SSS ice: Einstein SSS ice absorption
The Einstein Observatory SSS ice absorption. par1 ice thickness parameter
6.3.28 swind1: absorption by partially ionized material with large velocity shear
A model to fit the soft excess in AGN by partially ionized absorbing material with large velocity shear. It approximates this by using XSTAR kn5 photoionization absorption model grids (calculated assuming a microturbulent velocity of 100km/s), and then convolving this with Gaussian smearing. This is the model used by Gierlinski &
Done 2006, Sobolewska & Done 2006 and Done et al 2006. It is an update (uses a newer version of XSTAR) of the original model of Gierlinski & Done 2004. par1 = column density (10
22
cm
-2
) par2 = log(xi) where xi=L/nr
2 par3 = sigma : Gaussian sigma for velocity smearing (v/c) par4 = redshift
6.3.29 tbabs, ztbabs, tbgrain, tbvarabs: ISM grain absorption
The Tuebingen-Boulder ISM absorption model. This model calculates the cross section for X-ray absorption by the ISM as the sum of the cross sections for X-ray absorption due to the gas-phase ISM, the grain-phase ISM, and the molecules in the ISM.
In the grain-phase ISM, the effect of shielding by the grains is accounted for, but is extremely small. In the molecular contribution to the ISM cross section, only molecular hydrogen is considered. In the gas-phase ISM, the cross section is the sum of the
251
photoionization cross sections of the different elements, weighted by abundance and taking into account depletion onto grains.
In addition to the updates to the photoionization cross sections, the gas-phase cross section differs from previous values as a result of updates to the ISM abundances.
These updated abundances are available through the abund wilm
command. Details of updates to the photoionization cross sections as well as to abundances can be found in
Wilms, Allen and McCray (2000, ApJ 542, 914).
tbabs allows the user to vary just the molecular hydrogen column. par1 equivalent hydrogen column (in units of 10
22
atoms/cm
–2
)
ztbabs is similar, but allows the user to set a fixed redshift parameter par1 equivalent hydrogen column (in units of 10
22
atoms/cm
–2
) z
redshift
tbgrain allows the user to vary the molecular hydrogen column and the grain distribution parameters. par1 par2 par3 equivalent hydrogen column (in units of 10
22
atoms cm
–2
) molecular hydrogen column (in units of 10
22
atoms cm
–2
) grain density (in gm/cm
-3
) par4 par5 grain minimum size (in
m) grain maximum size (in
m) par6 power-law index of grain sizes redshift
tbvarabs additionally allows the user to vary the elemental abundances and the par1 equivalent hydrogen column (in units of 10
22
atoms cm
–2
)
252
par2 -par18 abundance (relative to Solar) of He, C, N, O, Ne, Na, Mg, Al, Si, S,
Cl, Ar, Ca, Cr, Fe, Co, Ni par19 par20 molecular hydrogen column (in units of 10
22
atoms cm
–2
) grain density (in gm/cm
-3
) par21 par22 grain minimum size (in
m) grain maximum size (in
m) par23 power-law index of grain sizes par24 par41 grain depletion fractions of He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl,
Ar, Ca, Cr, Fe, Co, Ni} par42 redshift
6.3.30 uvred: interstellar extinction, Seaton Law
A UV reddening using Seaton's law (M.N.R.A.S. 187, 75p). Valid from 1000–3704Å.
The transmission is set to unity shortward of the Lyman limit. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs
.
E(B-V) par1
6.3.31 varabs, zvarabs: photoelectric absorption
A photoelectric absorption with variable abundances using cross-sections set by the xsect command. The column for each element is in units of the column in a solar abundance column of an equivalent hydrogen column density of 10
22 cm
–2
. The Solar abundance table used is set by the abund command. These models differ from the models vphabs, zvphabs only by the units in which the abundances are expressed (vphabs, zvphabs define these relative to the solar abundance, not in terms of column density). par1- par18 equivalent columns for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl,
Ar, Ca, Cr, Fe, Co, Ni
The zvarabs variant allows the user to specify a (fixed) redshift, i.e. the parameters are: par1–par18 equivalent columns for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl,
Ar, Ca, Cr, Fe, Ni, Co
253
par19 redshift
6.3.32 sections wabs, zwabs: photoelectric absorption, Wisconsin cross-
A photo-electric absorption using Wisconsin (Morrison and McCammon; ApJ 270, 119) cross-sections.
n
H
( )
where
(E) is the photo-electric cross-section (NOT including Thomson scattering). Note that this model uses the Anders & Ebihara relative abundances (1982, Geochimica et
Cosmochimica Acta 46, 2363) regardless of the abund command. par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
)
The zwabs variant allows the user to specify a (fixed) redshift parameter, and uses the corresponding formula
n
H
E
1
z
par1= nH equivalent hydrogen column (in units of 1022 atoms cm–2) par2= z redshift
6.3.33 wndabs, zwndabs: photo-electric absorption, warm absorber
Photo-electric absorption from approximation to a warm absorber using Balucinska,-
Church, and McCammon (ApJ 400, 699) cross-sections. Relative abundances are set by the abund command.
M E
1
E > E
W
exp
n
H
( )
W
where
(E) is the photo-electric cross-section (NOT including Thomson scattering) and par1=
n
H
equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2=
E
W
window energy (keV)
254
The zwndabs variant allows the user to specify a (fixed) redshift and uses the corresponding formula: exp
n
H
E
1
z
M E
W
1
E > E
W
with parameters: par1= nH equivalent hydrogen column (in units of 1022 atoms cm–2) par2= EW window energy (keV) par3= z redshift
6.3.34 disk/ring xion: reflected spectrum of photo-ionized accretion
This model describes the reflected spectra of a photo-ionized accretion disk or a ring if one so chooses. The approach is similar to the one used for tables with stellar spectra.
Namely, a large number of models are computed for a range of values of the spectral index, the incident X-ray flux, disk gravity, the thermal disk flux and iron abundance.
Each model's output is an un-smeared reflected spectrum for 5 different inclination angles ranging from nearly pole-on to nearly face on, stored in a look-up table. The default geometry is that of a lamppost, with free parameters of the model being the height of the X-ray source above the disk,
h
X
, the dimensionless accretion rate through the disk,
m , the luminosity of the X-ray source, L
X
, the inner and outer disk radii, and the spectral index. This defines the gravity parameter, the ratio of X-ray to thermal fluxes, etc., for each radius, which allows the use of a look-up table to approximate the reflected spectrum. This procedure is repeated for about 30 different radii. The total disk spectrum is then obtained by integrating over the disk surface, including relativistic smearing of the spectrum for a non-rotating black hole (e.g., Fabian 1989).
In addition, the geometry of a central sphere (with power-law optically thin emissivity inside it) plus an outer cold disk, and the geometry of magnetic flares are available ( par
13 = 2 and 3, respectively). One can also turn off relativistic smearing to see what the local disk spectrum looks like ( par12
= 2 in this case; otherwise leave it at
4). In addition, par11
= 1 produces reflected plus direct spectrum/direct; par11
=2 produces (incident + reflected)/incident [note that normalization of incident and direct are different because of solid angles covered by the disk; 2 should be used for magnetic flare model]; and par11
=3 produces reflected/incident. Abundance is controlled by par9
and varies between 1 and 4 at the present. A much more complete description of the model will be presented in Nayakshin et al. 2001 (currently available at
http://adsabs.harvard.edu/cgi-bin/nph-
255 bib_query?bibcode=2001ApJ...546..406N&db_key=AST&data_type=HT
ML&format=&high=4230b2429423803
) par1 height of the source above the disk (in Schwarzschild radii) par2 par3 par4 ratio of the X-ray source luminosity to that of the disk accretion rate (in Eddington units) cos i
the inclination angle (1 = face-on) par5 par6 par7 inner radius of the disk (in Schwarzschild radii) outer radius of the disk (in Schwarzschild radii) photon index of the source par9
par10
par11
par12
par13
Fe abundance relative to Solar (which is defined as number relative to H)
5
by
Exponential high energy cut-off energy for the source
1
(reflected+direct)/direct
2
(reflected+incident)/incident
3
reflected/incident
2
no relativistic smearing
4
relativistic smearing
1
lamppost
2
central hot sphere with outer cold disk
3
magnetic flares above a cold disk
Note that setting par13 to 2 gives a central hot sphere with
dL dR
4
10
y
luminosity law . The inner radius of the sphere is
3 Schwarzschild radii and the outer radius is equal to par1. Only the case with par5 par1 has been tested so far.
256
6.3.35 zbabs: EUV ISM attenuation
The ISM attenuation due to neutral H, neutral He and once ionized He. This is a modified version of the
Rumph, et al. 1994
model, using the ismatten program by Pat Jelinsky, and allows the user to set the model redshift. par1
par2
par3 nH: H column density (10
22
atoms/cm
2
) nHeI: HeI column density (10
22
atoms/cm
2
) nHeII: HeII column density (10
22
atoms/cm
2
) par4 z: Redshift
6.3.36 zdust: extinction by dust grains
Extinction by dust grains from Pei (1992, ApJ 395, 130), suitable for IR, optical and UV energy bands, including the full energy ranges of the Swift UVOT and XMM-Newton
OM detectors. Three models are included which characterize the extinction curves of (1) the Milky Way, (2) the LMC and (3) the SMC. The models can be modified by redshift and can therefore be applied to extragalactic sources. The transmission is set to unity shortward of 912 Angstroms in the rest frame of the dust. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs. Parameter 1 (method) describes which extinction curve (MW, LMC or SMC) will be constructed and should never be allowed to float during a fit. The extinction at V, A(V) = E(B-V) x Rv. Rv should typically remain frozen for a fit.
Standard values for Rv are MW = 3.08, LMC = 3.16 and SMC = 2.93 (from table 2 of Pei
1992), although these may not be applicable to more distant dusty sources. par1 method: 1 = Milky Way, 2 = LMC, 3 = SMC par2 E(B-V): color excess par3 Rv: ratio of total to selective extinction
6.3.37 zigm: UV/Optical attenuation by the intergalactic medium.
This multiplicative model computes the mean attenuation of the optical/UV spectrum of an object at redshift z at a random position on the sky due to intergalactic medium (IGM) clouds following either Madau (1995, ApJ 441, 18) or Meiksin (2006, MNRAS, 365,
807). The model calculates the mean expected attenuation due to resonant scattering by
Lyman transitions and photoelectric absorption shortward of the Lyman limit.
Attenuation by Helium and metals are not included in the Meiksin model, but are expected to be small. The total attenuation is set to zero for wavelengths less than 900
Angstroms. The user chooses whether to include attenuation due to photoelectric absorption.
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par2 model: use Madau(0) or Meiksin(1)
6.3.38 zredden: redshifted version of redden
IR/optical/UV extinction from Cardelli et al. (1989, ApJ, 345, 245). The transmission is set to unity shortward of 900 Angstroms. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs.
par1 = E(B-V)
par2 = redshift
6.3.39 zsmdust: extinction by dust grains in starburst galaxies
Extinction by dust grains suited to starburst galaxies and the hosts of gamma ray bursts.
The model can be applied over the IR, optical and UV energy bands, including the full energy ranges of the Swift UVOT and XMM-Newton OM detectors. The transmission is set to unity shortward of 912 Angstroms in the rest frame of the dust. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs. The extinction curve contains no spectral features and is characterized by a powerlaw slope over spectral wavelength. This model has been justified by e.g. Savaglio & Fall (2004, ApJ, 614, 293) because the apparent low metallicities within GRB hosts result in no significant spectral features within the extinction curve, unlike those found in local galaxies. The extinction at V, A(V) = E(B-
V) x Rv. Standard values for Rv are Milky Way = 3.08, LMC = 3.16 and SMC = 2.93
(from table 2 of Pei 1992, ApJ, 395, 130), although these may not be applicable to more distant dusty sources. par1 E(B-V): color excess par2 ExtIndex: index of the extinction curve par3 Rv: ratio of total to selective extinction
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6.3.40 energy zvfeabs: photoelectric absorption with free Fe edge
Redshifted photoelectric absorption with all abundances tied to Solar except for iron. The
Fe K edge energy is a free parameter. par1 equivalent hydrogen column (in units of 10
22
atoms cm
–2
) par2 abundance relative to Solar par3 par4 iron abundance relative to Solar
Fe K edge energy
6.3.41 material zxipcf: partial covering absorption by partially ionized
This model uses a grid of XSTAR photionized absorption models (calculated assuming a microturbulent velocity of 200km/s) for the absorption, then assumes that this only covers some fraction f of the source, while the remaining (1-f) of the spectrum is seen directly. This is the model used by Reeves et al (2008) 'On why the iron K-shell absorption in AGN is not the signature of the local warm-hot intergalactic medium', and may also be more generally applicable to the spectral complexity seen in Narrow Line
Seyfert 1 AGN (Miller et al 2007, A&A, 463, 13). par1 = column density (10
22
cm
-2
) par2 = log(xi) where xi=L/nr
2 par3 = covering fraction par4 = redshift
6.4 Convolution Model Components
Convolution components apply a convolution operator to an input model flux calculated from a source (additive) model, as modified by other components (multiplicative factors or other convolution operators). They differ from multiplicative components, which only apply a bin-wise multiplicative factor, by allowing transformations of the flux across energy bins.
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6.4.1 cflux: calculate flux
A convolution model to calculate the flux of other model components. For example :
cflux*phabs*(pow + gauss) with the normalization of the power-law model fixed to a non-zero value gives the flux and error on the entire model.
phabs*cflux*(pow + gauss) again with the normalization of the power-law fixed to a non-zero value gives the unabsorbed flux and error. Finally,
phabs*(pow + cflux*gauss) with the normalizaton of the gaussian fixed to a non-zero value gives the flux and error on the gaussian component. Note that when the cflux model is used the normalization of one of the additive models must be fixed to a non-zero value. It is also important to ensure that the energy range over which the model is calculated (which is determined by the response matrix in use) covers the energy range for which the flux is calculated. If the model to which the cflux is applied integrates to zero then a divide-by-zero error will occur resulting in NaN values for the fit statistic.
Parameters are : par1=
min Minimum energy over which flux is calculated. par2=
max Maximum energy over which flux is calculated. par3=lg10Flux log (base 10) flux in erg/cm
2
/s
260
6.4.2 cpflux: calculate photon flux
A convolution model to calculate the photon flux of other model components. For example :
cpflux*phabs*(pow + gauss) with the normalization of the power-law model fixed to a non-zero value gives the photon flux and error on the entire model.
phabs*cpflux*(pow + gauss) again with the normalization of the power-law fixed to a non-zero value gives the unabsorbed photon flux and error. Finally,
phabs*(pow + cpflux*gauss) with the normalizaton of the gaussian fixed to a non-zero value gives the photon flux and error on the gaussian component. Note that when the cpflux model is used the normalization of one of the additive models must be fixed to a non-zero value. It is also important to ensure that the energy range over which the model is calculated (which is determined by the response matrix in use) covers the energy range for which the photon flux is calculated. If the model to which the cpflux is applied integrates to zero then a divide-by-zero error will occur resulting in NaN values for the fit statistic.
Parameters are : par1=
min
Minimum energy over which photon flux is calculated. par2=
max
Maximum energy over which photon flux is calculated. par3= Flux Photon flux in ph/cm
2
/s
6.4.3 gsmooth: gaussian smoothing
Gaussian smoothing with a variable width
( )
, which varies as the par2
power of the energy. The width at 6 keV is set with par1.
Note that the energy binning must be uniform. If the response energies are not uniformly spaced then the energies command should be used to set uniform energy binning.
( )
( )
1
E
/ 6
2 exp
1
2
( )
2
where : par1=
gaussian sigma at 6 keV
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par2=
power of energy for sigma variation
6.4.4 ireflect: reflection from ionized material
Convolution model for reflection from ionized material according to the method of Magdziarz & Zdziarski (1995, MNRAS, 273, 837). This is a generalization of the pexriv and bexriv models. Ionization and opacities of the reflecting medium is computed as in the absori model. The reflection component alone can be obtained for
rel
refl
0
Then the actual reflection normalization is |
rel
refl
|. Note that you need to change then the limits of
rel
refl
excluding zero (as then the direct component appears). If c
0 no cutoff in the power law. The metal and iron abundance are variable with respect to those set by the command abund.
When using this model it is essential to extend the energy range over which the model is calculated both on the high and low end. The high end extension is required because photons at higher energies are Compton down-scattered into the target energy range. The low energy extension may be required to calculate ionization fractions correctly. The energy range can be extended using the extend command. The upper limit on the energies should be set above that for which the input spectrum has significant flux. To speed up the model, calculation of the output spectrum can be limited to energies below a given value by using xset to define IREFLECT_MAX_E (in units of keV). For instance, suppose that the original data extends up to 100 keV. To accurately determine the reflection it may be necessary to extend the energy range up to 500 keV. Now to avoid calculating the output spectrum between 100 and 500 keV use the command xset
IREFLECT_MAX_E 100.0.
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached.
The precision can be changed by setting IREFLECT_PRECISION eg xset
IREFLECT_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1 par2 =
z
par3 par4 reflection scaling factor (1 for isotropic source above disk) redshift abundance of elements heavier than He relative to the solar abundances iron abundance relative to the above
262
par9 disk ionization parameter,
4
F ion n
, where
F
ion
is the 5eV – 20keV irradiating flux, n is the density of the reflector; see Done et al., 1992, ApJ,
395, 275.
6.4.5 kdblur: convolve with the laor model shape
A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a rotating black hole.. Uses Ari Laor's calculation including GR effects (ApJ 376, 90).
Modified from laor model by Andy Fabian and Roderick Johnstone. par1
Index: power law dependence of emissivity (scales as
R
–par1
) par2 inner radius (units of
GM c
2
) par3 outer radius (units of
GM c
2
)
6.4.6 kdblur2: convolve with the laor2 model shape
A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a rotating black hole. The accretion disk has a broken-power law emissivity profile. Uses
Ari Laor's calculation including GR effects (ApJ 376, 90). Modified from laor2 model by Andy
Fabian and Roderick Johnstone. par1 par2
Index: power law dependence of emissivity (scales as
R
–par1
) inner radius (units of
GM c
2
) par3 outer radius (units of
GM c
2
) par5 par6 radius at which emissivity power-law index changes
Emissivity power-law index for radii > par6
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6.4.7 kerrconv: accretion disk line shape with BH spin as free parameter
Convolves the current spectrum with the line shape from the kerrdisk model. A detailed description can be found in Brenneman & Reynolds (2006ApJ...652.1028B). This model is quite slow so is best used after models such as laor or diskline have been employed to get an estimate of the best-fit parameters.
par1 = emissivity index for the inner disk
par2 = emissivity index for the outer disk
par3 = break radius separating the inner and outer portions of the disk (gravitational radii)
par4 = dimensionless black hole spin
par5 = disk inclination angle to the line of sight (degrees)
par6 = inner radius of the disk in units of the radius of marginal stability
par7 = outer radius of the disk in units of the radius of marginal stability
6.4.8 lsmooth: lorentzian smoothing
Lorentzian smoothing with a variable width, which varies as the par2
power of the energy. The width at 6 keV is set with par1
.
( )
2
(
( )
)
2
E
2
( )
E
/ 6
where: par1=
par2=
lorentzian sigma at 6 keV power of energy for sigma variation
6.4.9 partcov: partial covering
A convolution model to convert some absorption model into a partial covering absorption. If the absorption model is M(E) then this is converted to (1-CvrFract) +
Cvrfact * M(E). Note that when specifying the model it is important to put parentheses in the right place. Let this model be P(E) which we want to apply to an absorption model
M(E) then use the result to multiply an additive model A(E). The combined model should be specified as (P*M)*A, not P*M*A or P*(M*A).
The parameters are : par1=CvrFract Covering fraction (0 < par1 < 1).
264
6.4.10 rdblur: convolve with the diskline model shape
A convolution model to smooth a spectrum by relativistic effects from an accretion disk around a non-rotating black hole.. Modified from diskline model (Fabian et al., MNRAS 238, 729) by Andy Fabian and Roderick Johnstone. par1
Index: power law dependence of emissivity (scales as
R
par1
).
If this parameter is 10 or greater then the accretion disk emissivity law
1
6 /
R
R
3
is used. par2 inner radius (units of
GM c
2
) par3 outer radius (units of
GM c
2
)
6.4.11 reflect: reflection from neutral material
Convolution model for reflection from neutral material according to the method of
Magdziarz & Zdziarski (1995, MNRAS, 273, 837). This is a generalization of the pexrav and bexrav models. The reflection component alone can be obtained for
rel
refl
0 reflection normalization is |
rel
refl
|. Note that you need to change then the limits of
rel
refl
excluding zero (as then the direct component appears). If c
0 metal and iron abundance are variable with respect to those set by the command abund. The opacities are those set by the command xsect. As expected in AGNs, H and He are assumed to be fully ionized.
When using this model it is essential to extend the energy range over which the model is calculated because photons at higher energies are Compton down-scattered into the target energy range. The energy range can be extended using the extend command. The upper limit on the energies should be set above that for which the input spectrum has significant flux. To speed up the model, calculation of the output spectrum can be limited to energies below a given value by using xset to define REFLECT_MAX_E (in units of keV). For instance, suppose that the original data extends up to 100 keV. To accurately determine the reflection it may be necessary to extend the energy range up to 500 keV. Now to avoid calculating the output spectrum between 100 and
500 keV use the command xset REFLECT_MAX_E 100.0.
The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method
which continues until a given estimated fractional precision is reached. The precision can be changed by setting REFLECT_PRECISION eg xset REFLECT_PRECISION 0.05. The default precision is 0.01 (ie 1%). par1 par2 =
z
reflection scaling factor (1 for isotropic source above disk) redshift par3 par4 abundance of elements heavier than He relative to the solar abundances iron abundance relative to the above
265
6.4.12 simpl: comptonization of a seed spectrum
The SIMple Power Law model: An empirical model of Comptonization in which a fraction of the photons in an input seed spectrum is scattered into a power-law component (
Steiner et al. 2009,
PASP, 121, 1279
). It is designed for use with soft thermal spectra that are not Compton thick and that have a photon index Gamma>1. Simpl offers the advantage of operating in a self consistent manner, linking the seed spectrum to the generated power law. Compared to powerlaw, simpl gives equally good fits while also employing just two parameters, and simpl has the virtue of eliminating the divergence of powerlaw at low energies. Because simpl redistributes input photons to higher (and lower energies), for detectors with limited response matrices (at high or low energies), or with poor resolution, the sampled energies should be extended to adequately cover the relevant energy range (for details and an example, see the appendix in Steiner et al. 2009). par1
Gamma
the photon power law index. par2 The scattered fraction (between 0 and 1). par3 A flag to switch between up-scattering only (>0) and both up- and downscattering (<=0).
6.4.13 Zashift: Redshift an additive model.
This convolution model redshifts an additive model. It takes the calculated model and shifts energies by 1/(1+z) then applies an additional 1/(1+z) factor to the model values.
The energies command must be to used to extend the maximum energy over which the model is being calculated to (1+z) times the maximum energy in the response.
The parameter is: par1 Redshift
An example model use is:
XSPEC> model phabs * zashift * (pow + ga) which redshifts the power-law and gaussian then multiplies by local absorption.
6.4.14 Zmshift: Redshift a multiplicative model.
This convolution model redshifts a multiplicative model. It takes the calculated model and shifts energies by 1/(1+z).
The energies command must be to used to extend the maximum energy over which the model is being calculated to (1+z) times the maximum energy in the response.
The parameter is: par1 Redshift
An example model use is:
XSPEC> model phabs * (zmshift*phabs) * pow which multiplies the power-law by both a redshifted and local absorption.
6.5 Pile-Up Model Components
6.5.1 pileup: CCD pile-up model for Chandra
CCD pile-up model used for brightish point sources observed by Chandra. This is an implementation of the fast pile-up algorithm proposed by John Davis (see
http://space.mit.edu/~davis/papers/pileup2001.pdf
). The frame time and maximum number of photons to pile up should be fixed. The grade morphing is expressed through a single parameter, alpha, which should be left as a free parameter. This model should be considered in beta test. Note that to calculate fluxes etc. for the model you must remove the pileup component. The pile-up model is similar to the operation of the convolution models, differing only in the treatment of the detector efficiency during the convolution.
Note that renorm will not work with pileup since increasing the normalization does not linearly increase the predicted count rate. Therefore you should set renorm none prior to doing a fit with pileup. par1 frame time (in seconds)
266
267
par2 par3 par4 par5 par6 maximum number of photons to pile up grade correction for single photon detection grade morphing parameter (good grade fraction is assumed proportional to par4 p-1 where p is the number of piled photons)
PSF fraction. Only this fraction will be treated for pile-up. Note that this is not the fraction of the PSF included in the extraction region but is the fraction of counts in the region which are from the point source whose pile-up is being modeled. For this model to work well the extraction region should be large enough to contain essentially all the PSF.
Number of regions. The counts to be piled-up will be distributed among par6
regions, which will be piled-up independently.
Value of FRACEXPO keyword in ARF. par7
6.6 Mixing Model Components
Mixing models perform transformations on the available spectra. The spectra must be assigned to more than one data group in order have any effect. Each data group is a
“region” of the observation, and the “mixing transformation” allows the model flux from one such “region” to influence another region. Thus, these models, unlike all the others, can be two-dimensional in effect. It follows they that differ from all the other models in that the data must be read before the model can be defined. In most cases also, the input data must contain additional information in order to use the model. This additional information can be in the form of the OGIP standard XFLT keys, which allow a set
(currently up to 10) of scalar real values, or in some cases additional files to be read containing spatial information.
XSPEC12 will return error messages if the data are not loaded, not compatible with the model (i.e. do not contain the required additional information), loaded inconsistently with the use of the model (the division of data into regions is incorrect, or data within a given region fail consistency checks). It will also return error messages if the data are subsequently changed to a set that violates these consistency checks, and additionally remove the model definition.
6.6.1 ascac: ASCA surface brightness model
Mixing model for ASCA data. Written for cluster data so uses beta or two power-law surface brightness models. Includes a calculation of the telescope effective area so no arf should be applied to input files. Note that this model is very slow if any of the parameters are free.
268
The model is used by reading spectra in as separate datagroups. Each input file requires the XFLT0001 keyword set to a different number (eg if concentric annuli are in use then number outwards). The normalizations for each datagroup should be linked since the ascac model takes care of the relative normalizations based on the surface brightness model used. A maximum of five different spatial regions is allowed. The absolute normalization is not reliable so this model should not be used to derive fluxes. par1 Alpha par2 Beta par4
0
beta model,
1
2-power-law
6.6.2 projct: project 3-D ellipsoidal shells onto 2-D elliptical annuli
This model performs a 3-D to 2-D projection of prolate ellipsoidal shells onto elliptical annuli. The annuli can have varying ellipticities and position angles but must have the same center. The user should extract spectra in a series of annuli. Each spectrum needs three additional keywords (XFLT0001, XFLT0002, XFLT0003) in the spectrum extension. These keywords contain the semi-major axis, semi-minor axis, and position angle (in degrees) for the outer boundary of the annulus. It is assumed that the inner boundary is specified by the outer boundary of the next annulus in. The lengths can be in any consistent units although for numerical accuracy they should have reasonable values.
Optional pairs of extra keywords (eg XFLT0004/5, XFLT0006/7, etc.) can be used to specify start and end angles for a partial annulus. These angles should be given relative to the same zero as the position angle.
The user reads in the spectra as separate datagroups and sets model parameters for each datagroup. The model for datagroup J will be the model in the shell whose outer boundary is a prolate ellipsoid of semi-major and semi-minor axes given by the semimajor and semi-minor axes in the XFLT keywords for dataset J. The projct model sums up the appropriate fractions of each ellipsoid model to make the projected spectrum.
For example, suppose we extract spectrum from three elliptical regions defined by
(1,0.5,0), (2,1,0), (3,1.5,0). That is the first region is in an ellipse of semi-major axis 1 and semi-minor axis 0.5. The second region is an elliptical annulus whose inner boundary has semi-major axis 1 and semi-minor axes 0.5 and whose outer boundary has semimajor axis 2 and semi-minor axis 1. The third region is defined similarly. The model fit has a temperature of 2 keV for the first datagroup, 3 keV for the second, and 4 keV for the third. The actual model fit to the first dataset has contributions from all three temperatures, the second only from the 3 and 4 keV components, and the third only from the 4 keV component. The weighting is the fraction of the ellipsoidal volume intersected
269
by the elliptical annular cross-section. Thus the normalizations correspond to the emission measure in each ellipsoidal shell.
If multiple observations are to be analyzed, data sets from different observations corresponding to the same annulus should be part of the same data group. For example, given the following 4 data files:
Data sets for obs 1: obs1_an1, obs1_an2
Data sets for obs 2: obs2_an1, obs2_an2
The proper data loading command is:
XSPEC12>data 1:1 obs1_an1 1:2 obs2_an1 2:3 obs1_an2 2:4 obs2_an2
The projct
model has 3 (fixed) parameters, which can be used to define the inner ellipse of the region being analyzed. For instance, in the example above we could have only read in spectra for the outer two regions but then set the projct parameters to
(1.0,0.5,0.0). This would have allowed us to determine the temperatures and emission measures of the outer two annuli without having to worry about fitting a model to the central region. par1 semi-major axis of inner boundary ellipse par2 par3 semi-minor axis of inner boundary ellipse position angle of inner boundary ellipse
6.6.3 suzpsf: suzaku surface brightness model
Mixing model for Suzaku data. Mixes the spectra between datagroups based on the PSF overlap between selected regions. A surface brightness model is required to calculate the mixing and this can be supplied in several ways. If SUZPSF-IMAGE has been set to some image file (using xset) then this image will be used for the surface brightness distribution. If SUZPSF-IMAGE has not been set then either a beta or two power-law model is used. In this case the model parameters determine the shape of the surface brightness distribution. If SUZPSF-RA and SUZPSF-DEC are set they are used as the center of the distribution. They should be specified either in decimal degrees or as hh:mm:ss.s and dd:mm:ss.s. If SUZPSF-RA and SUZPSF-DEC are not set then the centroid of the wmap will be used as the center of the surface brightness distribution.
The PSF used is an empirical model of a sum of two exponentials and a Gaussian with coefficients determined from an observation of MCG-6-30-15 performed early in the mission.
The model works by calculating the mixing factors. It will recalculate these factors if any of the SUZPSF-* or any of the model parameters are changed. Calculating the mixing factors is very slow so should be avoided as much as possible. To speed things up, it is possible to save the mixing factor array to a FITS file and re-use it during
270
a later calculation. To save a mixing factor calculation, prior to loading the mixing model (using the model command), use xset to set the variable SUZPSF-MIXFACT-
OFILEn to the name of the output FITS file, and where n is an integer corresponding to the observation number:
XSPEC12> xset SUZPSF-MIXFACT-OFILE1 fact_obs1.fits
Conversely, a saved factor array can be read in by setting SUZPSF-MIXFACT-
IFILEn:
XSPEC12> xset SUZPSF-MIXFACT-IFILE1 fact_obs1.fits
Multiple observations can be fit simultaneously. In this case the observations should be read in each datagroup in the same order, e.g.
XSPEC12> data 1:1 obs1reg1 1:2 obs2reg1 1:3 obs3reg1 2:4 obs1reg2 2:5 obs2reg2 par1 Alpha (not used if Switch=0 par2
Beta par3
Core (arcmin) par4
Switch (0 = beta model, 1 = 2-power-law)
6.6.4 xmmpsf: xmm surface brightness model
Mixing model for XMM data. Mixes the spectra between datagroups based on the
PSF overlap between selected regions. A surface brightness model is required to calculate the mixing and this can be supplied in several ways. If XMMPSF-IMAGE has been set to some image file (using xset) then this image will be used for the surface brightness distribution. If XMMPSF-IMAGE has not been set then either a beta or two power-law model is used. In this case the model parameters determine the shape of the surface brightness distribution. If XMMPSF-RA and XMMPSF-DEC are set they are used as the center of the distribution. They should be specified either in decimal degrees or as hh:mm:ss.s and dd:mm:ss.s. If XMMPSF-RA and XMMPSF-DEC are not set then the centroid of the wmap will be used as the center of the surface brightness distribution.
The model works by calculating the mixing factors. It will recalculate these factors if any of the XMMPSF-* or any of the model parameters are changed. Calculating
270
271
the mixing factors is very slow so should be avoided as much as possible. To speed things up, it is possible to save the mixing factor array to a FITS file and re-use it during a later calculation. To save a mixing factor calculation, prior to loading the mixing model (using the model command), use xset to set the variable XMMPSF-MIXFACT-
OFILEn to the name of the output FITS file, and where n is an integer corresponding to the observation number:
XSPEC12> xset XMMPSF-MIXFACT-OFILE1 fact_obs1.fits
Conversely, a saved factor array can be read in by setting XMMPSF-MIXFACT-
IFILEn:
XSPEC12> xset XMMPSF-MIXFACT-IFILE1 fact_obs1.fits
Multiple observations can be fit simultaneously. In this case the observations should be read in each datagroup in the same order, e.g.
XSPEC12> data 1:1 obs1reg1 1:2 obs2reg1 1:3 obs3reg1 2:4 obs1reg2 2:5 obs2reg2 par1 Alpha (not used if Switch=0 par2 Beta par3 Core (arcmin) par4 Switch (0 = beta model, 1 = 2-power-law)
A-272
Appendices
Appendix A The User Interface
A-1 Introduction
All communication with the user in XSPEC is performed through the tcl user interface.
When XSPEC starts, a tcl interpreter is initialized, and the XSPEC commands are added to it so that the tcl interpreter understands them. The XSPEC commands, which are C++ functions, define the syntax through a new built-in library of utility functions. The parser used in earlier versions of XSPEC has been discontinued: however the syntax understood by XSPEC12 is much the same as before.
A-2 XSPEC and tcl/tk
Because tcl is a full scripting language, users can write complex scripts with loops, branching, etc., which utilize XSPEC commands. Here we describe how to use those features of tcl necessary to give the user similar functionality to that available in previous versions of XSPEC, and to give information on the details of our tcl implementation that may be useful to experienced tcl users. For a description of tcl, see, for example,
Practical Programming in Tcl and Tk, B. Welch, (1997, Prentice Hall).
Tk, tcl's companion graphical user interface (GUI) toolkit, is also loaded by
XSPEC on startup. It is planned that future versions of XSPEC will provide an optional
GUI side-by-side with the command line interface (CLI). Although XSPEC does not currently use tk, its presence allows users to write XSPEC scripts with graphical interfaces using Tk commands.
A-3 A note on command processing
To emulate the performance of the former XSPEC parser, the command functions are programmed to react similarly to some of its features.
The # sign is used for comments in tcl, but may appear only at the beginning of a command. tcl and XSPEC both ignore carriage returns on a new line, but XSPEC also ignores the skip character ’/’. The character sequence ’/*’ entered during a command exits that command, sets any responses to the default response, and returns the user to the prompt. The ’\’ character is used in tcl for continuing a command onto the next line.
Additionally, note that in tcl, commands and their arguments are delimited by white space. They are terminated by a newline or semicolon, unless there is an open set of parentheses
’{ }’
constituting a loop or test structure. In other words, in tcl the following starts a loop: while { condition } {
….
} but
A-273
while { condition }
{
} is incorrect, since in the latter case the while
command terminates at the end of the first line.
The XSPEC/tcl interface also uses gnu readline for command input, which allows command line editing and interactive command recall. On most systems, the left and right arrow keys and the backspace/delete key can be used to navigate and edit the command line. The up and down arrow keys can be used to step thru the command history list. Gnu readline is highly customizable, and many more editing/recall functions are available. Readline documentation can be generated in either postscript or html format from the files in the xanadu/readline/doc directory distributed with the source.
The default implementation of tcl also supports a C-shell like command recall mechanism. The history
command gives a numbered list of the most recently entered commands. Any command in the list can be re-executed by entering
!n
, where n is the number of the command in the history list. The previous command can be re-executed by entering
!!
. The most recent command that begins with a string can be re-executed by entering
!prefix
, where prefix
is the string the command begins with.
Note that command recall is implemented using the tcl unknown
procedure, part of which is a script file loaded by tcl at run time. See the section on the unknown command for more details on how it is implemented in XSPEC.
A-5 Logging
The log
command can be used to open a log file to which all input and and output to tcl will be written. Reading these log files can potentially be confusing when logging tcl flow control commands such as while
or for
. This is because tcl treats the body of these commands as an argument of the command. Thus when the command is echoed to the log file, the entire body of the command is echoed with it.
In order to make this situation less confusing, before commands are echoed to the command file, all newline characters are replaced by semicolons, and the resulting command line is trucated to 80 characters. Then any commands executed with in the body of a flow control command are echoed as they are executed.
Consider the following sequence of tcl commands within XSPEC:
XSPEC12> log
Logging to file: xspec.log
XSPEC12> set i 1 ; set product 1
1
XSPEC12> while {$i <= 5} {
XSPEC12> set product [expr $product * $i]
XSPEC12> incr i
XSPEC12> }
XSPEC12> set product
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120
XSPEC12>
This would produce the following output in the file xspec.log
:
Logging to file: xspec.log
XSPEC12>
set i 1
set product 1
1
XSPEC12>
while {$i <= 5} {;set product [expr $product * $i];incr i;}
expr $product * $i
set product [expr $product * $i]
incr i
expr $product * $i
set product [expr $product * $i]
incr i
expr $product * $i
set product [expr $product * $i]
incr i
expr $product * $i
set product [expr $product * $i]
incr i
expr $product * $i
set product [expr $product * $i]
incr i
XSPEC12>
set product
120
XSPEC12> tcl attempts to match the name of any entered command as an abbreviation of a valid command (either a tcl or XSPEC command). If the entered command matches more than one valid command, tcl then lists the possible choices, but does not execute the command. For XSPEC commands, aliases have been constructed matching the command to its minimum abbreviation, as listed when typing `?' at the XSPEC prompt
(see under Aliases).
For example, the minimum abbreviation for the `plot' command is `pl'. Thus, typing `pl' will execute the plot command, even though this would otherwise be ambiguous with the tk command `place'. Command completion is also implemented using the tcl unknown
procedure, part of which is a script file loaded by tcl at run time, and may be different or not exist on your system. See the section in this help file on the unknown
command for more details on how it is implemented in XSPEC.
N.B. tcl explicitly switches off command completion for scripts. Because of the way scripts are implemented in XSPEC, however, command abbreviations nevertheless do work in scripts entered with the
@
command, but not when entered from the command line or using the source command. See below for more details about tcl scripting.
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tcl provides a facility whereby if it cannot match an entered command to its list of known commands, it calls the
unknown
procedure, with the unmatched command (along with its arguments) as its argument. The version of init.tcl
distributed with tcl contains a version of the unknown procedure. When tcl initializes, it looks in several standard places for a script file named init.tcl
, which it executes if found. The
unknown procedure is where tcl does command completion and automatic shell command execution.
At start up time, XSPEC loads its own
unknown
procedure, , which it uses to intercept script processing requests of the form
XSPEC12>@<script> and renames the previously defined unknown
procedure to tclunknown
. If XSPEC is not doing any special processing, it simply passes any unmatched commands on to tclunknown
, which then processes them as usual. XSPEC has its own special version of the unknown
procedure
These factors need to be taken into consideration for programmers writing tcl scripts for use within XSPEC. For example, if after initialization, users wishing to load a different version of the standard tcl unknown
procedure should name that procedure tclunknown
, rather than
unknown
.
A-8 Aliases
Command name aliases can be constructed using the tcl interp
command: interp alias {} <command_alias> {} <xspec_command> where
<xspec_command>
is the name of the command you wish to make an alias for, and
<command_alias>
is the name of the alias you wish to set for the command. The
{}
are required syntax.
To delete the alias
<command_alias>
, simply nullify it with: interp alias {} <command_alias> {}
When running interactively, the user has the option of providing an initialization script, which will be executed after XSPEC completes its startup procedure, ie. just before it begins prompting for commands. The file should be named xspec.rc
and located in the directory $HOME/.xspec. If one runs XSPEC in batch mode, by
specifying a script on the command line, this initialization script is not executed.
When multiple users are accessing a single system-wide XSPEC build, the installer can also provide additional initialization that will apply to all users. See the section “XSPEC Overview and Helpful Hints: Customizing XSPEC” for more details.
A-10 XSPEC Command Result
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After being executed, many tcl commands return a result string, which is echoed to the terminal when the command is entered on the command line. When writing complex tcl scripts, this result can be stored and/or used as a test in loops, etc. When
XSPEC commands are executed, they write information to the terminal by writing directly to the appropriate output channel. However, when running interactively, the tcl result string is also written to the terminal after the command is executed. The tclout command (see command description) creates tcl variables from xspec’s calculations.
A-11 Script Files
XSPEC/tcl script files can be executed in three different ways, as follows: xspec - <script>
XSPEC12>@ <script> executing script on initialization executing script from within the program
XSPEC12>source tclscript use tcl's source command from within the program.
Each of these usages does something slightly different. In the first form, XSPEC will execute a file called < script>
. One may execute a series of script files at startup with the following command syntax: unix> xspec - file1 file2 file3 ...
Note that the space following the
–
is required.
The second form is
@<name>
, where
<name>
is the name of the script file to be executed. Here the default extension of
.xcm
is assumed. Scripts containing valid tcl or
XSPEC commands will be executed using this form, and (unless the script ends in quit or
exit) will return to the interactive prompt after completion.
The final form, using tcl's source command, is intended for the special case where the script contains the implementation of a new command written in tcl/tk. See the section on writing custom commands for more details. In current tcl versions it compiles the script into bytecode representation for more efficient execution, and adds any procedures defined in the script to the set of commands understood by the interpreter.
It will not work for general scripts containing XSPEC/tcl commands, for example those produced by XSPEC's save command. These should rather be executed using
the @ form.
Note that only in the second case
@
is there a default filename suffix (i.e. .xcm) for both the other methods of script execution the filename must be given in full. tcl internally switches off the mechanism that expands command abbreviations when scripts are executed. If this were not done, the user could specify command abbreviations that change the behavior of the tcl command set (e.g. set
for the setplot command would redefine tcl’s command for setting variables). This behavior can be overridden with the statement set tcl_interactive 1
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near the beginning of the script, but it is not recommended to do so. Instead, we strongly recommend spelling out command names in full within XSPEC scripts.
By default, when XSPEC is executing a script file, it echoes each command to the terminal before it is executed. This can be controlled using the tcl variable xs_echo_script
, whose default value is 1. If this variable is set to 0, the commands from the script file will not be echoed to the terminal.
A-13 Summary
In summary, we suggest the following convention:
Running an xspec script from the unix command prompt is intended to be used for background processing or overnight batch jobs. Using the unix at
command, one can arrange to receive the log file by e-mail.
The
@
usage is intended for processing previously run xspec command sequences, such as are produced by the save command.
The source
usage, as well as executing the commands in the script, performs the equivalent of pre-compiling the script for later invocation. Its most appropriate use is in preparing new custom XSPEC command procedures. Once the script is working correctly, it can be placed in the user script directory and become part of the user's standard command set. For examples, see the scripts addline.tcl and modid.tcl in the directory
$SPECTRAL/scripts that implement the commands addline and modid. These also show how to make commands self-documenting.
Shell commands can be executed within XSPEC using the exec
command (see the help entry on the exec
command). When running interactively, if tcl cannot find a command that matches that entered on the command line, it will search for a shell command that matches the entered command. If it finds a match, it automatically executes the shell command via exec
. Note that this feature is implemented using the tcl unknown procedure, part of which is a script file loaded by tcl at run time, and may be different or not exist on your system. See the section in this help file on the
unknown
command for more details on how it is implemented in XSPEC.
Note that the tcl exec
command executes the given command directly, without first passing it on to the shell. Thus no globbing (ie. expansion of wildcards such
*.pha
) is performed. If you wish to pass you command through a shell for wildcard expansion, etc, use the syscall
command.
If you want to start a subshell from within XSPEC, simple type the command for starting that shell, ie. type
XSPEC12>csh
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in order to start a C-shell. Note that typing
XSPEC12>exec csh will not work properly.
Giving the
XSPEC12>syscall command with no arguments will start a subshell using your current shell (csh, tcsh, bash, sh, etc).
A-15 Writing Custom XSPEC commands
XSPEC commands can be written by users as tcl procedures, which have similarities with fortran subroutines. Within XSPEC, tcl procedures can take arguments and execute
XSPEC and tcl commands. The syntax for specifying arguments to a tcl procedure is as follows: proc my_proc {arg1 arg2}{
... data 1:1 ${arg1}_s0_20 data 2:2 ${arg2}_s1_20
...
}
Here, arg1, arg2 are values supplied by the user (here, part of a filename) from the command line, and substituted wherever
${arg1}
,
${arg2}
appear within the script.
One may also give an argument a default value, so that the command so created may be invoked even without needing to specify the argument: proc my_proc {arg1 {arg2 file2} } {
...
}
Note that the parentheses enclosing both
${arg2}
and file2
in this expression distinguish this from the case where 3 arguments are required for my_proc
. Once this file is created, it needs to be source
'd once, which compiles the script into an internal bytecode representation (this is similar to the way Java operates). Alternatively, one may place it in the user script directory and create an index in that directory, after which case it will be found automatically and compiled the first time it is invoked.
The user script directory is given by the line
USER_SCRIPT_DIRECTORY: in the Xspec.init file that is copied into $HOME/.xspec when the user starts xspec12 for the first time (the supplied default value for this directory is the $HOME/.xspec directory itself). After the script is placed there, perform the following command
%xspec12
XSPEC12>cd <USER_SCRIPT_DIRECTORY>
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XSPEC12>auto_mkindex .
XSPEC12>exit
This will instruct XSPEC to build an index of scripts to be loaded on xspec startup.
On the next invocation of XSPEC, the script will be sourced on startup and will appear in the list of commands XSPEC understands.
The my_proc
procedure is then defined such that one may type:
XSPEC12> my_proc eso103 eso104 and the data statement in the above example will be executed as if the following had been entered: data 1:1 eso103_s0_20 data 2:2 eso104_s1_20
The tcl info
command can be used to show which procedures have been defined:
XSPEC12> info commands <procedure name>
This will return <procedure name> if that procedure has been compiled (source’d) already or is a built-in command, or nothing if it has not (yet) been invoked or defined.
The commands model, editmod, addmod, newpar, and fakeit may prompt the user for more information when used interactively. In order to write scripts that use these commands, one must know how to force XSPEC to enter the information that would be prompted for. The technique is exemplified as follows. Suppose we defined a procedure xmode l that makes a model with certain predefined parameter values: set p1 {1.5 0.001 0 0 1.E05 1.E06} set p2 {1 0.001 0 0 1.E05 1.E06}
proc xmodel {modelString param1 param2 args} {
model $modelString & $param1 & param2 & /*
}
Here the
“&”
character is taken by XSPEC as a carriage return, delimiting the model string and parameter arguments into separate input lines.
The procedure xmodel
may be compiled with the command
XSPEC12>
source xmodel.tcl
This creates xmodel as a command with two arguments which sets subsequent parameters to their default values. It can be invoked e.g. by
XSPEC12> xmodel {wa(po + peg)} $p1 $p2
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Note that the model string, which contains spaces, needs to be entered in
{}
or double quotes. Note also that tcl understands a single string argument, args, as in proc tclscript { args } {
…
} to mean a variable number of arguments to a procedure (it is supplied as a tcl list, which can be split within the procedure into separate strings for digestion by xspec if present).
In the directory
$HEADAS/../spectral/session
is a script file called tclex.xcm
.
This script gives an example of how one might use the power of tcl's scripting language in an XSPEC session. This script should be executed with
XSPEC12> @tclex
# This script gives an example of how one might use the power of tcl's
# scripting language in an XSPEC session. In this example, XSPEC loops
# thru 3 data files (file1, file2 and file3) and fits them each to the
# same model `wabs(po+ga)'. After the fit the value of parameter 4
(the
# line energy for the gaussian) for each data set is saved to a file.
# Keep going until fit converges. query yes
# Open the file to put the results in. set fileid [open fit_result.dat w] for {set i 1} {$i < 4} {incr i} {
# Set up the model.
model wabs(po+ga) & /*
# Get the file.
data file$i
# Fit it to the model.
fit
# Get the values specified for parameter 4.
tclout param 4
set par4 [string trim $xspec_tclout]
# Turn it into a Tcl list.
regsub -all { +} $par4 { } cpar4
set lpar4 [split $cpar4]
# Print out the result to the file. Parameter value is
# the 0th element of the list `lpar4'.
puts $fileid "$i [lindex $lpar4 0]"
}
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# Close the file. close $fileid
The user is encouraged to read the voluminous on-line documentation and literature available about tcl in order to benefit fully its flexible command processing, graphical interfacing, and scripting capabilities. See http://www.tcl.tk for much more information and extensive bibliography.
Appendix B Statistics in XSPEC
B-1 Introduction
There are two operations performed in XSPEC that require statistics. The first is parameter estimation, which comprises finding the parameters for a given model that provide the best fit to the data and then estimating uncertainties on these parameters. The second operation is testing whether the model and its best-fit parameters actually match the data. This is usually referred to as determining the goodness-of-fit.
Which statistics should be used for these two operations depends on the probability distributions underlying the data. Almost all astronomical data are drawn from one of two distributions: Gaussian (or normal) and Poisson. The Poisson distribution is the familiar case of counting statistics and is valid whenever the only source of experimental noise is due to the number of events arriving at the detector. This is a good approximation for modern CCD instruments. If some other sort of noise is dominant then it is usually described by the Gaussian distribution. A common example of this is detectors that require background to be modeled in some way, rather than directly measured. The uncertainty in the background modeling is assumed to be Gaussian.
In the limit of large numbers of counts the Poisson distribution can be well approximated by a Gaussian so the latter is often used for detectors with high counting rates. In most cases this will cause no errors and does simplify the handling of background uncertainties however care should be exercised that no systematic offsets are introduced.
A fuller discussion of many of the issues discussed in this appendix can be found in
Siemiginowska (2011).
The standard statistic used in parameter estimation is the maximum likelihood. This is based on the intuitive idea that the best values of the parameters are those that maximize the probability of the observed data given the model. The likelihood is defined as the total probability of observing the data given the model and current parameters. In practice, the statistic used is twice the negative log likelihood.
For Gaussian data (chi)
The likelihood for Gaussian data is
L
N
i
1
i
1
2
exp
y i
m i
2
2
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where
y i
are the observed data rates,
σ i
their errors, and m
i
the values of the predicted data rates based on the model (with current parameters) and instrumental response. Taking twice the negative natural log of L and ignoring terms which depend only on the data
(and will thus not change as parameters are varied) gives the familiar statistic :
S
2
i
N
1
y i
i
2
m i
2 commonly referred to as χ
2
and used for the statistic chi option.
For Gaussian data with background (chi)
The previous section assumed that the only contribution to the observed data was from the model. In practice, there is usually background. This can either be included in the model or taken from another spectrum file (read in using the back command). In the latter case the
y i
become observed data rates from the source spectrum subtracted by the background spectrum and the
σ i
are the source and background errors added in quadrature. Since the difference of two Gaussians variables is another Gaussian variable, the
S
2
statistic can still be used in this case.
For Poisson data (cstat)
The likelihood for Poisson distributed data is:
L
N
i
1
S i
exp
where
S i
are the observed counts, t the exposure time, and m
i
the predicted count rates based on the current model and instrumental response. The maximum likelihood-based statistic for Poisson data, given in Cash (1979), is :
C
2
N
i
1
S i
ln(
tm i
S i
Castor (priv. comm) has pointed out that modifying this by a quantity that depends only on the data (and hence makes no difference to the best-fit parameters) to give :
C
2
i
N
1
S S i
ln
S i
ln
provides a statistic which asymptotes to
S
2
what is used for the statistic cstat option. in the limit of large number of counts. This is
For Poisson data with Poisson background (cstat)
This case is more difficult than that of Gaussian data because the difference between two
Poisson variables is not another Poisson variable so the background data cannot be subtracted from the source and used within the C statistic. The combined likelihood for the source and background observations can be written as:
L
i
N
1
i
b i
S i
exp
i
b i
S i
!
B i
exp
B i
!
A-283
where
t s
and
t b
are the exposure times for the source and background spectra, respectively,
B i
are the background data and
b i
the predicted rates from a model for the expected background. If there is a physically motivated model for the background then this likelihood can be used to derive a statistic which can be minimized while varying the parameters for both the source and background models.
As a simple illustration suppose the source spectrum is source.pha and the background spectrum back.pha. The source model is an absorbed apec and the background model is a power-law. Further suppose that the background model requires a different response matrix to the source, backmod.rsp say. The fit is set up by:
XSPEC12> data 1:1 source.pha 2:2 background.pha
XSPEC12> resp 2:1 backmod.rsp 2:2 backmod.rsp
XSPEC12> model phabs(apec)
XSPEC12> model 2:backmodel pow where the normalization of the apec model is fixed to zero for the second data group (i.e. the background spectrum) and the parameters of the background model are linked between the data groups.
If there is no appropriate model for the background it is still possible to proceed. Suppose that each bin in the background spectrum is given its own parameter so that the background model is
b i
=
f i
. A standard XSPEC fit for all these parameters would be impractical however there is an analytical solution for the best-fit
f i
in terms of the other variables which can be derived by using the fact that the derivative of L will be zero at the best fit. Solving for the
f i
and substituting gives the profile likelihood:
W
2
N
i
1
t m i
t s
t b
f i
S i
ln
t m i
t f
B i
ln
S i
where
f i
S i
B i
t s
t m i
d
2
t s
t b
i
S i
B i
B i
and
d i
t s
i
S B i
2
4
t s
i
The sign of
d i
in
f i
is chosen so that
f i
> 0. If any bin has
S i
and/or
B i
zero then its contribution to W (W
i
) is calculated as a special case. So, if
S i
is zero then:
W i
t m i
B i
log(
t b
(
t s
t b
))
If
B
i is zero then there are two special cases. If
m i
< S i
/ t s
then:
W i
t m i
S i
log(
t s
(
t s
t b
)) otherwise:
W i
t m i
S i
S
t m i
This W statistic is used for statistic cstat if a background spectrum with Poisson statistics has been read in. In practice, it works well for many cases but for weak sources can
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generate an obviously wrong best fit. It is not clear why this happens although binning to ensure that every bin contains at least one count often seems to fix the problem.
In the limit of large numbers of counts per spectrum bin a second-order Taylor expansion shows that W tends to :
N
i
1
S i
s i
i
f i
2
b i
2
which is distributed as χ
2 with N – M degrees of freedom, where the model m
i
has M parameters (include the normalization).
For Poisson data with Gaussian background (pgstat)
Another possible background option is if the background spectrum is not Poisson. For instance, it may have been generated by some model based on correlations between the background counts and spacecraft orbital position. In this case there may be an uncertainty associated with the background which is assumed to be Gaussian. In this case the same technique as above can be used to derive a profile likelihood statistic :
PG
2
N
i
1
i
f i
S i
ln
1
2
i
2
b i
2
S i
1 ln
S i
where
f i
t s
i
2
2
b i
d i
2
t b
2 and
d i
t s
i
2
t B i
t m i
2
4
t t s
i
2
m i
S i
i
2
t B m i
There is a special case for any bin with
S
i
equal to zero:
P t m i
B t t b
i t t b
)
2
This is what is used for the statistic pgstat option.
Bayesian analysis of Poisson data with Poisson background (lstat)
An alternative approach to fitting Poisson data with background is to use Bayesian methods. In this case instead of solving for the background rate parameters we marginalize over them writing the joint probability distribution of the source parameters as :
A-285
where {θ j
} are the source parameter, {b k
} the background rate parameters and I any prior information. Using Bayes theorem, that the {θ }, that the
{b k j
} and independent of the {b k
} are individually independent and that the observed counts are Poisson gives :
P =
N k
1
t t e
m t
J k
where :
k
S k b e
b k
b
To calculate J_k we need to make an assumption about the prior background probability distribution, p(b k b i max
|I). We follow Loredo (1992) and assume a uniform prior between 0 and
. Expanding the binomial gives :
1
b k max
S k j
0
m k j
k
k
b
Sk
1,
max k
+B j+ t +t
1
b
where :
0
x
α
1
x
Again, follow Loredo we assume that
b
max k
α
1
!
when
α
β
gives :
B k
and using the approximation
s b
Sk
+B +
1
b max k
S k j
0
m k j
S + B k
j !
j! S k
j !
b
j
Note that for m k
= 0 only the j = 0 term in the summation is non-zero. Now, we define lstat by calculating -2 ln P and ignoring all additive terms which are independent of the model parameters :
lstat =
2ln
2
N k=1
ln
S k j
0
m k j
S + B k
j !
j! S k
j !
b
k
For power spectra from time series data (whittle)
XSPEC has been used by a number of researchers to fit models to power spectra from time series data. In this case the x-axis is frequency (in Hz) and not keV so plots have to be modified appropriately. The correct fit statistic is that due to Whittle as discussed in
Vaughan (2010) and Barret & Vaughan (2012) :
S =
2
N i=1
y i m i
+
log
m i
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B-3 Parameter confidence regions
Fisher Matrix
XSPEC provides several different methods to estimate the precision with which parameters are determined. The simplest, and least reliable, is based on the inverse of the second derivative of the statistic with respect to the parameter at the best fit. The first derivative must be zero by construction and the second derivative provides a measure of how rapidly the statistic increases away from the best-fit. The faster the statistic increases, i.e. the larger the second derivative, the more precisely the parameter is determined. The matrix of second derivatives is often referred to as the Fisher information. Its inverse is the covariance matrix, written out at the end of an XSPEC fit.
The +/- numbers provided for each parameter in the standard fit output are estimates of the one-sigma uncertainty, calculated as the square root of the diagonal elements of the covariance matrix. As such, these ignore any correlations between parameters. Whether correlations are important can be seen by comparing with the off-diagonal elements of the covariance matrix. In general, these estimates should be considered lower limits to the true uncertainty.
Correlation information is also given in the table of variances and principal axes which also appears at the end of a fit. Each row in this table is an eigenvalue and associated eigenvector of the Fisher matrix. If the parameters are independent then each eigenvector will have a contribution from only one parameter. For instance, if there are three independent parameters then the eigenvectors will be (1,0,0), (0,1,0), and (0,0,1). If the parameters are not independent then each eigenvector will show contributions from more than one parameter.
Delta Statistic
The next most reliable method for deriving parameter confidence regions is to find surfaces of constant delta statistic from the best-fit value, i.e. where :
best fit
This is the method used by the error command, which searches for the parameter value where the statistic differs from that at the best fit by a value (Δ) specified in the command. For each value of the parameter being tested all other free parameters are allowed to vary. The results of the error command can be checked using steppar, which can also be used to find simultaneous confidence regions of multiple parameters. The specific values of Δ which generate particular confidence regions are calculated by assuming that
StatisticStatistic
best fit
is distributed as χ
2 with the number of degrees of freedom equal to the number of parameters being tested (e.g. when using the error command there is one degree of freedom, when using steppar for two parameters followed by plot contour there are two degrees of freedom). This assumption is correct for the S
2
statistic and is asymptotically correct for other statistic choices.
Monte Carlo
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The best but most computationally expensive methods for estimating parameter confidence regions are using two different Monte Carlo techniques. The first technique is to start with the best fit model and parameters and simulate datasets with identical properties (responses, exposure times, etc.) to those observed. For each simulation, perform a fit and record the best-fit parameters. The sets of best-fit parameters now map out the multi-dimensional probability distribution for the parameters assuming that the original best-fit parameters are the true ones. While this is unlikely to be true, the relative distribution should still be accurate so can be used to estimate confidence regions. There is no explicit command in XSPEC to use this technique however it is easy to construct scripts to perform the simulations and store the results.
The second technique is Markov Chain Monte Carlo (MCMC) and is of much wider applicability. In MCMC a chain of sets of parameter values is generated which describe the parameter probability distribution. This determines both the best-fit (the mode) and the confidence regions. The chain command runs MCMC chains which can be converted to probability distributions using margin (which takes the same arguments as steppar).
The results can be plotted in 1- or 2-D using plot margin however this is not quite as useful as it might be because what is plotted is the probability, not the probability within some region. If MCMC chains are in use then the error command will use them to estimate the parameter uncertainty.
B-4 Goodness-of-fit
Parameter values and confidence regions only mean anything if the model actual fits the data. The standard way of assessing this is to perform a test to reject the null hypothesis that the observed data are drawn from the model. Thus we calculate some statistic T and if T obs
> T critical
Ideally, T critical
then we reject the model at the confidence level corresponding to T critical
is independent of the model so all that is required to evaluate the test is a
. table giving T critical values for different confidence levels. This is the case for χ
2
which is one of the reasons why it is used so widely. However, for other test statistics this may not be true and the distribution of T must be estimated for the model in use then the observed value compared to that distribution. This is done in XSPEC using the goodness command. The model is simulated many times and a value of T calculated for each fake dataset. These are then ordered and a distribution constructed. This distribution can be plotted using plot goodness. Now suppose that T obs
exceeds 90% of the simulated T values, we can reject the model at 90% confidence.
It is worth emphasizing that goodness-of-fit testing only allows us to reject a model with a certain level of confidence, it never provides us with a probability that this is the correct model.
Chi-square (chi)
The standard goodness-of-fit test for Gaussian data is χ
2
(as defined above). At the end of a fit, XSPEC writes out the reduced χ freedom = number of data bins – number of free parameters). A rough rule of thumb is that the reduced χ
2
2
(= χ
2
/ν , where ν is the number of degrees of
should be approximately one. If the reduced χ
2 is much greater than one then the observed data are likely not drawn from the model. If the reduced χ
2 is much
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less than one then the Gaussian sigma associated with the data are likely over-estimated.
XSPEC also writes out the null hypothesis probability, which is the probability of the observed data being drawn from the model given the value of χ
2 and the number of degrees of freedom.
Pearson chi-square (pchi)
Pearson's original (1900) chi-square test was not for Gaussian data but for the case of dividing counts up between cells. This corresponds to the case of Poisson data with no background.
P
N i
1
y i
m i m i
2
Kolmogorov-Smirnov (ks)
There are a number of test statistics based on the empirical distribution function (EDF).
The EDF is the cumulative spectrum :
i j
1
y j
/
N j
1
y
j
and
i j
1
m j
/
N j
1
m
j
The EDF can be plotted using plot icounts. The best known of these tests is
Kolmogorov-Smirnov whose statistic is simply the largest difference between the observed and model EDFs :
D = supremum Y i
M i
The XSPEC statistic test ks option returns log D. The significance of the ks value can be determined using the goodness command.
Cramer-von Mises (cvm)
The Cramer-von Mises statistic is the sum of the squared differences of the EDFs :
N i
1
i
2
The XSPEC statistic test cvm option returns log w
2
and its significance should be determined using the goodness command.
Anderson-Darling (ad)
Anderson-Darling is a modification of Cramer-von Mises which places more weight on the tails of distribution :
N i
1
i
2
/
M i
1
M i
Runs (runs)
The Runs (or Wald-Wolfowitz) test checks that residuals are randomly distributed above and below zero and do not cluster. Suppose N residuals, N n then the Runs statistic is : p is the number of channels with +ve
the number of channels with negative residuals, and R the number of runs
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μ
1
μ
N
1
where :
n
As for the EDF tests, XSPEC returns log Runs.
μ =
2
N N n
N
+
1
B-5 References
Barret, D. & Vaughan, S., 2012. “
Maximum likelihood fitting of X-ray power density spectra: application to high-frequency quasi-periodic oscillation from the neutron star X-ray binary
4U1608-522”, ApJ 746, 131.
Cash, W., 1979. “Parameter estimation in astronomy through application of the likelihood ratio”, ApJ 228, 939.
Loredo, T., 1992. In “Statistical Challenges in Modern Astronomy”, eds. Feigelson, E.D. and Babu, G.J., pp 275-297.
Siemiginowska, A., 2011. In “Handbook of X-ray Astronomy” eds. Arnaud, K.A., Smith,
R.K. and Siemiginowska, A., Cambridge University Press, Cambridge.
Vaughan, S. 2010, “A Bayesian test for periodic signals in red noise”, MNRAS 402, 307.
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Appendix C Adding models to XSPEC
XSPEC includes a large collection of standard models that can be fit to data. However, sometimes these are not enough and a new model might be required. In order of increasing complexity the ways to do this are: use the mdefine command; create a table model; load a model function created by someone else; create and load your own model function. The mdefine command can be used for a model which can be described using a simple formula and is documented under the commands section of the manual so we do not discuss it further. This appendix describes the other three methods then finishes with a note about the more complex issue of mixing models.
A very simple way of fitting with user-defined models is available for a particular class of models. These are models that can be defined by a grid of spectra, with the elements of the grid covering the range of values of the parameters of the model. For instance, for a oneparameter model, a set of model spectra can be tabulated for different values of the parameter
(P1, P2, P3, etc.) The correct model spectrum for a value P is calculated by interpolation on the grid. The generalization to more parameters works in the obvious way. The table is specified in the model command by the special strings atable, mtable, or etable with the filename following in brackets – see the entries in the models section of the manual. Any number of table model components can be used simultaneously.
Table model components can be much slower than most standard models if there are significant numbers of parameters. The memory requirements increase as 2 n
where n is the number of parameters in the model. A table model with more than 3 or 4 fitting parameters is not recommended. Additionally, the interpolation is linear, which implies that the second derivatives used by the default Levenberg-Marquadt algorithm may not be accurate. If the fit does not work well it may be worth trying the migrad (minuit library) algorithm which makes no assumptions about the second derivative.
As with standard models, the spectra should be in terms of flux-per-bin and not flux-per-keV.
Any set of energy bins can be used, and XSPEC will interpolate the model spectra onto the appropriate energy bins for the detectors in use. It is therefore a good idea to choose energy bins such that the spectrum is well-sampled over the range of interest. The file structure for these models is a FITS format described at :
http://heasarc.gsfc.nasa.gov/docs/heasarc/ofwg/docs/general/ogip_92_009/ogip_92_009.html
or:
ftp://legacy.gsfc.nasa.gov/fits_info/fits_formats/docs/general/ogip_92_009
C-2 Loading a new model function
New model functions either downloaded from the XSPEC additional models webpage at :
http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/newmodels.html
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or acquired privately are added using the two commands initpackage, which prepares and compiles a library module containing them, and the lmod command which actually loads them into the program. These commands are described in the XSPEC commands section of the manual, to which the user is referred. Any number of different user model packages may be added to XSPEC from the user prompt, and the user has control over the directory from which models are loaded
Note that the lmod command requires write-access to the particular directory specified.
This is because lmod uses the Tcl ‘make package’ and ‘package require’ mechanisms for automatic library loads and these require Tcl write an index file (pkgIndex.tcl) to the directory.
Consequently we recommend using the Tcl load command instead of lmod if the library is being used by a number of users on a local network. Note that such a library can be loaded automatically by placin the command in the global_customize.tcl script (see the section
“Customizing XSPEC”).
C-3 Writing a new model function
A model function is a subroutine that calculates the model spectrum given an input array of energy bins and an array of parameter values. The input array of energy bins gives the boundaries of the energy bins and hence has one more entry than the output flux arrays. The energy bins are assumed to be contiguous and will be determined by the response matrix in use.
The subroutine should thus make no assumptions about the energy range and bin sizes. The output flux array for an additive model should be in terms of photons cm keV
-1
2 s
-1
(not photons cm
2 s
-1
) i.e. it is the model spectrum integrated over the energy bin. The output array for a
multiplicative model is the multiplicative factor for that bin. Convolution models are operators on the output from additive or multiplicative models. Model subroutines can be written in fortran, either in single or double precision, in C++ using either C++-style arguments or C style arguments, and in C.
The “model.dat” entry
In addition to the subroutine, XSPEC requires a text file describing the model and its parameters. The standard models are specified in the model.dat file so we usually refer to this text file by that name. A sample model.dat entry has the following form: modelentry 5 0. 1.e20 modelfunc add 0 0 lowT keV 0.1 0.0808 0.0808 79.9 79.9 0.001 highT keV 4. 0.0808 0.0808 79.9 79.9 0.001
Abundanc " " 1. 0. 0. 5. 5. 0.01
*redshift " " 0.0
$switch 1
The first line for each model gives the model name, the number of parameters, the low and high energies for which the model is valid, the name of the subroutine to be called and the type of model (add, mul, mix, or con, or acn). The final argument two arguments are flags: the first should be set to 1 if model variances are calculated by modelfunc and the second should be set to 1 if model should be forced to perform a calculation for each spectrum. This final flag is
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necessary because if multiple spectra have the same energy bins, the default behavior is to perform the model calculation for just one spectrum and copy the results for each of the others.
However if a model depends on information about the spectrum in addition to its energy ranges, it must be forced to perform a calculation for each spectrum.
The remaining lines in the text file specify each parameter in the model. For regular model parameters the first two fields are the parameter name followed by an optional units label.
If there is no units label then there must be a quoted blank (“ “) placeholder. The remaining 6 numerical entries are the default parameter value, hard min, soft min, soft max, hard max, and fit delta, which are described in the newpar command section.
There are three special types of parameter which can be used. If the name of the parameter is prefixed with a “*” the parameter is a “scale” parameter and cannot be made variable or linked to an other kind of parameter other than another scale parameter. Since the parameter value can never vary only the initial value need be given. If the name of the parameter is prefixed with a “$” the parameter is a “switch” parameter which is not used directly as part of the calculation, but switches the model component function’s mode of operation (i.e. calculate or interpolate). Switch parameters only have 2 fields: the parameter name and an integer value. If a
P is added at the end of the line for a parameter then the parameter is defined to be periodic.
During a fit, a periodic parameter will not be pegged if it tries to exceed its hard limits. Instead it will be assigned a value within its limits: f(max + delta) = f(min + delta), f(min-delta) = f(maxdelta). The soft min and max settings are irrelevant for period parameters and will be ignored.
The model subroutine function
The following table lists the function arguments required for the different language options. The second column is the way the function name should be included in the model.dat entry.
Call Type
Single precision fortran
Specification Arguments and Type
real*4 ear(0:ne) integer ne real*4 param(*) modelfunc integer ifl real*4 photar(ne) real*4 photer(ne)
Meaning
Energy array
Size of flux array
Parameter values.
(Dimension must be specified inside the function)
The spectrum number being calculated
Output flux array
Output flux error array (optional)
Double precision fortran
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integer ne real*8 param() integer ifl real*8 photar(ne) real*8 photer(ne) const Real* energy
“
“
“
“
“
C/C++, C-style c_modelfunc int Nflux const Real* parameter int spectrum
Real* flux
Real* fluxError
Energy array (size
Nflux+1)
Size of flux array
Parameter values
Spectrum number of model component being calculated
Output flux array
Output flux error array (optional) const char* init Initialization string
(see below)
Energy array const RealArray& energy const RealArray& parameter Parameter values int spectrum Spectrum number of model component being calculated
C++, C++ style C_modelfunc
RealArray& flux
RealArray& fluxError
Output flux array
Output flux error array (optional) const string& init Initialization string
(see below)
For example, a model component in double precision fortran is specified by:
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modelentry 5 0. 1.e20 F_modelfunc add 0
XSPEC then picks out the right function definition, and calls the function modelfunc which expects double precision arguments. The C-style call can clearly be compiled and implemented by either a C or a C++ compiler: however we recommend using the C++ call if the model is written in C++ as it will reduce overhead in copying C arrays in and out the XSPEC internal data structures. To prevent unresolved symbol linkage errors, we also recommend prefacing C++ local model function definitions with the extern “C” directive.
Example C/C++ function definitions:
/* C -style */ extern “C” void modelfunc(const Real* energy, int Nflux, const Real* parameter, int spectrum,
Real* flux, Real* fluxError, const char* init)
{
/* Model code: Do not allocate memory for flux and fluxError arrays. XSPEC’s
C-function wrapper will allocate arrays prior to calling the function (and will free them afterwards). */
}
// C++ extern “C” void modelfunc(const RealArray& energy, const RealArray& parameter, int spectrum, RealArray& flux, RealArray& fluxError, const string& init)
{
// Model code: Should resize flux RealArray to energy.size() - 1. Do the same for
// fluxError array if calculating errors, otherwise leave it at size 0.
}
Note on type definitions for (C and C++): XSPEC provides a typedef for
Real
, in the xsTypes.h header file. The distributed code has typedef Real double; i.e. all calculations are performed in double precision. This is used for C models and C++ models with C-style arguments.
The type
RealArray
is a dynamic (resizeable) array of Real. XSPEC uses the std::valarray template class to implement
RealArray
. The internal details of XSPEC require that the
RealArray
typedef supports vectorized assignments and mathematical operations, and indirect addressing (see C++ documentation for details). However, we do not recommend using specific features of the std::valarray class, such as array slicing, in case the typedef is changed in future.
The input energies are set by the response matrices of the detectors in use. IFL is an integer which specifies to which response (and therefore which spectrum) these energies correspond. It exists to allow multi-dimensional models where the function might also depend on eg pulse-phase in a variable source. The output flux array should not be assumed to have any
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particular values on input. It is assumed to contain previously calculated values only by convolution/pileup models, which have the nature of operators. The output flux error array allows the function to return model variances.
The C and C++ call types allow one extra argument, which is a character string that can be appended to the top line of the model component description. This string is read on initialization and available to the model during execution. An example of its use might be the name of a file with specific data used in the model calculation: this allows different models to be implemented the same way except for different input data by specifying different names and input strings.
C-4 Third-Party Libraries In Local Models Build
The Makefile that initpackage creates for building your local models library is based on the template file heasoft-[ver]/Xspec/src/tools/initpackage/xspackage.tmpl. If you need to add a path to a third-party library's header files, add: -I/path/to/your/3rdParty/library/include to the
HD_CXXFLAGS setting. Then type "hmake" and "hmake install" from the heasoft-
[ver]/Xspec/src/tools/initpackage directory.
To make sure the linker pulls in the library on Mac OS X:
Further edit the xspackage.tmpl file by adding a "-l" flag for the library (e.g. -lgsl) in the
HD_SHLIB_LIBS settings. Then reinstall xspackage.tmpl as mentioned above.
On Linux/Unix:
The XSPEC executable itself should be relinked with the new library included. So, edit the file heasoft-[ver]/Xspec/src/main/Makefile by adding a "-l" flag for the library to the
HD_CXXLIBS setting. Then from the same directory do: rm xspec hmake local hmake publish hmake install
After these modifications, you should be able to use initpackage and lmod in the normal way to build and load your local models library.
C-5 Writing new mixing models
Mixing models are fundamentally different from the other kinds of models since they apply a transformation to a set of modeled fluxes (as enumerated by the spectra in the fit), rather than modify the flux designed to fit a single spectrum. The need to store temporary results, as well as the requirements of the model calculation, lead to many workspace arrays: further, the transformations applied are often fixed during a fit, or can be split to avoid redundant calculations into parts that are fixed and parts that change during iteration in order. XSPEC’s internal organization (data structures) can be mapped straightforwardly to the requirements of these models so to implement them efficiently and handle memory allocation, we recommend that mixing models be written in C++ or C. At present only a C++ implementation is available.
Users considering adding new mixing model types should contact the developers of XSPEC at
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Appendix D Overview of PLT
As in previous versions, the initial release of XSPEC12 uses the PLT library, which is in turn based on PGPLOT
, to implement its plotting capabilities.
Future versions will be able to offer other plotting library options.
Extensive documentation for the PLT graphics routine is available in the
The
QDP/PLT Users's Guide
and from PLT’s interactive help. This appendix is intended to provide information to assist in using PLT from within the XSPEC program.
Within XSPEC, it is possible to set your graphics device using the CPD command. Any PGPLOT device supported by your local version of PGPLOT is accepted. The CPD command can also be used to display a list of all PGPLOT devices. If you fail to enter a device name, you will be prompted for a PGPLOT device every time you generate a new plot.
From XSPEC, there are two ways to call the PLT routine. Both have the same syntax which is described in the corresponding manual section.
The plot
<plot mode> command will produce a graph and control will return immediately to XSPEC.
The iplot
<plot mode>
command will put XSPEC into interactive plot mode. The
PLT>
prompt will appear after the XSPEC plot command has finished producing the same graph. At this point, you can enter PLT commands to inspect interesting parts of the graph, add labels, or make a hardcopy file for later printing.
D-1 Getting started with PLT
In the following description of PLT commands, the full command is descried.
Capital letters denote the shortest abbreviation of the command that will be recognized.
Here is a brief guide to some of the PLT commands that can be entered when iplot is invoked.
HElp will provide you with descriptions of the PLT commands.
Plot redraws the display using all of the commands that change the graph entered since the last plot.
Rescale
[<X,Y>]
4
PGPLOT is the name of a Graphics Subroutine Library written by T. J. Pearson at the California Institute of Technology
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followed by two numbers, will set the minimum and maximum of the plotted x-range to the numbers specified. Without further arguments, Rescale X or Y will reset the minimum and maximum values to their default values. Rescale also updates the screen immediately. Other commands allow you to make several changes to the the graph without having to wait for the screen to be updated after every change.
LAbel
<Top,X,Y> [<string>] add labels to various locations on the graph. For example, typing
LA Top EXOSAT was great
Will cause the message “EXOSAT was great” to appear at the top of the graph the next time the display is redrawn. Without the string argument the current label for Top,
X, or Y is set to the empty string.
Hardcopy [?, PGPLOT plot device]
Create a file that can later be printed. Since it redraws the graph and sends it to a file, it does not reproduce what currently is visible on the graphics display, but rather what you would see if you re-issued the Plot command. With the optional “?” argument,
Hardcopy returns the current hardcopy plotting device. This can be overridden with
Hardcopy
[PGPLOT device name]
.
EXit return control to XSPEC. Any changes you have made to the plot will be lost.
D-2 PLT Command summary
CLear
Immediately clear the graphics device
Change the default colour index
COlor
CONtour
Produce a contour plot
CPD
CQuit
CSize
Error
EXit
Fit
Change the plotting device
Clear the graphics device and return control to XSPEC
Change the default character size
Control whether errors are displayed and used in fitting
Exit PLT and return control to XSPEC
Fit the PLT model to the data
FNy
FOnt
Evaluate the model at the specified location
Change the default text font
Freeze a parameter value
Freeze
GAp
Change the default gap size between the data and the edge
Control the location of the major and minor tic marks
Grid
Hardcopy
Make a file that can later be printed
HElp
Imodel
Obtain help on any PLT command
Numerically integrate the model over specified range
LAbel
LIne
LOg
LStyle
LWidth
Add or remove labels from the plot
Control whether a line is used to connect data points
Control whether data is plotted using a log
10
scale
Change the default style of the line connecting the data points
Change the default line width
MArker
MOdel
Newpar
Control whether the data points are plotted with markers
Define a PLT model
Change a parameter value associated with the model
PLot
PRompt
Rescale
Immediately re-plot the data
Change the
PLT>
prompt
Reset the minimum and maximum plot range
Change the color representation of the specified color index
SCr
SHow
Display the values of PLT internal variables
Control how PLT divides data into vectors
SKip
STatistics
Compute various statistical properties of the data
THaw
Time
Allow a parameter value to vary during a fit
Control whether the time stamp is plotted
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Uncertainty Compute the uncertainty in a parameter value
VErsion
Display date of the most recent modification to PLT
Viewport
Control the size of the viewport plotting area
WData
Write a QDP data file to disk
WEnviron
Write both QDP data and header files to disk
WHead
Write a QDP header file to disk
WModel
Xaxis
Write a model file to disk
Define the method used to calculate the x-variable
Yaxis
Define the y-axis scale for a contour plot
Execute operating system commands
$
@filename
Read commands from a PLT command (.PCO) file
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Appendix E Associated programs
Introduction
The
HEAsoft
package provides a number of programs and subroutine libraries to manipulate the
FITS files used by XSPEC. A description of most tasks can be obtained by typing help taskname or to get a complete list fhelp ftools.
FTLIST
HEAsoft reading tasks
Prints the contents of a FITS file to the screen or to a file.
DMPRMF
Prints the contents of a FITS RMF file to the screen or to a file.This tool prints the RMF file in a more legible fashion than FTLIST.
HEAsoft manipulation tasks
FPARKEY
Changes the value of a keyword in a FITS extension header.
GRPPHA
Defines (or redefines) and/or displays the grouping and quality flags, the important keywords, and the fractional systematic errors.
RBNPHA
Compresses a FITS PHA file to a user-defined number of channels. The output is a new file containing the revised PHA extension plus a direct copy of any other extensions in the original file.
MATHPHA
Performs arithmetical operations on PHA files.
CMPPHA
Convert a type II pha file to a type I pha file.
RBNMF
Bins a FITS RMF file (the detector response matrix) in channel or energy space.
CMPRMF
Compress an RMF by removing all response below a threshold value.
ADDARF
Adds together ARFs.
ADDRMF
Adds together RMFs.
MARFRMF
Multiplies an RMF file by an ARF file.
GENRSP
A generic spectral response generator.
HEAsoft subroutines
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The directory ftools
/ callib/src/gen
in the HEAsoft distribution contains a number of subroutines for reading and writing the extensions in FITS format spectral and response files. More information on their use can be obtained from the xspec website at:
http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/fits/fitsfiles.html
RDPHA2
Read a spectrum extension
WTPHA3
Write a spectrum extension
RDRMF5
Read the matrix extension
WTRMF5 Write the matrix extension
RDEBD4
Read the channel boundaries extension
WTEBD4
Write the channel boundaries extension
RDARF1
Read the effective area extension
WTARF1
Write the effective area extension
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Appendix F Using The XSPEC Models Library In Other Programs
For those who wish to incorporate the standard XSPEC model functions library into their own programs, XSPEC provides a set of functions and wrappers that can be called from external C,
C++ or Fortran programs.
F-1 Calling Model Functions From C And Fortran
An increasing number of XSPEC model functions are written in C++, and have the C++style function interface described in Appendix C. XSPEC provides function wrappers for each of these to make them callable from Fortran or C programs. The wrappers are stored in the files funcWrappers.h and funcWrappers.cxx in the XSFunctions directory.
For each C++ model function there are 2 wrappers: one for passing single precision arrays and one for double precision, with the interfaces as shown in Appendix C for single precision
Fortran-style and C-style respectively. The single precision wrapper function name will be the original C++ function name appended with a “f_ “ prefix, while the double precision wrapper will have a “C_ prefix”.
For example, XSPEC’s model.dat entry for the power law model lists the function name
C_powerLaw. This shows that the actual function name is “powerLaw” and the “C_” indicates it has a C++ interface inside XSPEC. funcWrappers.cxx defines the following 2 wrappers: void f_powerLaw(const float* energy, int nFlux, const float* params, int spectrumNumber, float* flux, float* fluxError) void C_powerLaw(const double* energy, int nFlux, const double* params, int spectrumNumber, double* flux, double* fluxError, const char* initStr)
The second function is intended to be called from C programs, while Fortran programs may call either (funcWrappers.cxx also includes CERN <cfortran.h> definitions to make these accessible to
Fortran).
XSPEC also provides a set of functions for accessing some of the model functions’ internal data. The C++ functions are listed in the file FunctionUtility.h in the XSUtil/FunctionUtils directory. For C and Fortran access, equivalent wrapper functions are listed in the same directory in xsFortran.h. The wrapper functions have C-style function declarations, and are also made available to Fortran calling routines via the CERN <cfortan.h> interface.
The currently provided C/Fortran wrapper functions are (see xsFortran.h for the function signatures):
FNINIT
FGABND
Initializes data directory locations needed by the models.
See below for a fuller description.
Get an element abundance.
FGCHAT
FPCHAT
FGDATD
FPDATD
FGMODF
FGMSTR
FPMSTR
FPSLFL
FGSOLR
FPSOLR
FGXSCT
FPXSCT
RFLABD csmgh0 csmph0
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Get current chatter level setting for model functions’ output verbosity.
Set the chatter level. Default is 10, higher chatter levels produce more output.
Get the model .dat files path.
Set the model .dat files path.
Get the model ion data path.
Get a model string value (see XSPEC xset command).
Set a model string value.
Load values of a “file” solar abundance table (see abund command).
Get the solar abundance table setting.
Set the solar abundance table.
Get the cross section table setting.
Set the cross section table.
Read abundance data from a file, then load and set this to be the current abundance table. (Essentially this combines a file read with the FPSLFL and FPSOLR functions.)
Get the cosmology H0 setting (see the cosmo command).
Set H0. fzsq Computes the luminosity distance, (c/H0)*fzsq. The function is valid for small values of q0*z for the case of no cosmological constant and uses the approximation of
Pen (1999 ApJS 120, 49) for the case of a cosmological
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DGFILT constant and a flat Universe. The function is not valid for non-zero cosmological constant if the Universe is not flat.
Get a particular XFLT keyword value from a data file.
DGNFLT xs_getVersion (or xgvers)
Get the number of XFLT keywords in a data file.
Retrieve XSPEC’s version string.
F-3 Initializing the Models Library
The external program should always call the FNINIT routine prior to any other call into the models library. This initializes the locations of the various data files needed by the models, and also sets the abundance and cross-section tables. Unless the user has overridden the model ion data directory location with the XSPEC_MDATA_DIR environment variable, the initial settings are:
$HEADAS/../spectral/modelData Model ion data location
Abundance and crosssection .dat files location
$HEADAS/../spectral/manager
Solar abundance table
Photoelectric crosssection table angr bcmc
F-4 Building with the Models Library
The XSFunctions library depends on three lower-level XSPEC libraries, XS, XSUtil, and
XSModel, and also the CCfits and cfitsio libraries distributed with HEASOFT. A Makefile for a small Fortran program linking with the models library therefore may look like this on Linux: myprog : myprog.o g77 -g myprog.o -o myprog \
-lXSFunctions -lXSModel -lXSUtil -lXS -lCCfits_2.1 -lcfitsio_3.11 myprog.o: myprog.f g77 -g -c myprog.f
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Appendix G Adding a Custom Chain Proposal Algorithm
When running a Monte Carlo Markov Chain with the chain command, XSPEC provides several built-in proposal options from which to draw trial parameter values for the next step in the chain. A built-in proposal is selected prior to the chain run with the command: chain proposal <distribution> <source> where <distribution> is the statistical distribution used to randomize the parameter values (e.g. gaussian
, cauchy)
, and <source> refers to the source of the applied covariance information (see the chain command for details).
It is also possible for the user to create an arbitrary new proposal scheme and add it to the options available under the chain proposal command. This is done in a way similar to the adding of local models described in Appendix C, though in this case the code can only be written in C++.
Essentially three steps are involved, each described in greater detail below:
Create a small text file named randomize.dat.
Write a class which inherits from XSPEC’s abstract base class RandomizerBase.
Run XSPEC’s initpackage and lmod commands to build and load the shared library containing the new proposal class(es).
G-1 The randomize.dat Initialization File
This file must be placed in the same directory as the user’s proposal code files, and plays a role similar to the local models’ .dat initialization files, though it has a much simpler structure. It also MUST be named randomize.dat, for this name is the only clue initpackage has to distinguish between creating a chain proposal or local models library.
All that needs to be entered into this file is a line of the form:
<class name> [<opt string arg1> <opt string arg2> … <opt string argN>] for each proposal class that will go in the library. <class name> must be a case-sensitive match to the actual C++ class name, and is the only required entry on the line. The class should also be stored in code files <class name>.h and <class name>.cxx.
Any additional arguments on the line will be placed in a single C++ string (including any separating whitespace), and passed to the class constructor. This is to allow the option of setting initialization parameters at the class construction stage. Therefore if optional arguments are included, the class must have a constructor which takes a single string argument. Otherwise, the constructor should contain no arguments.
For example, a randomize.dat file declaring two classes might contain:
MyProposal1
MyProposal2 1.4773 on false
In the code files, the constructor declarations corresponding to this would then be:
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MyProposal1.h class MyProposal1 : public RandomizerBase
{ public:
// …
};
MyProposal1();
// …
MyProposal2.h class MyProposal2 : public RandomizerBase
{ public:
// …
};
MyProposal2(const string& initArgs);
// …
G-2 Writing Chain Proposal Class
All user proposal classes must inherit from XSPEC’s abstract class RandomizerBase, whose interface is defined in the file: headas-<version>/Xspec/src/XSFit/Randomizer/RandomizerBase.h.
The proposal class must declare a constructor as described in the previous section, and which explicitly calls the RandomizerBase constructor, passing it a lower-case name string. This name will become the proposal identifier when making a selection using the chain proposal
option during an XSPEC session. For example:
MyProposal1.cxx
MyProposal1::MyProposal1()
: RandomizerBase(“myprop1”)
{
}
In XSPEC:
XSPEC12> chain proposal myprop1 [<optional initializing args>]
The RandomizerBase class contains 5 private virtual functions: doRandomize, doInitializeLoad, doInitializeRun, doAcceptedRejected, and getCovariance: doRandomize is the only pure virtual function and therefore is the only one which must be overridden in the inheriting class. Its signature is: virtual void doRandomize(RealArray& parameterValues, const Fit* fit) where RealArray is a typedef for std::valarray<double> and is defined in src/main/xsTypes.h. This function is called by XSPEC for each chain iteration, and XSPEC passes in the current variable
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model parameter values. The overridden doRandomize function performs the necessary parameter modifications and sends them back in the same array.
The function’s second argument is a const pointer to XSPEC’s global Fit class object. For those willing to further explore XSPEC’s internals, this pointer provides access to various fit and chain information (such as covariance matrices), which may be necessary for the user’s proposal scheme. doInitializeLoad and doInitializeRun may be optionally overridden to perform initialization tasks at different stages during runtime. The default versions of these functions in RandomizerBase do nothing. doInitializeLoad is called by XSPEC immediately after the proposal is selected with the chain proposal command. Therefore one may find it useful to have this function process any additional arguments which may be entered on the command line: chain proposal myprop [<optional initializing args>]
XSPEC automatically bundles
[<optional initializing args>]
into a single string and places it in the m_initString data member of RandomizerBase, to which the inheriting class has access. doInitializeRun is called once at the start of a chain run, and is useful for any tasks which must be performed one time immediately after the chain run
command is entered. doAcceptedRejected is called after each iteration in the chain. Its first argument is an array filled with the most recently attempted model parameter values, and its second argument is a boolean true or false indicating whether the attempt was accepted or rejected. The base class function does nothing with this, but an inherited class may want to use this information in an overriden function.
In its simplest form, a proposal class may be declared and defined as in the following example. This doesn’t actually do anything since the doRandomize function is empty and the parameterValues array is left unchanged.
MyProposal.h
#ifndef MYPROPOSAL_H
#define MYPROPOSAL_H
#include <xsTypes.h>
#include <XSFit/Randomizer/RandomizerBase.h> class Fit; // only a forward declaration is required for Fit class MyProposal : public RandomizerBase
{ public:
MyProposal(); virtual ~MyProposal(); private: virtual void doRandomize(RealArray& parameterValues, const Fit* fit);
};
#endif
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MyProposal.cxx
#include “MyProposal.h”
#include <XSFit/Fit/Fit.h>
MyProposal::MyProposal()
: RandomizerBase(“myprop”)
{
}
MyProposal::~MyProposal()
{
} void MyProposal::doRandomize(RealArray& parameterValues, const Fit* fit)
{
// This is where the proposal algorithm should modify the variable
// model parameters in the parameterValues array.
}
G-3 Building and Loading the Proposal Class Library
Once the randomize.dat file and the class(es) have been written, the library can be built and loaded during an XSPEC session using the same initpackage and lmod sequence that is used for local model libraries. To create a Makefile and build the library:
XSPEC12> initpackage <name> randomize.dat <directory>
To load the new proposal(s) into XSPEC:
XSPEC12> lmod <name> <directory> where
<name> is the name you choose for the package collection of proposal classes. It will also become the library file name. The only differences from the local models case are that here the initializer file MUST be named randomize.dat, and that the directory path to the proposal classes
(either relative or absolute) must be provided on the command line. If this is left off XSPEC will default to looking in the directory set by LOCAL_MODEL_DIRECTORY, and these classes should NOT be stored in the same directory as local models. If the building and loading has successfully completed, you should see the proposal name (the same name string that was passed to the RandomizerBase constructor) appear in the chain proposal list displayed by typing chain proposal
with no other arguments.
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Appendix H Changes between v11 and v12
In 1998 we decided to re-engineer XSPEC using modern computer science methods so it could continue fulfilling its role as a mission-independent X-ray spectral fitting program.
The program’s internal design, layout, and data structures have largely been rewritten in
ANSI C++ using
object oriented design techniques
, generic programming techniques, and
design patterns
. The thoroughgoing reanalysis has also allowed a number of improvements in overall design and, at robustness, as well as maintainability, without changing the familiar
syntax. With a few exceptions here and there, the new program syntax is fully backwardcompatible with that of v11: most of the exceptions support new features that are enhancements
(and can be ignored if not relevant to the user’s problems). Some features of v11 previously declared to be deprecated have been removed.
At the same time, the core of the XSPEC calculation scheme has been retained, in particular the models library, written almost exclusively in fortran77.
Model implementation has been rewritten to support allow models written not only in single precision fortran, but double precision fortran, C, and C++. Further, XSPEC can now be used as a development environment for local models by allowing recompilation from the command prompt.
In v12, spectra can be fit with more than one distinct model simultaneously, provided separate model components can be assigned distinct response functions. This is particularly useful for spectra from coded aperture masks.
A new internal dynamic expression implementation allows more complex (multiplynested) models, and also allows parameter links to be polynomial functions of one or more parameters.
Great care has been taken to optimize the program for memory usage and execution speed. A revision of the numerical derivative algorithm has reduced the number of convolution operations required during fitting. On the other hand, v12 performs its calculations in double precision (apart from the models library), and this with the more complex model expression evaluations reduces execution speed. Taken together, v12 should outperform v11 when the number of channels is large and the model to be fitted is relatively simple and should be comparable in other circumstances.
The default fitting algorithm (Levenberg-Marquadt) has been retained intact. New fitting algorithms and objective functions (statistics) may be added to the program at runtime. The
CERN Minuit/migrad algorithm has been better integrated into the code and its documentation is now directly accessible during XSPEC sessions.
Type II (multi-spectrum) OGIP files are now fully supported. Multiple ranges can be selected in the data command, and support is present for Type II background and arf files.
Observation simulations (the fakeit command) now operate on Type II inputs.
The online documentation scheme is now implemented using pdf or html files, replacing the older VMS-style help system. The help scheme can be configured to use external applications such as Adobe Acrobat or the xpdf readers as well as web browsers. Users can document their own local models and tcl-scripted procedures in pdf and html files and add them to the help system.
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Plotting within v12 is backward compatible with a few small extensions. Although it is currently implemented using PLT, explicit dependence on the plot library has been removed.
This will allow alternative plotting libraries to be used in future. The PLT plotting package is described briefly in Appendix D and in more detail in the “QDP/PLT User's Guide” (Tennant,
1989). v12 communicates with the user through the familiar command line interface. The input/output streams, however, can in future be easily redirected to communicate with the user through a graphical user interface (GUI).
Finally, the design implements a new error handling system can return the program safely to the user prompt when an error occurs and leave the program in a state from which the user can continue working. Also, for the first time there is now an undo command.
Integral Spectrometer/Coded Mask Instrument Support
The
INTEGRAL
Spectrometer (
SPI
) is a coded-mask telescope, with a 19-element
Germanium detector array. There are several complications regarding the spectral deconvolution of coded-aperture data. For XSPEC the most obvious problem is the source confusion issue; as there may be multiple sources in the FoV leading to different degrees of shadowing on different detectors. Thus, a separate instrumental response must be applied to a spectral model for each possible source, for each detector. If there are multiple sources in the
FoV, then additional spectral models can be applied to an additional set of response matrices, enumerated as before over detector and dither pointing. This capability —to model more than one source at a time in a given minimization procedure—did not exist in XSPEC prior to v12.
The other unique aspect of the INTEGRAL analysis is that the background is modeled along with the source(s) in a single de-convolution.
XSPEC analysis of INTEGRAL/SPI data is very different from other instruments is the manner in which the response matrices are handled. Since there are a large number of responses involved in the de-convolution problem, memory use becomes a concern. To load the required response matrices (as XSPEC normally does), would require ~(N ch
)
2
N p
N d floating-point memory locations per source. This could become quite large for high-spectral resolution and/or long observation scenarios. To address this problem, a methodology has been developed to reconstruct the required 2-D response matrices from a basis set, consisting of a small number (3) of 2-D objects (template RMFs), and a larger number of 1-D objects (component ARFs). The full matrices can then be reconstructed "on the fly" at the minimization step of the calculation, and discarded after each use. This, in principle, occurs all very transparently to the user.
A fuller description of Integral data analysis appears in section 2 of this manual and a walkthrough example is given in 4.6.
Feature
Current Exclusions
The v11 commands and features not provided in v12 are:
Rationale for exclusion recornorm With version 12.5.0, this has been replaced and improved upon by
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thleqw extend the recorn mixing model.
Rarely used command not yet implemented.
Beginning with version 12.3.0, this has been replaced by the more flexible energies command. background models This has been replaced by v12’s multiple source modeling techniques
Additionally, we have withdrawn seldom-used fitting methods anneal and genetic. Future development will add new techniques.
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Appendix I Older Release Notes
v12.8.0 Dec 2012
New features:
Parallel-processing capability for specific tasks has been added by way of the new "parallel" command. This allows the user to set a maximum number of processes to spawn when running certain XSPEC commands. Currently the options for parallel-processing are limited to use with the "fit" and "error" and commands, though we plan to implement more in the near future. This first implementation is considered to be a BETA release, and we look forward to hearing your comments and suggestions.
XSPEC now distinguishes between the 'fit' statistic and the 'test' statistic. The fit statistic is used to find the best-fit parameter values and errors while the test statistic is used to provide a goodness-of-fit. Consequently, the goodness command now uses the test statistic. Separating these two classes of statistic has allowed us to add a number of new test statistics. These include Kolmogorov-
Smirnov and the related Anderson-Darling and Cramer-von Mises. Also new are the runs statistic, based on the number of runs of consecutive positive (or negative) residuals, and the Pearson Chi-Square (pchi) statistic, Pearson's original test statistic.
The basic Levenberg-Marquardt fit algorithm has undergone a number of changes. The most visible is an additional column in the output during the fit.
|beta|/N is the norm of the vector of derivatives of the statistic with respect to the parameters divided by the number of parameters. At the best fit this should be zero so provides another measure of how well the fit is converging. |beta|/N can also be used as the criterion to stop the fit instead of the statistic delta although this is still considered experimental.
Other internal changes to the fit algorithm are to treat the first iteration as a special case where only normalizations are allowed to change and to add the option of using delayed gratification, which can speed up convergence.
New models: compmag, comptb, rgsxsrc. The latter is reinstated from it use in
XSPEC v11.
New plotting command "plot goodness", for plotting a histogram of the most recent "goodness" simulation.
New tclout option "goodness sims".
Added the option of using the Goodman-Weare algorithm instead of Metropolis-
Hastings when using the chains command to run MCMC.
Added the Whittle statistic for fitting models to power density spectra.
If a data file is read which has RESPFILE="[]" then the response extensions
(MATRIX, EBOUNDS) are read from the same file.
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Added support for a new type of model component: a mixing component which operates on the model pre-multiplied by the effective area. This is similar to the pile-up model type but allows for a models which require mixing between multiple spectra.
Table model files can now have interpolated and additional parameters intermixed provided that additional parameters are indicated by METHOD=-1 in the PARAMETERS extension.
Enhancements previously released as patches to 12.7.1:
The "plot chain" has a new "thin" option for thinning the display of chain points.
Added a "tclout ignore" option for easy retrieval of currently ignored channels.
Similar capability added to PyXspec's Spectrum class.
All bug fixes to v12.7.1 released as patches are included in v12.8.0. In addition the following problems have been corrected:
The eqpair model used wrongly-sized arrays when multiple spectra were used with RMFs having varying numbers of photon energy bins. Eqpair (plus eqtherm and compth) also needed a new default value for its optical depth parameter, which fixes the problem if parameter 4 is zero.
A fit parameter which started close to the minimum/maximum could under some circumstances be incorrectly pegged at the maximum/minimum.
When the "error" command was run on a model with soft limits (ie. soft limits for some parameters set to a narrower range than hard limits), and the best fit value fell within the soft limit region, the displayed differences (in parentheses) were not consistent with the reported ± limits.
Problem occurred in apec model when zero width lines were in the final energy bin.
Fix to a potential normalization problem occurring in lorentz model with lowenergy large-width lines.
When running initpackage/lmod from PyXspec on certain Linux builds, local models calling functions in XSPEC's xslib library producing unresolved symbol link errors.
v12.7.1 March 2012
New features:
New models: gadem, vgadem, eplogpar, logpar, optxagn, optxagnf, and pexmon.
The convolution models rdblur, rdblur2, kdblur and kerrconv have been sped up.
They are now O(N) instead of O(N^2) where N is the number of energy bins in the response.
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Continued rationalization of Compton reflection routines. eqpair, eqtherm, compth, compps, ntee now all use the same routines as reflect and ireflct. For models with ionized reflector there may be changes in results because the new code uses the actual input spectrum to calculate the ionization fractions while the old code assumed a power-law.
The parameter simulation arrays used for the calculation of eqwidth and flux error are now accessible through tclout.
Initpackage now works on Cygwin. The static_initpackage work-around is no longer needed and has been removed.
New Fortran interface wrapper function RFLABD, for reading new abundance tables into external programs using the XSPEC models library.
Added an xsetbl function for use in external programs. This provides access to
XSPEC's internal exponential table model routines, similar to what xsatbl and xsmtbl do for additive and multiplicative table models.
Bayes command is now supported for response parameters (ie. gain).
New 'show version' option.
Improved 'error' command output messaging. The error results now have lower chatter level (5) than most of the warning messages (10), thus making it easier to filter out the warnings.
PyXspec beta version upgraded to v1.0. See the PyXspec release notes for details.
Enhancements previously released as patches to 12.7.0:
New tclout options: nullhyp, rerror.
All bug fixes to v12.7.0 released as patches a-u are included in v12.7.1. In addition the following problems have been corrected:
Program aborted when attempting to fit with gain parameters attched to dummy responses.
Program aborted when removing a spectrum with a response containing gain parameters, AND while that response was temporarily replaced with a dummy response.
The 'save' command did not add the default .xcm extension for file names that included a path.
A crash could occur if the EBOUNDS array wasn't the right size.
It was not possible to plot 2 or more models in a multi-panel 'plot model' display.
v12.7.0 May 2011
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The primary new feature of 12.7.0 is the addition of the Python module, PyXspec v0.9 beta. PyXspec is built and installed by defaulton most platforms along with the regular XSPEC build, and simply requires an "import xspec" statement to load into
Python. XSPEC can now be run from object-oriented Python scripts, or interactively from a Python shell prompt. Detailed instructions can be found in PyXspec.pdf.
While most features of standard XSPEC are already supported in this beta release, some still remain to be implemented. Please let us know if any missing feature is of particular importance to you, or if you have suggestions and ideas for improvement.
Other new features:
New models: cplinear: Piecewise linear non-physical background model for low-count spectra developed for Chandra by Patrick Broos. eqpair, eqtherm, compth: Paolo Coppi's hybrid hot plasma emission models. vvapec, bvvapec: APEC models allowing all 30 elemental abundances to vary
(for use with AtomDB 2.0). zigm: Multiplicative model, computes the mean attenuation of the optical/UV spectrum by the intergalactic medium. zashift, zmshift: Convolution models for applying redshifts to additive and multiplicative models respectively.
Also note that the default APEC model data files have been updated to
AtomDB 2.0. This version of AtomDB includes contributions from more elements than earlier versions. When using the apec and vapec models these extra elements have Solar abundance by default. To change this use "xset
APEC_TRACE_ABUND".
The 'statistic' command may now be applied to individual spectra. This makes it possible to simultaneously fit spectra which require different fit statistics.
Added the 'pgstat' option to the statistic command. This is similar to using 'cstat' with a background file except that the background is assumed to have Gaussian statistics (not Poisson) read from a STAT_ERR (and optionally SYS_ERR) column.
Modified the pileup model for consistency with Sherpa and ISIS. A new parameter 'fracexpo' is added which should be set to the FRACEXPO keyword value in the ARF.
It is now possible to choose proportional or fixed fit deltas from the startup
Xspec.init file. The initial default setting is now proportional deltas rather than fixed deltas.
Improvements made to the output generated during a fit. The parameter names are listed at the top of columns, not just their numbers. Column alignment has been improved, and is no longer limited to a maximum width of 5 columns.
Added reporting of the Bayesian contribution (if any) to the fit statistic output.
Enhancements previously released as patches to 12.6.0:
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Initpackage now recognizes and builds files with .f03 extensions for Fortran
2003, and .f90 extensions for Fortran 90.
Added a new 'fakeit' option for setting the fake background exposure time.
Added a new 'tclout version' option for returning the XSPEC version string.
Improved XSPEC's internal update mechanism to reduce the number of model calculations.
All bug fixes to v12.6.0 released as patches a - ab are included in v12.7.0. In addition the following problems have been corrected:
A crash occurred if 'tclout notice energies' was performed on a spectrum containing only a dummy response with no channels.
The 5 redundant 'xset' options (those which merely duplicate other existing
XSPEC commands) weren't passing their arguments to the command handlers correctly.
Fit error messages were misleading for the case where the data was missing a suitable response, or when the only existing models were inactive.
A fatal error could occur in 'fakeit' when attempting to generate a background file while only a dummy was used for the response.
The 'bayes' command handler was not properly handling the case where the prior type option string was abbreviated.
A crash occurred when ‘flux’ was run in error mode and the specified energy was entirely outside the range of one or more spectra.
v12.6.0 March 2010
The main improvements in version 12.6.0 are to XSPEC's plotting capabilities:
Multi-panel plotting is now supported for all combinations except contour plots.
For example, "plot data model resid ratio" will produce a 4-panel plot on a single page. Up to 6 panels can be plotted in this manner.
There are many choices for axis units. These can be selected using the "setplot energy" and "setplot wave" commands. For example, "setplot energy GeV" uses
GeV on the x- and y-axes. "setplot wave" also has a new "perhz" option for displaying the Y-axis in 1/Hz units.
The "setplot" command has a new "redshift <z>" option for shifting displayed energies to the source frame.
Other new features:
New models: ireflect is a convolution model based on the pexriv code. sirf is a multiblackbody self-irradiated funnel
The normalizations on all power-law models (ie. powerlaw, bknpow, bkn2pow, cutoffpl)can be changed to a flux over an energy range by setting POW_EMIN
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and POW_EMAX keywords in "xset". The powerlaw model then becomes equivalent to the pegpwlw model.
The Compton reflection models (b/p)exr(a/i)v and (i)reflect have been restructured to use adaptive Gauss-Kronrod quadrature for the Greens' function integrals. The precision to which the integrals are calculated can be set allowing a trade-off between speed and precision.
The wrapper functions additiveTable and multiplicativeTable give external C++ models access to XSPEC's table model interpolation routines (equivalent to the xsatbl and xsmtbl functions for Fortran models).
The display of link expressions has been simplified to show only the parameter numbers and not the extraneous component information. Also "show model" will now only display the model components and not the individual parameters.
The parameters can be seen with "show par".
Additional enhancements previously released as patches to 12.5.1:
Added the solar abundance data set of Asplund, Grevesse, and Sauval (2006) to the list of available tables accessed with the "abund" command.
New "tclout nchan" option for returning the number of channels in a spectrum.
The "save" command now stores relative rather than absolute paths to allow easier porting to other machines.
The recorn model component has been converted from a mixing to a multiplicative type. This allows a model to define multiple recorn components.
A warning message is now issued if a user attempts to load a response for a source n when there are still slots to fill for source n-1. This is intended to catch cases where a user mistakenly reverses the source and spectrum number input to the "response" command.
All bug fixes to v12.5.1 released as patches a - o are included in v12.6.0. In addition the following problems have been corrected:
It was possible for the addition of a systematic model error to actually decrease the overall variance, when it was applied to a zero-variance bin that was artificially increased by XSPEC for chi-square fitting.
Bug in "plot ratio" when using "setplot wave" with Hz units. Y-axis model values < 10^-20 were not displayed in plot.
The comptt model no longer stops and prompts the user when it fails during its incomplete gamma calculation.
The powerlaw model has been modified to avoid a numerical instability that could occur if the index were within 10^-12 to 10^-15 of 1.0.
v12.5.1 Aug. 2009
Gain parameters can now be used in the error, freeze, newpar, thaw, and untie commands by prefixing the command name with the letter 'r' (for "response
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parameter", the more general category to which gain parameters belong).
Steppar can now also handle gain parameters. Gain parameters can be displayed either with "show parameter" or the new "show rparameter" option.
The gain command syntax has changed when using multiple sources. To better conform with the rest of XSPEC, it now requires <source number>:<spectrum number> rather than the reverse.
Gain parameter limit values can be stored in response files, using the keywords GSLOP_MIN, GSLOP_MAX, GOFFS_MIN, and GOFFS_MAX.
All input and output data filenames can now include
CFITSIO/FTOOLSextended-syntax for specifying particular HDUs. As a result, XSPEC can now handle files which contain spectra, ARFs and RMFs in multiple extensions.
Partial derivative calculations during fitting can now be performed numerically rather than with an approximated analytical expression. This option is chosen in the Xspec.init initialization file.
If a new minimum is found during a steppar run, steppar now prompts the user for acceptance of the new values. Also the delta statistic column of a steppar run is now obtainable with the tclout steppar delstat option.
The output warning message has been improved in the case where Levenberg-
Marquardt fitting runs into a zero diagonal element in the second derivative matrix. Similarly, the more frequent pegged-parameter messages (due to running into hard limits) is now output at higher chatter levels only.
All calls to the xanlib dynamic memory allocation function udmget have been removed from the Fortran models in XSPEC's models library. The relevant code has been converted to C++. If a user's local models library still requires the udmget code, they'll need to run initpackage with the new -udmget option.
Additional enhancements previously released as patches to 12.5.0:
Setplot wave x-axis units can be toggled from Hz to angstroms through
WAVE_PLOT_UNITS entry in Xspec.init file.
New tclout gain and sigma options.
New xs_getVersion function available for those linking their own programs to the XSPEC models library.
The show parameters option can now take a range of parameters for displaying subsets.
All bug fixes to v12.5.0 released as patches a - an are included in v12.5.1. In addition the following problems have been corrected.
After running the ARF command, any gain previously applied to the associated RMF will be removed. Previously it was erroneously applying the gain to the new ARF.
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Additional header file inclusions needed in code files to compile with g++-4.4.0
Extra line-feed characters removed from Ascii text files in the modelData directory. These were causing problems on Solaris 10 w/f90.
The nthcomp model's internal arrays were hardcoded to a maximum size of 5000 energy bins. The size is now dynamically allocated. (This also affects the diskir model.)
A Levenberg-Marquardt fit now immediately stops if the fit statistic becomes NaN due to an erroneous model calculation.
C++-style comments have been removed from xsFortran.h for the benefit of users compiling their own C programs with the models library.
Plotting fix for case where "setplot area" is selected and no models are currently loaded.
Model parsing fix for case of nested parentheses with no '+' operator, ie.
A(B(C*D)).
v12.5.0 Nov. 2008
Two of the remaining unimplemented v11 commands have now been added.
mdefine
allows dynamic definition of models that can be expressed algebraicly. recornrm has been replaced by the
recorn
model. This allows the correction norm to be treated as a fit parameter, a better solution than the v11 recornrm command.
The complete HTML help files are included in a tar file. These can be made available on a local machine if remote access is now available and selected in the Xspec.init file.
Convolution components can now operate on multiplicative components. For example, in the model = (CM)A, the convolution component acts on only the multiplicative component. Previously this would have been treated the same as C(MA). The
partcov
partial covering model takes advantage of this new capability.
There is a new simple way of estimating fluxes (and their errors) from parts of the model. Apply the
cflux
convolution model to the component(s) for which the flux is required.
The following models have been added as standard
diskir
: irradiated disk
kerrdisk
: broad iron line from a disk around a Kerr BH
nsmax
: NS magnetic atmosphere
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nthcomp
: thermally Comptonized continuum
spexpcut
: super-exponential cut-off
swind1
: partially ionized absorbing material with velocity shear
zxipcf
: partial covering of partially ionized absorbing material
cflux
: calculate the flux from model component(s)
kerrconv
: broadening due to rotation around a Kerr BH
partcov
: partial covering modifier for absorption models
simpl
: Comptonization of a seed spectrum
recorn
: Vary the correction file normalization
The
lrt.tcl
and
simftest.tcl
scripts perform the likelihood ratio and F-tests, respectively.
The
writefits.tcl
script writes filenames and current fit parameters and errors to a single row of a FITS file. This script can be used as a template for saving other information.
A response of "/*" to a "y/n" prompt will jump out of the current operation and return to the XSPEC command prompt. This is particularly useful for escaping nested fits during an
error
command run.
The units have been changed for
setplot
wave plots. model and ufspec have a y-axis in photons/cm^2/s/Hz, emodel and eufspec in Jy (10^-23 erg/cm^2/s/Hz), eemodel and eeufspec in erg/cm^2/s.
Fakeit
can now work with multiple-extension response files. It also works correctly when multiple models are in use (this was release in patch v12.4.0r).
The active|inactive|options can be applied to the default (unnamed) model
(released in patch v12.4.0v).
Support for GLAST GBM extensions to the standard file formats including multiple response matrix extensions in the same file (released in patch
12.4.0am).
There are additional diagnostics available at high chatter levels from MCMC
chain
runs. User's custom proposal classes have access to information about acceptances and rejections.
Initial support for multicore processors using the OpenMP parallel processing compiler option. Multiplication of the model and response is performed in parallel across the multiple spectra in a datagroup.
All bug fixes to v12.4.0 released as patches a - ar are included in v12.5.0. In addition the following problems have been corrected.
A-322
When a runtime error is encountered during the calculation of a parameter's error bounds (using the
error
command), the value is now filled in with 0.0 rather than retaining its previous value.
Steppar
will now correctly step in reverse direction if the range values were entered in high-to-low order.
Model expression parsing has been improved for nested expressions.
Log file output has been fixed so '#' comments are placed correctly.
The chi-square calculation includes the
corfile
contribution even if there is no background file associated with the spectrum.
There are minor plotting fixes to the confidence line in 1-D steppar/margin plots, the rescaling of the Y=0 green line in lower-panel plots, and the Yaxis label in plot delchi.
Tclout
peakrsid no longer fails for a spectrum whose model was not assigned to source 1.
The XSFunctions library now also depends on XSModel, requiring the addition of a -lXSModel flag to the Makefile of external programs linking with the XSPEC model functions library. (See
Appendix F
)
The modelIonData model data files directory has been renamed to modelData.
Portions of some model functions have been translated from Fortran to C++ to reduce use of the udmget memory allocation function. Future versions will remove all references to udmget.
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Key Features
- Command-driven interactive program
- Detector-independent for any spectrometer
- Used for analyzing data from a variety of observatories
- Supports multiple data formats
- Includes a wide range of spectral models
- Provides tools for fitting and plotting data
- Offers extensive documentation and support
- Supports parallel processing
- Open-source software
