TOWARDS THE HABITABLE ZONE: DIRECT IMAGING OF

TOWARDS THE HABITABLE ZONE: DIRECT IMAGING OF
TOWARDS THE HABITABLE ZONE: DIRECT IMAGING OF
EXTRASOLAR PLANETS WITH THE MAGELLAN AO SYSTEM
by
Jared Robert Males
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF ASTRONOMY
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
2013
2
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Jared Robert Males
entitled Towards the Habitable Zone: Direct Imaging of Extrasolar Planets with the
Magellan AO System
and recommend that it be accepted as fulfilling the dissertation requirement for the
Degree of Doctor of Philosophy.
Date: 8 May 2013
Philip M. Hinz
Date: 8 May 2013
Dennis Zaritsky
Date: 8 May 2013
Olivier Guyon
Date: 8 May 2013
Glenn Schneider
Date: 8 May 2013
Final approval and acceptance of this dissertation is contingent upon the candidate’s
submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and
recommend that it be accepted as fulfilling the dissertation requirement.
Date: 8 May 2013
Dissertation Director: Laird M. Close
3
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an
advanced degree at the University of Arizona and is deposited in the University
Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission,
provided that accurate acknowledgment of source is made. Requests for permission
for extended quotation from or reproduction of this manuscript in whole or in part
may be granted by the head of the major department or the Dean of the Graduate
College when in his or her judgment the proposed use of the material is in the
interests of scholarship. In all other instances, however, permission must be obtained
from the author.
SIGNED:
Jared Robert Males
4
ACKNOWLEDGEMENTS
First and foremost I must give credit to my parents, Jim and Marcia Males. I’m
eternally grateful for the opportunities that you’ve given me. I grew up in a house
with Mom’s calculus textbooks on the shelf and Dad on his way to one science
experiment or another. Of course I ended up getting a Ph.D.
I also want to thank my advisor, Laird Close. You once told me that you thought
we would do a lot of good work together, and you were right. Thanks for your
patience, for your trust, and for giving me the freedom to explore and do it my
way. I’m extremely proud of what we accomplished during my Ph.D.
I’m incredibly grateful to the ladies of the Phoenix ARCS foundation, who have
helped fund my astronomical adventures for the last three years. ARCS is a truly
great organization with a noble purpose, and they also know how to throw a party.
Thanks to the whole MagAO Team, including: my office-mate and fellow Ph.D.
student Derek Kopon; our patient, responsive, flexible, and handy project manager/mechanical engineer/plumber/heavy lifter/etc., Victor Gasho; though she
was late to the party, Katie Morzinski has been a huge part of our success and
has helped make the VisAO blog a hit; Alfio Puglisi has been incredibly helpful
and tolerant of the many changes and tweaks I made to his code; Kate Follette
has contributed much in the way of science cases and establishing the VisAO blog;
Jason Lewis did great work both in the lab with VisAO and in Chile; MagAO
wouldn’t have worked — wouldn’t have even fit on the telescope — without
Alan Uomoto and Tyson Hare of Carnegie; to the whole Arcetri team, lead by
the incomparable Simone Esposito, the infallible Armando Riccardi, and their
incredible crew including Enrico, Marco, Runa, Fernando, Lorenzo, Javier, Paulo,
and many more; the Microgate team, especially Roberto Biasi ; the LCO staff and
crew, including Povilas Polunas and Dave Osip.
Thanks to Andy Skemer for letting me tag along on MMT runs and helping me get
some good data. Thanks also to Phil Hinz and Bill Hoffmann for lots of advice,
guidance, and encouragement.
MagAO itself received funding from several sources. Our adaptive secondary was
supported by the NSF MRI program. Our pyramid wavefront sensor and telescope
interfaces were developed with help from the TSIP program and the Magellan
partners. The VisAO camera and system commissioning were supported with funds
5
from the NSF ATI program. We also received a great deal of support from Steward
Observatory, and for that special thanks goes to Peter Strittmatter.
Much of the work presented here has been published previously. Parts of Chapter
2 and Chapter 3 appeared in SPIE proceedings as Males et al. (2010) and Males
et al. (2012a), and/or in MagAO technical documents (MAOPs), which can be
viewed on-line at https://visao.as.arizona.edu/documentation/. Chapter 6
was published in the Astrophysical Journal as Males et al. (2013). My second year
project, which appears here as Appendix C, was published in the Astrophysical
Journal as Males et al. (2012b).
6
DEDICATION
To Mom and Dad.
7
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
CHAPTER 1 INTRODUCTION
1.1 Adaptive Optics . . . . . .
1.2 LBTAO To Magellan . . .
1.3 Visible AO . . . . . . . . .
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CHAPTER 2 THE MAGELLAN ADAPTIVE OPTICS SYSTEM
VISAO CAMERA . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The VisAO Camera . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Control Software . . . . . . . . . . . . . . . . . . . . . .
2.2.2 VisAO Components . . . . . . . . . . . . . . . . . . . . .
2.3 CCD-47 Characterization . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Measurements of Gain and RON . . . . . . . . . . . . .
2.3.2 The 80 kHz Frame-Transfer Dark Current . . . . . . . .
2.3.3 CCD-47 Linearity . . . . . . . . . . . . . . . . . . . . . .
2.4 The VisAO Photometric System . . . . . . . . . . . . . . . . . .
2.4.1 Photometry in the r′ i′ z ′ bandpasses . . . . . . . . . . . .
2.4.2 Photometry in YS . . . . . . . . . . . . . . . . . . . . . .
2.4.3 The Impact of Water Vapor on z ′ and YS . . . . . . . . .
2.4.4 Exposure Time and Gain scalings . . . . . . . . . . . . .
2.5 Performance Simulations . . . . . . . . . . . . . . . . . . . . . .
2.6 Tower Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Seeing Validation . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Fitting Error . . . . . . . . . . . . . . . . . . . . . . . .
2.6.3 Tower Test Results . . . . . . . . . . . . . . . . . . . . .
2.7 On-sky Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Astrometric Calibration . . . . . . . . . . . . . . . . . .
2.7.2 Beamsplitter Ghost Calibration . . . . . . . . . . . . . .
2.7.3 Ys Strehl Ratio . . . . . . . . . . . . . . . . . . . . . . .
2.7.4 Throughput . . . . . . . . . . . . . . . . . . . . . . . . .
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TABLE OF CONTENTS – Continued
2.7.5
VisAO Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
CHAPTER 3 REAL TIME FRAME SELECTION . . . .
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
3.2 A Generic Frame Selection Algorithm . . . . . . . .
3.2.1 WFS Telemetry Based RTFS . . . . . . . .
3.3 The Costs & Benefits of Frame Selection . . . . . .
3.3.1 Signal to Noise Ratio and Duty Cycle . . . .
3.3.2 Encircled Energy and Aperture Size . . . . .
3.3.3 Effective Duty Cycle . . . . . . . . . . . . .
3.3.4 The Speckle Limited Case . . . . . . . . . .
3.3.5 The Halo Limited Case . . . . . . . . . . . .
3.3.6 Background and Read Noise Limited . . . .
3.3.7 Simulated Faint Guide Star Strehl Selection
3.4 RTFS Implementation . . . . . . . . . . . . . . . .
3.4.1 Mechanical Shutter Performance . . . . . . .
3.4.2 Telemetry . . . . . . . . . . . . . . . . . . .
3.4.3 GPU Based Reconstruction . . . . . . . . .
3.4.4 Digital Filter Design . . . . . . . . . . . . .
3.4.5 Reconstructor Calibration . . . . . . . . . .
3.4.6 Strehl Classification Algorithms . . . . . . .
3.5 Laboratory Demonstration . . . . . . . . . . . . . .
3.5.1 Experimental Setup . . . . . . . . . . . . . .
3.5.2 Results . . . . . . . . . . . . . . . . . . . . .
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . .
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CHAPTER 4 HIGH CONTRAST IMAGING WITH VISAO: OBSERVATIONS OF β PICTORIS B . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1.1 Disk Observations and Variability . . . . . . . . . . . . . . . . 97
4.1.2 Detection of β Pictoris b . . . . . . . . . . . . . . . . . . . . . 98
4.2 High Contrast Observations of β Pictoris with VisAO . . . . . . . . . 99
4.2.1 The VisAO Coronagraph . . . . . . . . . . . . . . . . . . . . . 99
4.2.2 Observations and Data Reduction . . . . . . . . . . . . . . . . 101
4.2.3 VisAO YS Contrast Limits . . . . . . . . . . . . . . . . . . . . 112
4.3 Detection of β Pictoris b with VisAO . . . . . . . . . . . . . . . . . . 113
4.4 Prior Measurements of β Pic b photometry in J, H, and KS . . . . . 117
4.5 Prior Exoplanet Photometry in the Y Band . . . . . . . . . . . . . . 118
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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TABLE OF CONTENTS – Continued
4.7
Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . 126
CHAPTER 5 DETECTABILITY OF EGPS IN THE HZ
5.1 The Habitable Zone . . . . . . . . . . . . . . . . .
5.2 Are there planets in the HZ? . . . . . . . . . . . .
5.3 The Radius and Temperature of a Giant Planet .
5.4 Thermal Infrared Brightness of EGPs . . . . . . .
5.5 Habitable Zone EGPs in the Visible . . . . . . . .
5.6 Blazing The Trail . . . . . . . . . . . . . . . . . .
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CHAPTER 6 DIRECT IMAGING IN THE HABITABLE ZONE AND
PROBLEM OF ORBITAL MOTION . . . . . . . . . . . . . . . . . .
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Motivation and Related Work . . . . . . . . . . . . . . . . . . .
6.2.1 Nearby Habitable Zones . . . . . . . . . . . . . . . . . .
6.2.2 A Different Regime . . . . . . . . . . . . . . . . . . . . .
6.2.3 Long Integration Times . . . . . . . . . . . . . . . . . .
6.2.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Quantifying The Problem . . . . . . . . . . . . . . . . . . . . .
6.3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Impact on Signal-to-Noise Ratio . . . . . . . . . . . . . .
6.3.3 Impact on Statistical Sensitivity . . . . . . . . . . . . . .
6.4 Blind Search: Recovering SNR after Orbital Motion . . . . . . .
6.4.1 Limiting Trial Orbits . . . . . . . . . . . . . . . . . . . .
6.4.2 Choosing Orbital Elements . . . . . . . . . . . . . . . . .
6.4.3 De-orbiting: Unique Sequences of Whole-Pixel Shifts . .
6.4.4 Norb Scalings . . . . . . . . . . . . . . . . . . . . . . . .
6.4.5 Recovering SNR . . . . . . . . . . . . . . . . . . . . . . .
6.4.6 Correlations And The True Impact On PF A . . . . . . .
6.4.7 Impact on Completeness of the Double Test . . . . . . .
6.4.8 Tractability of a Blind Search . . . . . . . . . . . . . . .
6.5 Cued Search: Using RV Priors . . . . . . . . . . . . . . . . . . .
6.5.1 Constraints . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2 Initial Detection . . . . . . . . . . . . . . . . . . . . . . .
6.5.3 Calculating Orbits and Shifts . . . . . . . . . . . . . . .
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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THE
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CHAPTER 7 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10
TABLE OF CONTENTS – Continued
APPENDIX A POINT SPREAD FUNCTION RADIOMETRY
TOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 PSF Modeling . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Characterizing the PSF . . . . . . . . . . . . . . . . . .
A.3 Tip & Tilt Errors, FWHM, and Strehl Ratio . . . . . .
A.4 Gaussian PSF Photometry . . . . . . . . . . . . . . . . .
A.5 Propagation of Errors . . . . . . . . . . . . . . . . . . . .
A.5.1 Absolute Magnitude . . . . . . . . . . . . . . . .
A.5.2 Physical Photometry . . . . . . . . . . . . . . . .
APPENDIX B SYNTHETIC PHOTOMETRY
B.1 Filters . . . . . . . . . . . . . . . . . .
B.1.1 The Y Band . . . . . . . . . . .
B.1.2 The 2MASS System . . . . . .
B.1.3 The MKO System . . . . . . . .
B.1.4 The NACO System . . . . . . .
B.1.5 The NICI System . . . . . . . .
B.2 Synthetic Photometry . . . . . . . . .
B.3 Photometric Conversions . . . . . . . .
B.3.1 Converting 2MASS to MKO . .
B.3.2 Y Band Conversions . . . . . .
B.3.3 J Band Conversions . . . . . .
B.3.4 H Band Conversions . . . . . .
B.3.5 K Band Conversions . . . . . .
AND PHO. . . . . . . 186
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AND CONVERSIONS
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APPENDIX C FOUR DECADES OF IRC +10216: EVOLUTION OF A CARBON RICH DUST SHELL RESOLVED AT 10µM WITH MMT ADAPTIVE
OPTICS AND MIRAC4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
C.1.1 The carbon star IRC +10216 . . . . . . . . . . . . . . . . . . 207
C.1.2 SiC dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
C.1.3 IRC +10216 in the spatial domain . . . . . . . . . . . . . . . . 209
C.1.4 New results from the MMT . . . . . . . . . . . . . . . . . . . 211
C.2 Observations and data reduction . . . . . . . . . . . . . . . . . . . . . 211
C.2.1 2009 bandpass photometry . . . . . . . . . . . . . . . . . . . . 212
C.2.2 2010 grism spectroscopy . . . . . . . . . . . . . . . . . . . . . 214
C.3 Archival data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
C.3.1 Introduction to the spectral datasets . . . . . . . . . . . . . . 219
C.3.2 Bandpass photometry archives . . . . . . . . . . . . . . . . . . 221
11
TABLE OF CONTENTS – Continued
C.3.3 Comparison of Archival Data . . . . . . . . . . . . . . .
C.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.4.1 Changes in the 10 µm spectrum of IRC +10216 . . . . .
C.4.2 The spatial signature of SiC emission . . . . . . . . . . .
C.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.6 Appendix: The possibly erroneous 8.7µm photometry from 2009
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REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
12
LIST OF FIGURES
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
The W-unit . . . . . . . . . . . . . . . . . . .
The W-unit as built. . . . . . . . . . . . . . .
80 kHz dark frame . . . . . . . . . . . . . . .
80 kHz dark frame standard deviation . . . .
80 kHz 41 sec frame . . . . . . . . . . . . . . .
80 kHz dark current . . . . . . . . . . . . . .
80 kHz dark current at different temperatures
80 kHz dark current at histograms . . . . . . .
80 kHz column standard deviation . . . . . . .
CCD-47 Linearity . . . . . . . . . . . . . . . .
VisAO SDSS bandpasses . . . . . . . . . . . .
VisAO z ′ and YS bandpasses . . . . . . . . . .
Simulated 1x1 binning performance of MagAO
Seeing limited profile in the tower . . . . . . .
MagAO fitting error . . . . . . . . . . . . . .
Test tower results . . . . . . . . . . . . . . . .
Test tower performance vs. predictions . . . .
Ys PSF . . . . . . . . . . . . . . . . . . . . . .
θ1 Ori C . . . . . . . . . . . . . . . . . . . . .
θ1 Ori B . . . . . . . . . . . . . . . . . . . . .
HR 4796 with VisAO . . . . . . . . . . . . . .
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23
24
32
33
34
35
36
36
38
39
41
42
47
49
50
52
53
58
63
64
66
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
Simulated Strehl selection results
Simulated Strehl selection FWHM
Shutter performance . . . . . . .
Schematic of RTFS . . . . . . . .
Reconstructed Strehl ratio . . . .
Predicting Strehl ratio . . . . . .
Short exposure S statistics . . . .
RTFS images . . . . . . . . . . .
RTFS laboratory results . . . . .
RTFS duty cycle . . . . . . . . .
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and duty cycle
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78
81
82
84
87
88
91
93
95
96
4.1
4.2
4.3
Transmission of the VisAO Coronagraph (log scale) . . . . . . . . . . 100
Transmission of the VisAO Coronagraph . . . . . . . . . . . . . . . . 102
VisAO PSFs under the coronagraph . . . . . . . . . . . . . . . . . . . 103
13
LIST OF FIGURES – Continued
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
Raw PSF FWHM under the mask . . .
Ratio of FWHMs under the mask . . .
VisAO YS Coronagraphic PSF . . . . .
β Pic Median ADI . . . . . . . . . . .
β Pic Reduction steps . . . . . . . . .
VisAO YS Contrast Limits . . . . . . .
β Pic Flux and S/N Map . . . . . . . .
β Pic b S/N . . . . . . . . . . . . . . .
2M1207b and HR 8799b . . . . . . . .
β Pic b Colors . . . . . . . . . . . . . .
β Pic b brown dwarf close matches . .
β Pic b Spectral Type . . . . . . . . .
β Pic b SpType without various filters
β Pic b HR Diagrams . . . . . . . . . .
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104
105
108
109
111
114
115
116
120
122
123
124
125
127
5.1
5.2
5.3
5.4
Projected HZs of select nearby stars . .
EGPs around α Cen A . . . . . . . . .
EGPs around Sirius . . . . . . . . . . .
Visible reflected light contrast of EGPs
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131
136
137
140
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
Orbital speed . . . . . . . . . . . . . .
SNR with orbital motion . . . . . . . .
Ground-based SNR with orbital motion
Statistics after orbital motion . . . . .
Whole-pixel shift sequences . . . . . .
Trial orbits for α Cen A . . . . . . . .
Orbital motion scalings . . . . . . . . .
Possible starting points for Gl 581d . .
Trial orbits for Gl 581d . . . . . . . . .
Trial orbits for Gl 581d . . . . . . . . .
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150
152
154
157
166
167
170
178
180
182
B.1
B.2
B.3
B.4
B.5
B.6
B.7
B.8
B.9
Y-band filters . . . . . . . . .
J-band filters . . . . . . . . .
H-band filters . . . . . . . . .
K-band filters . . . . . . . . .
2MASS to MKO Conversions
Y Band Conversions . . . . .
J Band Conversions . . . . .
H Band Conversions . . . . .
K Band Conversions . . . . .
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196
197
197
198
202
203
203
204
205
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14
LIST OF FIGURES – Continued
C.1 MIRAC4 grism observations of IRC +10216 . . . . . . . . . . . . .
C.2 Spatial profiles of IRC +10216 and PSF . . . . . . . . . . . . . . .
C.3 FWHM vs wavelength . . . . . . . . . . . . . . . . . . . . . . . . .
C.4 Slit-loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C.5 IRC+10216 spectrum . . . . . . . . . . . . . . . . . . . . . . . . . .
C.6 IRC +10216 10µm spectra and photometry from 1973 to 1978 . . .
C.7 IRC +10216 10µm spectra from 1983 to 1988 . . . . . . . . . . . .
C.8 IRC +10216 10µm spectra from 1993 to 1996 . . . . . . . . . . . .
C.9 IRC+10216 N band spectra over four decades . . . . . . . . . . . .
C.10 Fν (12.5µm)/Fν (10.55µm) vs. time . . . . . . . . . . . . . . . . . . .
C.11 IRC +10216 on the “Carbon-Rich Dust Sequence” . . . . . . . . . .
C.12 The spectral and spatial signatures of SiC dust around IRC +10216
C.13 MIRAC4 detector linearity measurement . . . . . . . . . . . . . . .
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232
233
234
235
236
237
238
239
240
241
242
243
244
15
LIST OF TABLES
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
CCD-47 Gain and RON . . . . . . . . . . .
VisAO Photometry . . . . . . . . . . . . . .
Predicted VisAO error budget . . . . . . . .
Tower Test Fitting Error . . . . . . . . . . .
Clio astrometry of θ1 Ori B1 and B2 . . . .
VisAO YS platescale and rotator calibration
50/50 ghost calibration . . . . . . . . . . . .
Strehl measurements at YS (0.984µm) . . . .
VisAO Observation Log: LHS 14 . . . . . .
VisAO Throughput . . . . . . . . . . . . . .
4.1
4.2
4.3
4.4
Observations of β Pictoris . . . . . .
Astrometry of β Pictoris b . . . . .
Photometry of β Pictoris b . . . . .
Estimated YS and NACO photometry
6.1
6.2
6.3
6.4
Trial orbit statistics . . . . . . . . . . . .
SNR recovery after orbital motion . . . .
False alarm probabilities after de-orbiting
Gl 581d parameters . . . . . . . . . . . .
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of 2M1207b
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28
43
46
51
55
56
57
61
61
62
. . . . . . . . .
. . . . . . . . .
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and HR 8799b
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106
114
118
119
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168
171
173
175
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A.1 PSF Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.1 Atmospheres. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.2 Synthetic Photometric System . . . . . . . . . . . . . . . . . . . . . . 199
B.3 Photometric conversion coefficients. . . . . . . . . . . . . . . . . . . 206
C.1 IRC+10216 Obervations . . . . . . . . . . . . . . . . . . . . . . . . . 245
C.2 Bandpass photometry of IRC +10216 . . . . . . . . . . . . . . . . . . 246
C.3 Grism photometry of IRC +10216 . . . . . . . . . . . . . . . . . . . . 247
16
ABSTRACT
One of the most compelling scientific quests ever undertaken is the quest to find
life in our Universe somewhere other than Earth. An important piece to this puzzle is finding and characterizing extrasolar planets. This effort, particularly the
characterization step, requires the ability to directly image such planets. This is
a challenging task — such planets are much fainter than their host stars. One of
the major solutions to this problem is Adaptive Optics (AO), which allows us to
correct the turbulence in the Earth’s atmosphere, and thereby further the hunt for
exoplanets with ground based telescopes. The Magellan Adaptive Optics system
has recently obtained its first on-sky results at Las Campanas Observatory, marking a significant step forward in the development of high-resolution high-contrast
ground-based direct imaging. MagAO includes a visible wavelength science camera,
VisAO, which — for the first time — provides diffraction limited imaging, in long
exposures, on a large filled-aperture (6.5 m) telescope. In this dissertation we report
on the design, development, laboratory testing, and initial on-sky results of MagAO
and VisAO, which include the first ground-based image of an exoplanet (β Pictoris
b) with a CCD. We also discuss some of the exciting science planned for this system
now that it is operational. We close with an analysis of a new problem in direct
imaging: planets orbiting their stars move fast enough in the habitable zone to limit
our ability to detect them.
17
CHAPTER 1
INTRODUCTION
1.1 Adaptive Optics
Everyone knows that stars appear to twinkle. While many have a fond attachment to
this phenomenon, for astronomers it presents a significant problem. This twinkling
is caused by turbulence in our own atmosphere, and sets a natural limit to the
resolution achievable in ground based astronomical imaging. No matter how big we
build a telescope, the twinkle-causing turbulence limits our resolution to about 1
arcsecond.
There is, of course, a solution. Using a technology called adaptive optics (AO),
we can partially correct for atmospheric turbulence in real-time, effectively “detwinkling” the stars. In what follows, we report on the development and first onsky results with a new AO system — the Magellan AO system, or MagAO. MagAO
was developed at the UA, with funds from the NSF MRI, TSIP, and ATI programs
under principle investigator Laird Close. MagAO is now resident at Las Campanas
Observatory (LCO), Chile, where it is installed on the 6.5 m Magellan Clay Telescope
for dedicated observing runs.
MagAO uses an adaptive secondary mirror (ASM), a technology proven at the
MMT telescope on Mt. Hopkins, Az (Wildi et al., 2003). By minimizing the number
of warm surfaces in the optical train, the thermal performance of the system is
improved compared to a conventional AO system (Lloyd-Hart, 2000). ASMs offer
other benefits as well. Their larger size, relative to conventional deformable mirrors,
makes it easier to achieve high actuator densities. ASMs also employ a contactless face-sheet. A significant benefit of this design over other technologies is that it
allows failed actuators to be deactivated without creating surface discontinuities.
An important innovation developed for the LBT and now in use at Magellan is
18
the pyramid wavefront sensor (WFS). A significant improvement this provides over
a conventional Shack-Hartmann WFS is the ability to re-bin the detector, which
improves its performance on faint guide stars. Pyramid WFSs also suffer from
much lower aliasing than other WFS implementations, allowing higher contrast to
be reached.
All of these benefits have been taken advantage of in the latest generation of
ASM AO systems, first at the Large Binocular Telescope (LBT), on Mt. Graham
in Arizona, and now at Magellan.
1.2 LBTAO To Magellan
The MagAO system consists of a near clone of the LBT ASMs. One might initially
think that this is a downgrade, as the diffraction-limited spatial resolution of a
telescope is given by
λ
arcseconds
D
where F W HM means the full-width at half-maximum of the point spread function
F W HM = 0.2063
(PSF) in arcseconds, λ is the wavelength of light being observed in µm, and D is the
diameter of the telescope in meters. The 8.4 m LBT primaries should have nearly
30% better resolution (smaller F W HM ) than the 6.5 m Magellan Clay telescope1 .
Furthermore, the sensitivity (“light-grasp”) of the telescope goes as at least D2 , that
is with the collecting area. With AO, in fact, we expect to see D4 improvement in
point-source sensitivity due to the complimentary effects of increased collecting area
and smaller PSF reducing background noise.
But there is another consideration: actuator pitch. When projected over the
pupil, that is the primary mirror, the actuators have an effective spacing of
s
π 2
1
2
d=
meters.
D (1 − ǫ )
4
Nact
where ǫ is the central obscuration ratio and Nact is the total number of illuminated
actuators2 . At the LBT, with D = 8.4m and Nact = 666, we find d = 28.7 cm. At
1
2
Here we are ignoring details such as undersized cold stops
Taking into account the central obscuration
19
Magellan, with D = 6.5m and Nact = 561, we have d = 23.3 cm. Note that we
have accounted for the central obscurations so Nact is not actually 672 and 585 for
the two systems, respectively. The point to this calculation is that on the smaller
primary mirror at Magellan, the same physical actuators are closer together when
projected onto the sky.
To appreciate the impact actuator spacing has, we must consider the quantity
called Strehl ratio, which we will denote as S. This is a measure of image quality
defined as the ratio of the PSF peak obtained with an imaging system to that
expected if that system were perfect (Hardy, 1998). Theoretical calculations of
S typically proceed by determining the errors from different sources. The error
concerning us here is the so-called “fitting-error”, which quantifies the fact that
we can only correct atmospheric turbulence up to a certain spatial frequency. The
fitting-error for a continuous face-sheet deformable mirror is given by (Hardy, 1998)
σf2it
= 0.28
d
r0
5/3
rad2 .
The quantity r0 is the Fried coherence length, a measure of seeing. If we assume that
all sources of error add in quadrature, we can employ the Marechal approximation
(Born and Wolf, 1999) to calculate S due to fitting error:
2
Sf it = e−σf it .
Finally, to fully apply these formulas, we need an estimate for r0 . It can be
expressed in terms of the seeing F W HM , θ, as
r0 = 0.2022
λ
meters
θ
where λ is in µm and θ is in arcseconds. On Mt. Graham, Arizona, the location
of the LBT, median seeing at V band (0.55µm) is 0.8”. So at the LBT median
r0 = 13.9 cm. At LCO median seeing at V is 0.625” (Floyd et al., 2010)3 , so
3
This is median DIMM seeing, measured seeing on the full 6.5m aperture is better than this
due to outer scale effects.
20
median r0 is 17.8 cm. Using the relationship r0 ∝ λ6/5 , we can make the following
comparison:
At the LBT, observing at J band (1.2µm):
Sf it = 81%
F W HM = 0.029′′
At Magellan, observing at i′ (0.77µm):
Sf it = 80%
F W HM = 0.024′′
So we see that the smaller effective actuator spacing, combined with the better
seeing at LCO, means that the same AO technology should be able to provide
the same level of spatial correction at i′ at LCO as it does at J at the LBT —
but actually realizing an improvement in resolution due to the shorter λ despite
the smaller primary D. The full story is more complicated than this, as we have
ignored such things as errors due to servo lag, but these simple arguments illustrate
the advantage a smaller primary mirror provides for an AO system.
The high performance of the LBT ASMs has been demonstrated on sky at Mt.
Graham (Esposito et al., 2010). Using the smaller Magellan primary, the relatively
higher projected actuator pitch allows the same technology to provide the same
excellent performance at shorter wavelengths. This motivated the development of a
visible wavelength science camera for Magellan, which we call VisAO.
1.3 Visible AO
Other groups have implemented visible light AO in one form or another. ViLLaGEs
is a MEMs-based visible wavelength AO testbed on the 1.0 m Nickel telescope
at Lick Observatory, in California (Morzinski et al., 2010). Baranec et al. (2012)
21
have developed a visible AO capability on a 1.5 m telescope at Palomar observatory (Robo-AO). The USAF 3.6 m AEOS telescope has also worked in the visible
(Roberts and Neyman, 2002), achieving moderate correction. The Palomar AO system had some capability to work in the visible, particularly when employing Lucky
imaging (Law et al., 2009). The largest telescope with a visible AO capability is
the 8.2m Subaru, with the AO188 system, which can achieve the diffraction limit in
the visible utilizing Lucky imaging techniques in the Fourier domain (Garrel et al.,
2010).
The Magellan VisAO camera represents a true step forward. In the following
pages we report on the design, performance analysis, laboratory testing, and finally
the on-sky demonstration of the world’s first truly diffraction limited visible light
imager on a large (> 6m) telescope. The distinction setting VisAO apart from previous efforts is that it delivers filled-aperture, long exposure images, with diffraction
limited cores, and Strehls greater than 20% — at visible wavelengths.
In Chapter 2 we present an overview of VisAO, and the simulation and laboratory
characterization of the MagAO/VisAO system carried out prior to shipping to LCO.
We also describe our initial on-sky characterization efforts. In Chapter 3 we discuss
our version of the Lucky imaging technique, Real Time Frame Selection (RTFS),
which uses a fast shutter to select images using WFS telemetry. In Chapter 4 we
present observations of the exoplanet host star β Pictoris, demonstrating the first
high-contrast exoplanet science with a CCD on the ground. Then in Chapter 5 we
lay out some of the future exoplanet science goals for the system, namely a search
for extrasolar giant planets (EGPs) in the habitable zones (HZs) of the nearest stars.
Finally, in Chapter 6, we consider the far future, when the next generation of giant
telescopes will enable HZ observations of many more stars, but the higher projected
orbital speeds of these planets will degrade our sensitivity.
22
CHAPTER 2
THE MAGELLAN ADAPTIVE OPTICS SYSTEM AND VISAO CAMERA
2.1 Introduction
In this chapter we present an introduction to the VisAO camera, and an overview of
the work done to prepare it and the MagAO system to go on-sky. We then present
some of our first on-sky results, and show some of our early efforts to characterize
the system.
Some of the work presented in this chapter has appeared in print in Males
et al. (2010) and Males et al. (2012a). Much is also contained in one form or
another in MagAO technical documents (MAOPs), which can be viewed on-line at
https://visao.as.arizona.edu/documentation/
2.2 The VisAO Camera
The main focus of this dissertation is MagAO’s visible light science camera, VisAO.
VisAO is the world’s first diffraction-limited imager on a large telescope capable of
working at visible wavelengths. On the 6.5m Magellan Clay Telescope, VisAO is
capable of 19 milliarcsecond resolution at 0.62µm (the r′ central wavelength) (Close,
et al., (2013, submitted)).
A very basic visible camera is part of the LBT W-unit baseline, where it is
used almost exclusively as a wide-field seeing-limited acquisition camera. Here we
provide an introduction to the VisAO camera and highlight the many upgrades
and optimizations we have made to ready the system to record some of the highest
resolution filled aperture images ever taken.
This 1024x1024 CCD camera provides 0.0079” pixels, Nyquist sampling the
diffraction limited PSF down to ∼ 0.5µm with an 8.1” field of view (FOV). A
23
Figure 2.1 The Magellan AO system WFS and VisAO camera.
24
Figure 2.2 The Magellan AO system WFS and VisAO camera, as built. Shown here
prior to installation of the CCD and shutter cooling system. Note that orientation
is flipped with respect to Figure 2.1.
25
key feature of this design regarding VisAO performance is that the CCD47 is on a
common mount with the WFS. Figure 2.1 illustrates the design of our Magellan AO
WFS and VisAO optical board, and Figure 2.2 shows the as built system.
2.2.1 Control Software
Adding significant science observation capability to what is essentially a static acquisition camera offered many challenges. An important one identified early on was
the need to not break the LBT AO system software, that is to make sure that the
system operated at Magellan as similarly as possible to the LBT. In addition, the
LBT makes use of a Microgate basic computational unit (BCU) as the framegrabber for the CCD-47. It became apparent that this architecture did not offer enough
flexibility to fully exploit the capabilities of the VisAO camera. To compensate, we
implemented our own framegrabber using a PCI card provided by Scimeasure, and
developed a software system for emulating the BCU so that the AO system doesn’t
notice the missing device. All VisAO extensions to the LBT AO “adopt” software
are seamlessly integrated, such that there are very few changes to the core of the AO
control software. We took pains to ensure that process control (starting, stopping,
state reporting, etc.) are identical to the “adopt” system. In short, VisAO functions
as a native component of the LBT AO software used to control the MagAO system.
An important consideration was to ensure that the AO system, or rather the AO
operator, could not inadvertently corrupt a science operation by, say, changing a filter wheel. Conversely, during AO acquisition the VisAO astronomer must be careful
to not reconfigure the CCD-47 or other components lest the acquisition sequence
fail. We implemented a hierarchical system of control, whereby all VisAO processes
have a control state — REMOTE when under control of the AO system, LOCAL
when under control of the VisAO astronomer, and SCRIPT when an observation
script is running. For instance, the VisAO astronomer can not change filters unless
she explicitly takes control of the filter wheel first.
We also developed several real-time components, mainly in support of the Real
Time Frame Selection (RTFS) technique, which is described in full in Chapter 3.
26
Included in this system is real-time reconstruction of WFS slopes, which are used
to calculate instantaneous Strehl ratio. We also use this system to record wavefront
error (WFE) and write the average value of WFE during an exposure to the FITS
headers. Details of this are also provided in Chapter 3, and we demonstrate the use
of WFE to estimate Strehl ratio below.
The resulting software system, written almost entirely by the author, consists
of over 300 files of source code in C, C++, idl, python, and BASH scripts. These
files contain over 57000 lines of code, including code and comments but ignoring
whitespace. The source, source documentation, and a user’s guide can be browsed
at https://visao.as.arizona.edu/software_files/visao/html/index.html.
2.2.2 VisAO Components
VisAO has several custom components which optimize the camera for high-contrast
diffraction-limited circumstellar science. These components are additions to the
LBT W-unit baseline. Here we provide a brief overview of the major components.
For more information on these and other components see the MagAO technical documents (MAOPs) provided at https://visao.as.arizona.edu/documentation/.
The Wollaston: A Wollaston beamsplitter prism is located just before the
gimbal on a manually actuated elevator stage. When placed in the beam, the beam
is split vertically allowing simultaneous differential imaging (SDI) using custom
double filters located in filter wheel 3.
The Gimbal: The VisAO gimbal mirror is actuated, providing steering of the
beam on the CCD-47 detector. This is broadly necessary as each beamsplitter has
a different tilt. It is also necessary for coronagraph alignment, and optimizing the
FOV for various targets. The mechanical FOV of the gimbal is ∼ 12×17 arcseconds,
compared to ∼ 8 × 8 arcseconds on the detector.
The Focus Stage: The VisAO focus stage moves the CCD47, shutter, and
VisAO filter wheel assembly in the z direction. The AO keeps the system focused
on the tip of the pyramid at all times, so the VisAO focus stage only compensates
for changes in the relative focus between the CCD-47 detector and the pyramid tip.
27
This depends on wavelength (filter selection), and whether or not the Wollaston
prism is in the beam. Further information about the focus stage and its operation
is provided in MAOP-706.
Filter Wheels: The VisAO camera has 2 filter wheels, instead of the one in
the LBT baseline. The first wheel contains our broad bandpass filters: SDSS r’, i’,
z’, and what we call Y short (YS ) at 1µm. The second wheel contains custom SDI
filters (filters with two bandpasses on a common substrate), an ND 3, and a partially
transmissive coronagraphic occulting mask (see Chapter 4). The filter curves and
other characteristics of the filters are shown later in this chapter.
The CCD-47: The MagAO CCD 47 is the system acquisition camera and the
main sensor of the visible wavelength science camera (VisAO). It is an EEV CCD-47
detector, with a Scimeasure Little Joe controller. Though the hardware is the same
as those in a standard LBT W-unit, we acquired several unique operating modes
(programs). Visible AO works best with a bright natural guide star (NGS), so one of
our biggest challenges is avoiding saturation. As such, we frequently operate in high
speed modes, up to 42 fps. For sensitive work, such as high-contrast circumstellar
science, we take longer exposures in more sensitive gain settings. In the next section
we describe our extensive characterization of these different modes.
2.3 CCD-47 Characterization
During laboratory integration, and now in on-sky testing, we have characterized the
CCD-47 sensitivity and linearity. The results reported here are also provided in
MAOP-702.
2.3.1 Measurements of Gain and RON
Each CCD-47 program defines a readout speed, window (or sub-array) size, binning,
and gain. Each combination of readout speed, window,and binning has 4 possible
choices of gain: high, medium-high, medium-low, and low. These correspond to
most sensitive to least sensitive, respectively. Together, the readout speed and gain
28
set the readout noise (RON) of the camera. The CCD-47 is a 14 bit camera, which
has important system sensitivity implications. The lowest sensitivity gain is ∼ 13
electrons per ADU. That means that it takes 13 electrons to register a signal. At
low flux levels, e.g. in the wings of the PSF halo, this makes the camera much less
sensitive than from RON and photon noise alone. N.B. that when in this sensitivity
√
setting, integrating longer will not reduce noise as expected ( N ).
Gain and read-out noise were measured in the Magellan AO lab at Steward
Observatory in February 2010, prior to being mounted on the W-Unit board. For
these measurements the CCD head was wrapped in Al foil, place in a cardboard box,
and had liquid cooling applied. The cardboard box had a hole cut in it, a paper
placed over the hole to provide a somewhat flat illumination, and an LED flashlight
was used as the source. The lab thermostat was set to minimum to provide a cool
ambient temperature to minimize the impact of dark current. For these tests the
Little Joe case temperature was 20C. CCD47 Head temperature was -36C, except in
the 64x64 and 32x32 modes when it rose to -33C due to the high frame rate. At each
pixel rate and gain setting we took 2 darks and 2 flats, which were then analyzed
using the findgain task in IRAF. Two sets of data were taken at each setting, and
typical variations between these sets was 0.01 for gain and 0.02 ADU for RON. The
64x64 and 32x32 modes had larger variations, and the numbers presented are the
average of the two sets. Results are presented in Table 2.1. These data are also
published in MAOP-702.
Table 2.1: CCD-47 Gain and readout noise measurements
Measured
Mode
Gain
Setting
Scimeasure
Gain
RON
Gain
RON
(e− /ADU)
(e− )
(e− /ADU)
(e− )
2500 kHz
High
0.53
9.7
0.55
10.2
1024x1024
Med High
1.93
9.55
1.97
9.83
Bin 1x1
Med Low
3.58
10.74
3.62
10.4
continued on next page
29
Table2.1– continued from previous page
Measured
Mode
Gain
Setting
Scimeasure
Gain
RON
Gain
RON
(e− /ADU)
(e− )
(e− /ADU)
(e− )
3.53 fps
Low
13.23
15.47
13.3
15.3
2500 kHz
High
0.54
9.62
-
-
64x64
Med High
1.93
9.58
-
-
Bin 1x1
Med Low
3.58
10.86
-
-
31.48 fps
Low
13.14
15.49
-
-
250 kHz
High
0.47
4.52
0.49
5.81
1024x1024
Med High1
1.77
4.67
1.71
5.66
Low2
3.34
5.28
3.29
6.59
Bin 1x1
Med
0.44 fps
Low1
12.3
11.11
12.1
10.8
80 kHz3
High
0.48
7.35 / 3.54
0.48
3.37
1024x1024
Med High
1.78
6.3 / 3.69
1.79
3.53
3.33
6.23 / 4.38
3.31
4.28
12.43
12.35 / 11.02
12.2
10.3
Bin 1x1
Med
Low1
0.143 fps
Low
1
80 kHz3
High
0.48
5.69 / 3.62
0.48
3.28
1024x1024
Med High
1.74
5.98 / 3.72
1.79
3.61
Bin 2x2
Med Low1
3.27
6.18 / 4.43
3.31
3.29
0.551 fps
Low
11.08
12.1 / 9.68
12.2
10.3
80 kHz
High4
0.47
9.76 / 6.85
0.46
3.62
1024x1024
Med High4
1.76
10.07 / 7.31
1.74
3.95
Bin 16x16
Med Low4
3.25
10.42 / 7.43
3.31
4.63
10.42 fps
Low4
12.38
14.43 / 12.13
11.6
10.3
2500 kHz
Low
0.53
9.59
-
-
512x512
Med Low
1.93
9.54
-
-
Bin 1x11
Med High
3.57
10.71
-
-
6.70 fps
High
13.26
15.55
-
-
2500 kHz
High
0.54
9.46
-
-
32x32
Med High
1.88
9.57
-
-
continued on next page
30
Table2.1– continued from previous page
Measured
Mode
Gain
Setting
Scimeasure
Gain
RON
Gain
RON
(e− /ADU)
(e− )
(e− /ADU)
(e− )
3.5
10.59
-
-
Bin 1x1
Med Low
42.78 fps
Low
12.61
14.51
-
-
250 kHz
High
0.48
3.84
-
-
512x512
Med High
1.77
4.25
-
-
Bin 1x1
Med Low
3.32
4.88
-
-
1.49 fps
Low
12.36
10.52
-
-
80 kHz
High5
0.47
9.06 / 8.66
-
-
512x512
Med High
1.74
4.13 / 3.36
-
-
Bin 1x1
Med Low
3.32
4.82 / 4.24
-
-
0.535 fps
Low
12.46
10.94 / 10.58
-
-
1Used
1 pass of 5σ clipping
2One
bad dark frame here gives odd results. Ignored.
3The
80kHz RON measurements require special handling due to excess
frame-transfer dark current. The 2nd number is from the alternate 100
frame method described in 2.3.2.
4The
bad results here are explainable by the excess dark current. Taking
into account both the decreased frame time and the larger number of
pixels in each bin, there is 3.5 as much dark current per pixel in these
images
5This
mode appears to be genuinely out of spec. We had to adjust black
levels in this mode (a consequence of low Joe temperature) but it would
be surprising if this affects RON.
2.3.2 The 80 kHz Frame-Transfer Dark Current
As noted in Table 2.1, the raw 80kHz RON was significantly worse than expected.
The number one suspect is dark current since we did not measure RON with 0
exposure time. Upon investigating, we found that a dark current is the likely culprit,
31
however it appears that it is not simply a dark current which scales with exposure
time.
To start our investigation we took 100 dark frames (cap on) at 80 kHz. Figure
2.3 shows the median of these frames. We next took the standard deviation of
the 100 frames on a pixel by pixel basis, shown in Figure 2.4. It appears that the
signal shown in Figure 2.3 is a source of Poisson noise, which is at the same level
as expected to explain the high RON results. This dark signal is much higher than
expected based on the E2V specifications for our CCD47.
In Figure 2.5 we show the median of 50 41 second dark frames. Here we see the
first hint that the dark signal in Figure 2.3 is not scaling with time1 . A separate
pattern is now becoming visible. In Figure 2.6 we show the median dark current,
which was calculated by subtracting a 6.9 second exposure from a 94 second exposure. The short exposure was not scaled, so we see that the dark signal in Figure
2.3 is indeed not scaling with time, and once it is subtracted a dark signal more in
line with that expected is evident.
Our best guess to explain these results is that the high dark signal found in
Figure 2.3, which causes the high RON at 80kHz, is associated with the frametransfer architecture and that it depends only on readout time which is a constant
set by pixel-rate and is independent of exposure time. In other words, this is dark
current on the transfer frame and its impact is controlled by how long charge sits
on the transfer frame during the readout process, not on how long charge sits on
the exposed science frame.
We found that this frame-transfer dark signal does scale with temperature. At
a head temperature of -29.5C RON was 11.32 electrons, and at -33C RON was
8.41 electrons. To further test this, we added a second cold plate which got head
temperature down to -36C. In Figure 2.7 we show a side-by-side comparison of this
signal at -32C and -36C, demonstrating the reduction in the dark signal. In Figure
2.8 we show the change in the histogram of the RON of all pixels on the array with
the reduced temperature.
1
We note that temperature did not change significantly during these measurements.
32
Figure 2.3 Median of 100 80 kHz dark frames, showing the structure of the excess
dark current. Exposure time of individual frames was 6.9 secs.
33
Figure 2.4 Pixel by pixel standard deviation of 100 80 kHz dark frames. The excess
structure seen in Figure 2.3 appears to be a source of Poisson noise.
34
Figure 2.5 Median of 50 41 sec frames, at 80 kHz. The structure evident in Figure
2.3 does not scale with exposure time. This, and all images that follow, are full
1024x1024 frames.
35
Figure 2.6 This is the dark current, calculated by subtracting a 6.9 second frame
from a 94 second frame (80kHz) and dividing by exposure time. Note that the
structure in the first image has almost completely subtracted out, but the pads and
the waves are clearly visible.
36
Figure 2.7 6.9 sec images at different temperatures, same stretch and colorbar. The
dark current is lower at -36C.
Figure 2.8 Histograms of the full array at two different temperatures, in the 80kHz
readout speed. As temperature is lowered, it appears that we might approach the
expected value of ∼ 3.5e− RON.
37
In Figure 2.9 we plot the column-wise standard deviation, at -32C and -36C. We
see that the signal is lowest at column 0, so we assume that this is the first column
read out and column 1023 is the last column read out. To provide an estimate of
our true RON measured in the lab, we calculate the value of the column 0 standard
deviation by fitting a line to the first 100 columns and taking its intercept, which
is 3.54 electrons in this case. This technique provides the second measurements in
the 80kHz sections of Table 1.
If we achieved a -50C head temperature — which would require a 0-10C ambient
temperature — linear extrapolation predicts that we will achieve the expected (based
on Sciemeasure’s measurements) value of 3.37 electrons. In practice we do not
achieve this temperature very often at LCO, the coldest seen so far is roughly -45C.
As such, the 80 kHz readout speed is not used as it has worse sensitivity than the
250kHz 3.8e− RON mode due to this excess “frame-transfer” dark current.
2.3.3 CCD-47 Linearity
We measured the linearity of the VisAO CCD-47 using ambient light in the Auxiliary
building at LCO, and varying the exposure time in the 2500 kHz full frame mode.
This was done only in the LOW gain setting, as the higher gains will all digitally
saturate at 16383 ADU before reaching non-linearity. Data was dark subtracted
to remove the bias, and the median of a subarray was calculated at each exposure
time. The subarray was chosen to correspond to the brightest part of the ambient
light pattern. The results are shown in Figure 2.10. The CCD-47 is linear up to at
least 9000 ADU, which corresponds to 119000 electrons. The manufacturer quoted
typical value for well depth is 100000 electrons. In all other modes the CCD-47 is
linear to 16383 ADU. In future work we plan to analyze the linearity of each pixel
separately.
38
Figure 2.9 Column-wise standard deviation in the 80kHz mode. We hypothesize
that column 0 is the first read out, and so has minimal frame-transfer dark current.
Column 0 has the expected ∼ 3.5e− RON.
39
Figure 2.10 CCD-47 linearity measurement. The CCD-47 is linear up to 9000 bias
subtracted ADU.
40
2.4 The VisAO Photometric System
The VisAO camera has 4 broadband filters: r′ , i′ , z ′ and YS (Y -short). The r′ i′ z ′
filters are based on the Sloan Digital Sky Survey (SDSS) specifications (Fukugita
et al., 1996), and were provided by Asahi Spectra. The YS bandpass is defined
by a Melles-Griot long wavepass filter (LPF-950) which passes λ & 0.95µm. We
convolved the transmission curves provided by the respective filter manufacturers
with the quantum efficiency (QE) for our EEV CCD47-20 with near-IR coating, and
included the effects of 3 Al reflections. We also photon-weighted, as appropriate for
a CCD, using the following equation (Bessell, 2000)
T (λ) =
1
λT0 (λ)
hc
(2.1)
where T0 is the raw energy-weighted profile.
The resultant VisAO filter profiles are shown in Figure 2.11 along with comparable Johnson and SDSS filter profiles. The 0 airmass (AM) transmission profiles for
z ′ and YS are shown in Figure 2.12 along with examples of Y and J filters commonly
used in exoplanet observations.
The SDSS system is an AB system (Fukugita et al., 1996), however to-date
most, if not all, exoplanet direct-imaging observations have been reported in Vega
based magnitudes (as are most galactic observations of any type). To facilitate
comparisons of results from VisAO, we here define the VisAO photometric system
such that for Vega V = r′ = i′ = z ′ = 0.03 mag. We integrated the filter profiles
with the HST CALSPEC spectrum of Vega from Bohlin (2007) to determine the
flux densities of a 0 mag star in each filter. The results, along with other relevant
filter characteristics, are shown in Table 2.2.
2.4.1 Photometry in the r′ i′ z ′ bandpasses
In the AB magnitude system the flux of a 0 magnitude star in any bandpass is defined
as 3631 Jy. Using the 0 mag flux shown in Table 2.2 we find the transformations
Normalized Transmission (0 AM)
41
1.0
r
V
i
z
R
I
0.8
0.6
r’
i’
z’
0.8
λ (µm)
0.9
Ys
0.4
0.2
0.0
0.5
0.6
0.7
1.0
1.1
Figure 2.11 The VisAO broadband filters are shown in red. For comparison the
SDSS riz filter profiles are shown. We also how the V RI profiles from Bessell
(1990).
1.0
Y
0.8
z’
Ys
J
0.6
IRCS Z
0.4
0.2
SDSS z
Normalized Transmission (0 AM)
42
0.0
0.8
0.9
1.0
1.1
1.2
λ (µm)
1.3
1.4
Figure 2.12 A comparison of the VisAO z ′ and YS bandpasses with near-IR filters used to observe exoplanets. The Y bandpass is from Hillenbrand et al.
(2002). The Keck/NIRC2 “Z” bandpass was digitized from a plot obtained at
http://www2.keck.hawaii.edu/inst/nirc2/filters.html, and appears identical to the
Subaru/IRCS Z filter. The J profile is also from Keck/NIRC2. Atmospheric transmission for 2.3mm precipitable water vapor is from the ATRAN models (Lord, 1992)
provided by Gemini Observatory.
43
Table 2.2 The VisAO Photometric system
Filter
r′
[OI]
[OI]/Hα Cont.
Hα
[SII]
[SII] Cont
i′
z′
YS
1
R∞
0
λT (λ)dλ/
∆λ 2
0 mag Fλ 3
(µm) (ergs/s/cm2 /µm)
0.112
2.510 × 10−5
0.005
2.435 × 10−5
0.007
2.285 × 10−5
0.005
1.733 × 10−5
0.006
1.997 × 10−5
0.006
1.768 × 10−5
0.132
1.353 × 10−5
0.121
8.453 × 10−6
0.091
6.957 × 10−6
0 mag Fν
(Jy)
3221
3228
3149
2491
3012
2889
2616
2302
2230
3
0 mag Fγ 3
(γ/s/m2 /µm)
7.822 × 1010
7.727 × 1010
7.394 × 1010
5.728 × 1010
6.760 × 1010
6.228 × 1010
5.177 × 1010
3.839 × 1010
3.431 × 1010
R∞
T (λ)dλ where T (λ) is filter transmission.
R∞
Effective width, such that Fλ (λ0 )∆λ = 0 Fλ (λ)T (λ)dλ.
3
Using the STIS calibration spectrum of Vega from Bohlin (2007), which has an uncertainty of
1.5%.
2
λ0 =
AM0 λ0 1 FWHM
(µm)
(µm)
0.626
0.125
0.630
0.004
0.643
0.006
0.656
0.005
0.673
0.005
0.700
0.005
0.767
0.137
0.910
0.116
0.984
0.081
0
r′ (Vega-mag) = r′ (AB-mag) − (0.130 ± 0.016)
i′ (Vega-mag) = i′ (AB-mag) − (0.356 ± 0.016)
(2.2)
z ′ (Vega-mag) = z ′ (AB-mag) − (0.495 ± 0.016)
Rodgers et al. (2006) gives transformations from U BV RcIc to u′ g ′ r′ i′ z ′ (AB).
As a consistency check we can transform the photometry of Vega from Bessel (1990)
which yields the alternative transformations
r′ (Vega-mag) = r′ (AB-mag) − (0.141 ± 0.034)
i′ (Vega-mag) = i′ (AB-mag) − (0.349 ± 0.039)
z ′ (Vega-mag) = z ′ (AB-mag) − (0.499 ± 0.046).
Comparing results, we see that all three bandpasses agree within the 1σ errors.
44
2.4.2 Photometry in YS
The observations reported here were taken during commissioning, and we have not
yet fully calibrated the YS filter. This filter has a central wavelength very close to
the 99 filter of the 13-color photometric system (Johnson and Mitchell, 1975). For
stars with published photometry in this system we can just use the 99 magnitude
as the YS magnitude. For other stars, one approach is to use the Stellar Spectral
Flux Library of Pickles (1998), the calibrated Vega spectrum from Bohlin (2007),
and our 0 AM filter profile to calculate V − YS colors for main sequence (M.S.)
stars, setting YS = 0.03 for Vega. To assess the accuracy of this technique, we
applied it to the synthetic V RI (Johnson) profiles of Bessell (1990) and compared
the results to the intrinsic M.S. colors compiled by Ducati et al. (2001). Based on
these calculations we estimate the uncertainty of V − YS colors determined in this
fashion as σV −YS = 0.1 mag.
2.4.3 The Impact of Water Vapor on z ′ and YS
Both our z ′ and YS filters are affected by telluric water vapor. Using the ATRAN
models (Lord, 1992) for Cerro Pachon provided by Gemini Observatory2 we assessed
the impact changes in both AM and precipitable water vapor (PWV) have on these
filters. For AM ≥ 1 both the mean wavelength λ0 and the mean total transmission
of the filter changes. In the z ′ filter mean transmission changes by ±2% over the
ranges 1.0 ≤ AM ≤ 1.5 and 2.3 ≤ PWV ≤ 10.0 mm. In the same range YS
transmission changes by ±3%. This change in transmission has little impact on
differential photometry so long as PWV does not change between measurements,
and the overall effect of extinction changes due to airmass can be removed.
AM has almost no effect on λ0 but changes in PWV do change it by 2 to 4 nm.
This is relatively small and since we have no contemporaneous PWV measurements
for the observations reported here we neglect this effect.
2
http://www.gemini.edu/?q=node/10789
45
2.4.4 Exposure Time and Gain scalings
It is useful to convert from ADU to electrons per second when comparing images
taken with different exposure times. To convert we calculate the scaling factor (SF)
to multiply each pixel by. The formula is:
SF =
GAIN
10N D
EXP T IM E
(2.3)
Where:
SF = scale factor which converts ADU to electrons/seconds
GAIN = the gain factor, in electrons/ADU. This depends on the gain setting
(LOW, MLOW, MHIGH, HIGH) which is given in the fits header as V47GAIN, and
the pixel rate which is V47PIXRT, and very weakly on the window size and binning.
See Table 2.1 for the measured gains.
EXPTIME = the exposure time of the image, in VisAO fits headers it is given
by the standard EXPTIME keyword.
ND = value of the neutral density filter if used, 0 otherwise.
2.5 Performance Simulations
To predict the performance of the Magellan AO system we made use of the Code
for Adaptive Optics System (CAOS) package (Carbillet et al., 2005). This IDL
based “problem solving environment” provides good off-the-shelf functionality and
flexibility, and has been used to simulate the LBT AO system (Carbillet et al., 2003).
Our atmosphere model is derived from the GMT site survey of LCO (ThomasOsip et al., 2008). We use 6 turbulent layers with Cn2 and wind speed and direction as
determined by the survey. We also made use of recent work establishing L0 = 25m at
LCO (Floyd et al., 2010). Based on these data we use von Karman turbulence with
r0 = 14cm as our performance baseline, which corresponds to the ∼ 75th percentile
at LCO (Thomas-Osip et al., 2008).
The CAOS calibration procedure allows us to calculate interaction matrices for
various pyramid sensor configurations. A typical simulation for a bright (R ∼ 7 mag)
46
Table 2.3 The predicted VisAO error budget for a spectral type G2 R=7 magnitude
guide star. Assumptions include r0 = 14cm at 550nm, science wavelength of 0.7µm,
and the LCO site atmosphere layer model. Estimates using standard AO thumbrules agree very well with our simulation results. For this analysis the assumed
performance of our VisAO tip-tilt loop is 5mas r.m.s. At 10mas r.m.s. tip-tilt
control our long exposure Strehl would degrade to 0.2.
VisAO 0.7µm Error Budget
Error Term
Est. (nm) Sim. (nm)
Fitting
77.2
···
Servo
47.4
···
Recon.
47.0
···
Loop Total
102.1
102.4
Static.
30
30
Non-Com. Path
30
30
Resid. T/T
52.6
52.6
Total
122.4
122.7
0.7µm Strehl
0.3
0.3
for an R=7 G2 Guide Star
notes
Estimates from standard thumb-rules
Roddier, F. (1999). These are added in
quadrature for loop total.
CAOS simulations as described in the text.
Based on LBT design specifications.
Based on 4D interferometer measurements.
For 5 mas residual. (Sandler et al., 1994)
Sum in quadrature.
Using extended Marechal approximation.
guide star uses 392 modes with 1 khz sampling, a gain of 0.4, pyramid modulation
of 2λ/D, and pyramid sensor CCD39 parameters based on the manufacturer specification. We simulate with 1ms time steps and apply a 2ms delay to each update to
account for WFS readout, calculations, and mirror motion. For each setup (guide
star magnitude, etc.) we allow 100ms for loop closing, and then run the simulation
for 2 seconds of loop time. At each time step we save a simulated science image
at various wavelengths. These images are stored with no sources of noise and we
use a 1nm wide bandpass, which allows us to make a very accurate Strehl measurement. The Strehl ratio at each point is measured by comparison to a perfect Airy
pattern for a 6.5m telescope with a 29% central obscuration. We typically use the
mean short exposure Strehl from these time series, since this value does not include
tip-tilt (which we add in quadrature from our error budget).
Table 2.3 shows the error budget for the Magellan AO system at 0.7µm band on
a spectral type G2 R=7 magnitude guide star. We compare estimates for the fitting,
servo, and reconstruction errors with our CAOS simulation results and find good
47
Figure 2.13 Simulated performance of the Magellan AO system vs. guide star R
magnitude for 75th percentile seeing at LCO. Based on CAOS simulations as described in the text, each curve includes the error terms listed Table 2.3. Since the
primary focus of this dissertation is performance at visible wavelengths, we do not
present results for fainter guide stars where VisAO will not perform as well. We
expected VisAO to consistently provide Strehl ratios > 0.2 for bright guide stars,
and usable correction out to at least R=9.5.
agreement. The error calculated from simulations is based on the mean short exposure Strehl ratio. We then add (in quadrature) the unsimulated errors from static
mirror aberrations, non-common path aberrations, and finally the long exposure
degradation of Strehl due to tip-tilt. In Figure 2.13 we show our simulation-based
performance predictions vs. guide star magnitude at various wavelengths. These
curves are calculated in similar fashion to the Strehl in Table 2.3, with appropriate
differences for wavelength.
2.6 Tower Tests
MagAO was integrated and tested in Arcetri, Italy, between March 2011 and March
2012. This period culminated with a successful pre-ship review (PSR) by an external
panel in late February 2012. Here we provide a brief overview of our results from this
48
testing and describe our attempts to validate the simulated atmospheric turbulence
and how we correct our results to produce estimates of on-sky performance.
2.6.1 Seeing Validation
In the test tower, atmospheric turbulence is generated using the ASM itself. A precalculated phase screen is applied to the mirror in parallel to the AO corrections.
A full description of how turbulence is generated using the ASM was provided by
Esposito et al. (2010). To provide a baseline for evaluating performance we took
data with AO off but the phase screen propagating across the ASM, that is we took
simulated seeing limited data. We then used this data to test whether the seeing
produced by the ASM matches expectations from theory. We typically used a phase
screen generated to have a seeing limited full-width at half-maximum (F W HM ) of
0.8” at 0.55µm, or r0 = 0.14m. For SDSS i’, with central wavelength λ0 = 0.765µm,
we have r0 (0.765µm) = 0.21m. So in the SDSS i’ bandpass, assuming Kolmogorov
turbulence, we expect the seeing limited PSF to have F W HM = 0.75”.
We must also consider that simulated turbulence outer scale was set to L0 = 40m
(which does not depend on wavelength). Assuming von Karmen statistics on a
large aperture, this causes a reduction in FWHM by a factor 0.8159 at 0.765µm
(Tokovinin, 2002). So our expected F W HM (0.765µm) = 0.611”. In Figure 2.14 we
show a cut through the seeing limited PSF generated by this phase screen, recorded
at SDSS i’ with the CCD 47. The best Moffat profile fit to the seeing limited data
is F W HM = 0.617”, assuming a plate scale of 0.0080”, corresponding to f/52.6.
Of note, the Moffat index of the fit was β = 3.9. It has been reported that β = 4
provides a good match to a telescope seeing limited PSF using on-sky data (Racine,
1996). We conclude that the seeing generated in the test tower using the ASM does
a very good job of producing the expected image at the CCD 47.
49
Figure 2.14 A cut through a seeing limited image, and a cut through the best fit
Moffat profile. We also show the best fit Gaussian for comparison. The fits were
conducted in two dimensions.
2.6.2 Fitting Error
The MagAO ASM influence functions were measured in the Arcetri test tower using
an interferometer. The best fit projection of these into a Karhunen-Loeve (KL)
basis set was then computed. As is done at the LBT, these KL modes are used
during on-sky closed-loop operations at Magellan. To determine the fitting error
of our modal basis, 500 independent Kolmogorov phase screens were generated and
fit with progressive numbers of our KL modes 3 . The residuals for each number of
compensated modes were computed, and these points were fit with a function of the
standard form:
σ 2 = A(jmax )B (D/r0 )(5/3)
3
these calculations were carried out by Fernando Quiros-Pacheco at Arcetri
(2.4)
50
Figure 2.15 Fitting error of the MagAO ASM after correcting jmax modes. We show
the measured residuals after fitting with the KL modes that will be used on-sky, the
residuals expected using Zernike polynomials, and the best fit of Equation 2.4 to
the KL mode residuals in red. Note that our KL modes become less efficient than
Zernikes after about mode 400.
with
A=
0.232555
B = −0.840466
A comparison of this function with the fitting error expected from a pure Zernike
polynomial basis is shown in Figure 2.15. The MagAO basis is less efficient than
Zernikes for modes greater than number 400, a different result than obtained for the
LBT ASMs with an identical procedure. We speculate that this is due in part to
the asymmetry caused by the machined slot at the outer edge of the shell.
As discussed above, in the test tower atmospheric turbulence is simulated using
the ASM itself, so the phase screen contains only a limited number of spatial frequencies corresponding to the maximum degrees of freedom of the mirror. In the
case of MagAO this means that only the first 495 modes of turbulence are simu-
51
Table 2.4 Tower Test fitting error corrections for 0.8” seeing. Any S measurement
made in the tower can be multiplied by the appropriate Scorr to determine an estimate of the on-sky S.
Filter
r′
i′
z′
YS
λ(µm)
0.626
0.767
0.910
0.984
σ 2 (rad2 )
0.60
0.40
0.28
0.24
Scorr
0.55
0.67
0.75
0.78
lated, so we must correct our laboratory results for the wavefront variance caused by
modes 496 − ∞ which will be present on-sky. We can use Equation 2.4 to estimate
the correction factors to apply to our results. Table 2.4 lists the correction factors
for our standard VisAO filters.
2.6.3 Tower Test Results
Over the course of the Arcetri tower testing we took data in many different system
configurations, including different magnitude guide stars and different VisAO filter
selections. A typical experiment involved taking measurements without simulated
turbulence to capture the small amount of turbulence present in the test tower tube,
due to internal convection and tip/tilt from flexure caused by the outside wind. We
then took an identically configured data set with the ASM simulating turbulence
as described above. Finally we nearly always took seeing limited data. Figure 2.16
shows an example of results from such an experiment conducted on a bright star with
the loop operating at 800Hz. There we compare the three measurements to a theoretical Airy pattern. Figure 2.17 compares the same experiment to the simulation
based performance predictions made above, and also shows the magnitude of the
fitting error correction which we apply to form an on-sky performance prediction.
See Close et al. (2012a) for additional tower test results .
52
Figure 2.16 Example tower test results. In this case the system was correcting 400
modes at 800Hz, and data were taken in the SDSS i’ bandpass. At upper left is
a theoretical Airy pattern. At upper right is the MagAO PSF with no simulated
turbulence applied, so that the system was correcting only the small amount of turbulence present in the test tower tube. At lower left is the PSF with 0.8” simulated
turbulence applied. At lower right is the result with the AO correction off, showing the seeing limited PSF in the same simulated atmosphere. Note that S values
quoted in the figure do not have a fitting error correction applied.
53
Figure 2.17 A comparison of predicted performance and our SDSS i’ test tower
results. The solid curves are the same as in Figure 2.13. The data points connected
by a vertical line show the raw measured SDSS i’ S from our results shown in Figure
2.16 and the value obtained after applying the correction for fitting error from Table
2.4. We also highlight the predicted value for an 8th magnitude guide star. This
plot shows that MagAO is performing as expected, if not a bit better.
54
2.7 On-sky Results
MagAO saw first light in December, 2012, and completed commissioning in May,
2013. Here we present some of the on-sky calibration and characterization, and close
with a brief survey of some of images obtained with VisAO so far.
2.7.1 Astrometric Calibration
To calibrate the VisAO platescale and rotator orientation, we used the Orion Trapezium cluster stars. The primary stars used for VisAO calibration were θ1 Ori B1 and
B2. These stars were observed repeatedly throughout the commissioning run, and
with a separation of ∼ 0.94” B2 is well within the isoplanatic path when guiding
on B1. This separation is also convenient for dithering the stars around the chip to
test for distortions. Other asterisms in Trapezium are challenging to work with due
to anisoplanatism and the FOV of VisAO. The drawback to using these two stars
is that they have been shown to be in orbit around each other, albeit slowly (see
Close, et al., (2013, submitted)).
To avoid uncertainty from the orbits of B1 and B2, we boot-strapped their current astrometry using the wider FOV Clio camera. With Clio we were able to first
use combinations of Trapezium stars to measure the platescale and orientation of
Clio. This was done by distortion correcting Clio to match the astrometry given
in Close et al. (2012c) which used LBTAO/Pisces. We then measured the separation and position angle of B1 − B2. The results are shown in Table 2.5. We
track the contribution of errors in the Clio astrometry from measurement and from
LBTAO/Pisces separately so that we can compare results between the cameras as
well as with other measurements.
The θ1 Ori B1 − B2 − B3 − B4 “mini-cluster” was dithered around the CCD-47
using the gimbal in the YS filter on 2012 Dec 3 UT with the rotator tracking. Each
dither position was reduced separately: frames were selected for good correction,
registered, and median combined. The images were not de-rotated. At each dither
position, the separation and PA of B1 − B2 were measured using the starfinder.pro
55
Table 2.5 Clio astrometry of θ1 Ori B1 and B2 (Dec 2012)
.
Value
sep
PA
0.9400”
254.87 deg
Measurement
Uncertainty
0.0011”
0.10 deg
Astrometric
Uncertainty
0.0023”
0.3 deg
Total
Uncertainty
0.0025”
0.32 deg
idl program (Diolaiti et al., 2000), making use of B1 itself as the PSF. We also
measured the position of the optical beam splitter ghost of B1, as well as its relative
flux. Since the beam splitter is very near a pupil, we expect this ghost to be very
stable.
The relative x and y positions of B1 − B2 were found to depend on position
on the chip, consistent with a focal plane tilt. The primary symptom of this was a
∼ 0.25 degree scatter in PA measurements, which was well outside the formal errors
from the PSF fitting astrometry. We found that fitting a plane through the ∆x and
∆y measurements of B1 − B2 reduced this scatter to be consistent with the formal
errors. The equations to correct measurements to the center of the chip (512x512)
are
δx = −0.0003892(x − 512) + 0.0008432(y − 512)
(2.5)
δy = −0.0002576(x − 512) − 0.0024045(y − 512).
These corrections are then added to the measured ∆x and ∆y to get the centerof-chip value.
After applying these corrections we measured the center-of-chip
platescale and the value of N ORT HV isAO , which is used to de-rotate images by
DEROTV isAO = ROT OF F + 90 + N ORT HV isAO
These results are presented in Table 2.6.
(2.6)
56
Table 2.6 VisAO YS platescale and rotator calibration. Measurement uncertainty
includes both Clio and VisAO scatter. Astrometric uncertainty is propagated from
LBTAO/Pisces
.
Value
Platescale
N ORT HV isAO
0.007910”
-0.59 deg
Measurement
Uncertainty
0.000009”
0.10 deg
Astrometric
Uncertainty
0.000019”
0.3 deg
Total
Uncertainty
0.000021”
0.32 deg
2.7.2 Beamsplitter Ghost Calibration
The WFS beamsplitters control how much light is sent to the pyramid sensor vs. the
VisAO camera. They are selectable in a filter wheel, and the choice of beamsplitter is
an integral part of AO system setup based on what the science goal of the observation
is. Each beamsplitter has an optical ghost, which is slightly out of focus. We use
these ghosts for both registration and photometry when the central star is either
saturated, or under the coronagraph. As noted above, we extracted both the relative
flux and position of the ghost in the 50/50 beamsplitter as part of our analysis of
the Trapezium astrometric field. The relative flux of the ghost did not depend on
position, but the position of the ghost does. In Table 2.7 we present the ghost
parameters for the 50/50 beamsplitter, in the YS filter with filter wheel 3 open,
when the guide star is at 512x512 (counting from 0).
In our second commissioning run, we dithered HIP 56004 around the detector
in the same setup as above, but this time the coronagraph was in the beam. The
results are also shown in Table 2.7. It appears that the astrometric properties of
the ghost change slightly when the coronagraph is in. This change is on the order
of 0.5 pixels, which can be significant for techniques based on angular differential
imaging (ADI).
The position of the ghost depends on the position of the guide star. As before
we fit a plane to the B1-ghost data and found the following correction for F/W 3
open:
57
Table 2.7 Photometric and astrometric parameters of the 50/50 beamsplitter ghost
in the YS filter.
.
Value
F/W 3 Open
Rel. Flux. 0.00718 ± 0.00013
∆x
160.369
∆y
-9.040
F/W 3 Coronagraph
∆x
159.745
∆y
-9.483
Notes
independent of position
at 512, 512
at 512, 512
at 512, 512
at 512, 512
δxg = −0.0004939(x − 512) − 0.0003123(y − 512)
(2.7)
δyg = −0.0005014(x − 512) − 0.0039757(y − 512)
and when the coronagraph is in the correction equations are:
δxg = −0.0004812(x − 512) − 0.0007174(y − 512)
(2.8)
δyg = −0.0003305(x − 512) − 0.0037534(y − 512)
2.7.3 Ys Strehl Ratio
Of particular interest to this dissertation, we observed the known exoplanet host β
Pictoris several times during the first MagAO commissioning run. Our best correction was obtained on 2012 Dec 4, when we were observing in Ys using the VisAO
coronagraph. The high contrast data reduction and analysis of our detection of β
Pic b are discussed later. Here we present our off-coronagraph PSF and photometric
calibration image.
To avoid saturation, the off-coronagraph data was taken in the 2500 kHz pixelrate, full frame mode, resulting in 0.283 individual exposure times. The camera
was in the LOW gain setting, allowing access to the full well-depth. Even with
58
∆ y(")
0.2
0.0
−0.2
−0.2
0.0
∆ x(")
0.2
Figure 2.18 Image of β Pictoris, a Ys = 3.5 mag A5V star, made by shifting and
adding 0.283 sec exposures. This is a log stretch. This image has a raw Strehl of
∼ 32%, and an optical Strehl (corrected for PRF) of ∼ 40%. Instantaneous Strehl
ratio was > 50%, but there was a ∼ 0.9 pixel RMS jitter.
these settings, we saturated the peak pixel in roughly a third of the exposures. To
compensate, and avoid any possible non-linearity, we selected only frames with peak
pixel between 8000 and 9000 ADU. This cut out roughly half the frames, and has the
effect that we are using data between approximately the 75th and 25th percentiles
— so not the very best. We also applied a WFE cut at 130 nm RMS phase, using the
VisAO real time telemetry stream. The 491 selected frames were then registered,
and median combined. The result is shown in Figure 2.18.
The resultant PSF core has a FWHM of 4.73 pixels (37 mas). The diffraction
59
limit at YS is 3.87 pixels (31 mas). We expect some broadening due to the pixel
response function (PRF) - mainly from charge diffusion. When a photon is detected
by a CCD pixel, the resulting photo-electron can diffuse into a neighboring pixel.
This causes a blurring effect, which has been well documented in the HST ACS
and WFPC cameras. See Krist (2003), Anderson and King (2006), and the ACS
handbook for more on charge diffusion PRFs.
We measured the PRF of the CCD-47 in the lab, by switching between it and
a well over-sampled CCD. The effects of charge diffusion lessen as more pixels
are placed across the PSF, so this allowed us to compare the true optical PSF
to the PSF measured on the CCD-47. Using a blurring kernel developed from
these measurements, we find that a perfectly diffraction limited PSF should measure F W HM = 4.18 pixels. So we have ∼ 0.5 pixels of broadening. This implies
an RMS tip-tilt residual error of 0.94 pixels (see Equation (A.4)).
Strehl from WFE and PRF: We can use the real-time reconstructed WFE
recorded in the VisAO fits headers to form an initial estimate of SR in the PSF
shown in Figure 2.18. The mean WFE for the images included in the final SAA was
123.37 nm RMS phase. This gives us
Si = 0.54
for the instantaneous Strehl ratio. Using Equation A.5 and our estimate of jitter
from F W HM broadening we estimate
Stt = 0.75
so
Swf e = Si Stt = 0.40
The PRF also lowers measured Strehl ratio. After broadening a theoretical Airy
pattern by the PRF kernel, we find that
Sprf = 0.80.
60
This means the expected focal plane Strehl ratio due to WFE reconstruction and
PRF is
Srec = Si Stt Sprf = 0.32.
Core-to-Halo Strehl: Another way to measure Strehl is to use the ratio of the
flux enclosed in the core (to the first Airy minimum) to the total flux. This will tend
to be robust against effects like the PRF and T/T broadening. For MagAO, with
a 29% central obscuration, the first Airy minimum occurs at 1.12λ/D and encloses
74.7% of the total flux at S = 1 (see Section A.2 in the Appendix). We measured
the total flux in the PSF with IRAF imexam, with a photometric aperture of 239
pixels, a sky radius of 240 pixels, and a sky width of 5 pixels. This should enclose
99.6% of the flux. We then changed the aperture radius to 4.42 pixels and measured
the core flux. We estimate the core-to-halo S from these measurements by
Sc/h =
E(1.12λ/D)
= 0.34
0.747E(∞)
where E(r) denotes encircled flux at radius r.
Peak-to-Halo Strehl: We can use the total flux in the image to calculate the
expected peak height for S = 1
Io =
πPtot (1 − ǫ2 ) 0.249
.
4
λ2
See Appendix A for the derivation of this expression. We fit a Gaussian to the PSF,
and comparing the resultant peak height Ipk we find
Sp/h =
Ipk
Sprf = 0.30
Io
is the peak-to-halo estimate of S.
Theory Strehl: Finally, we can compare the PSF shown in Figure 2.18 to a
theoretical Airy pattern. We first broaden the theoretical PSF using the PRF kernel.
Then normalizing the theory PSF with the same 239 pixel photometric aperture,
we find
Stheory = 0.30
61
Table 2.8 Strehl measurements at YS (0.984µm)
Srec
Sc/h
Sp/h
Stheory
Average
Swf e
Strehl
0.32
0.34
0.30
0.30
0.32 ± 0.02
0.40
Notes
reconstructed WFE
core-to-halo
peak-to-halo
PRF broadened Airy
before PRF
Table 2.9 Observation log for LHS 14, observed on 2012 Dec 3 UT
Filter
r′
i′
z′
YS
Gain
Med.
Med.
Med.
Med.
High
High
High
High
Exp Time
(sec)
0.283
0.283
0.283
0.283
No. Exp.
199
271
263
225
Tot. Exp
(sec)
56.3
76.7
74.4
63.7
We summarize our Strehl measurements in Table 2.8. These four different ways
of estimating Strehl ratio agree well. An interesting quantity is the optical Strehl,
that is the calculated Swf e . We can estimate this by dividing by Sprf . This quantity
is noteworthy as PRF is easily removed by deconvolution, allowing us to recover the
optical resolution achieved by the AO system.
2.7.4 Throughput
On 2012 Dec 3 UT we observed LHS 14, an M2.5V star with published u′ g ′ r′ i′ z ′
photometry, in all four VisAO broad bandpasses. These observations, summarized in
Table 2.9, were used to measure system throughput. The 50/50 WFS beamsplitter
was selected. Data were taken in 5 point dither patterns to minimize corruption
from dust spots, and images were manually selected, dark subtracted, registered,
and median combined.
Next the IRAF task daophot was used to conduct aperture photometry on each
62
Table 2.10 VisAO total throughput measurements on LHS 14 in 50/50 beam-splitter.
Filter
r′
i′
z′
YS
Mag
(AB)
9.481
8.547
8.104
—
Mag
(Vega)
9.356
8.194
7.611
7.084
0AM Flux
(phot/sec)
5.248 × 107
3.430 × 107
3.806 × 107
4.401 × 107
Meas. Flux
(phot/sec)
7.990 × 106
1.177 × 107
8.348 × 107
1.201 × 106
Expected
Throughput
15.9%
17.0%
12.5%
3.6%
Measured
Throughput
15.2%
34.3%
21.3%
2.7%
final image. The photometry was converted from ADU to e− / s using Equation
(2.3). We then compared these results to the photometry of LHS 14 from Smith
et al. (2002), converting from AB to Vega magnitudes using Equation (2.3) and
making use of the parameters presented in Table 2.2. The YS magnitude of LHS 14
was estimated using the Pickles spectral library as described in Section 2.4.2 above.
The resulting throughput measurements are shown in Table 2.10.
We also calculated our expected throughput given the beamsplitter, atmosphere,
and the filter curves calculated as described above. These numbers are also presented
in Table 2.10. Of note, our measured throughput is roughly a factor of two higher
than expected in i′ and z ′ . Two effects may account for this. In i′ especially, our
filters are redder than the standard SDSS bandpasses, due to our IR-coated CCD
QE being higher in this region. It is also possible that our CCD QE is somewhat
better in this region than assumed in our filter profiles, as the QE is based only
on a catalog plot and is not a measurement of the actual device. The lower than
expected YS throughput is conversely possibly explained by over-estimating the tail
of Silicon QE for λ > 1µm, and also possibly on a poor quality catalog transmission
curve for the filter itself.
2.7.5 VisAO Images
Here we very briefly present some other on-sky results from the MagAO commissioning periods. We do no astrophysical analysis here, in essence we are just offering
pretty pictures to establish that MagAO and VisAO are working well on-sky. Later
63
Figure 2.19 Image of the θ1 Ori C binary, obtained with VisAO in December, 2012.
We resolved this binary at only 31 mas separation — the first time this has been
done with a filled aperture long exposure. These images, from Close, et al., (2013,
submitted), show data taken in [OI] (630 nm), r′ (centered at 624 nm), and Hα, at
(656 nm). These reductions are by L. Close. SAA is shift-and-add, and PRF was
corrected where indicated by deconvolution.
we will present a detailed analysis of our observations of an exoplanet host star.
As discussed above we used the Trapezium cluster in Orion for astrometric calibrations. We have also been able to do some science with these data. In Figure
2.19 we show the first filled-aperture long exposure images to resolve the θ1 Ori C
binary. We also demonstrate how, using the high speed readout modes and our well
characterized PRF we can achieve 21 mas resolution with VisAO. In Figure 2.20 we
show a z ′ image of the θ1 Ori B “mini-cluster”. These data have been used in Close,
et al., (2013, submitted) to demonstrate that the B2-B3 barycenter is orbiting B1,
along with B4.
64
1.0
∆Dec (")
0.5
0.0
−0.5
z’
−1.0
−0.5
0.0
0.5
∆RA (")
1.0
Figure 2.20 An image of the θ1 Ori B cluster, obtained with VisAO in December,
2012. VisAO observations of this system have shown, for the first time, conclusive
evidence for orbital motion of the B2-B3 barycenter around B1. See Close, et al.,
(2013, submitted) for details.
65
During the May 2013 commissioning 2 run we observed HR 4796A, a star with
a well known circumstellar disk, as part of a program with TJ Rodigas and Alycia
Weinberger. Data on this star was taken simultaneously on Clio and VisAO, covering
6 filters in total. We present a very quick reduction of the VisAO data in Figure
2.21.
1.0
0.5
0.5
0.5
0.0
−0.5
−1.0
∆Dec(")
1.0
∆Dec (")
∆Dec (")
1.0
0.0
−0.5
i’
−1.0
−1.0
−0.5
0.0
0.5
∆RA (")
1.0
0.0
−0.5
z’
−1.0
−1.0
−0.5
0.0
0.5
∆RA (")
1.0
YS
−1.0
−0.5
0.0
0.5
∆RA (")
1.0
Figure 2.21 Images of HR 4796A and its circumstellar disk, obtained with VisAO in May, 2013. Only basic ADI
processing, with a radial profile subtraction step, and high-pass filtering (unsharp mask) was used to produce these
images. Look for higher fidelity reductions and analysis of these data in Rodigas, et al., (in prep).
66
67
CHAPTER 3
REAL TIME FRAME SELECTION
3.1 Introduction
Lucky imaging is a technique which selects the best images from a series of short
exposures, then shifts and adds them to produce a final image with higher spatial
resolution than a single long exposure. First proposed by Fried (1978) to counter
the effects of atmospheric seeing, it is now in common use at several telescopes
(Law et al., 2006). It has also been adapted for use with an AO system, where
the correction quality in the visible was1 typically low, but has short periods of
high Strehl (Law et al., 2009, 2008). By selecting images based on Strehl ratio, it
has been shown that both resolution (Law et al., 2009) (measured by full width
at half maximum (FWHM)) and sensitivity (Gladysz et al., 2008a) (measured by
signal-to-noise ratio (S/N)) can be improved.
To be effective, lucky imaging typically uses very short exposures, requiring cameras that operate faster than ∼ 10 frames-per-second (fps). For normal astronomical
CCDs this imposes a significant readout noise (RON) penalty, as each read will produce a few electrons of noise which then quickly adds to overwhelm faint signals.
This has been overcome to great effect using EMCCDs, which offer very low RON
- typically ∼ 0.1e− per read (Daigle et al., 2009) - when operated in the photon
counting mode. Photon counting EMCCDs have some (small) drawbacks though.
If flux is higher than 1 photon/pixel/read the device effectively has its quantum efficiency (QE) lowered by 50% (Mackay et al., 2004). On VisAO, however, we almost
always have a very bright guide star in our FOV, and if we had low to moderate
Strehl ratios we will have a bright uncorrected halo from the star spread over the
detector, making this QE penalty impossible to ignore.
1
prior to the MagAO era
68
An additional issue we identified with any lucky imaging system is the trade-off
between FOV and camera speed. The isoplanatic patch at visible wavelengths at
LCO will typically be ∼ 4” in radius. To provide good sampling across this FOV
we need a 1024x1024 array. When we began the investigations detailed here the
fastest EMCCD cameras of this size could only be operated at ∼ 10 fps (EMCCDs
have since become a little faster, now achieving ∼ 30 fps over arrays of this size).
As we will show 10 fps is not quite fast enough to fully take advantage of the peaks
in Strehl ratio, which are typically shorter than 100ms in our simulations. The
common solution with an EMCCD is to window such a device and operate at 50fps
or faster, which also helps to mitigate the high-flux penalty. This carries its own
drawback in that FOV is cut by 25% in area, which for many observations is itself
equivalent to a QE penalty.
A final consideration, and perhaps most important, is that the Magellan VisAO
system was largely based on an already designed instrument. Since the VisAO
CCD47 is used as an acquisition camera integral to AO system operation, changing
detectors was judged too risky to overall performance. Changing detectors would
significantly increase the cost of this system, but we still desire to take advantage
of frame selection.
Given the bright guide star specific and FOV vs. speed drawbacks of EMCCD based lucky imaging, and the pre-existing system designs, we developed a
new imaging concept which we call real time frame selection (RTFS). In this mode
of operation, we make use of a high speed mechanical shutter and telemetry from
the AO system to only expose our CCD47 when Strehl is high. The shutter is both
fast and responsive enough to provide the equivalent temporal resolution of a 100fps
camera, and can do this over the entire 8.7” FOV of our 1024x1024 array. As we will
show, this technique can improve resolution (when compared with doing nothing)
by nearly 100% of λ/D.
We first present a generic frame selection algorithm, providing a formal definition
of frame selection. Then we present a model of S/N in AO imaging, which we use to
analyze the costs and benefits of frame selection and to compare different imaging
69
techniques. Using this model and the output of performance simulations we calculate
the performance of an ideal RTFS system both in terms of resolution and sensitivity.
We then describe our implementation of RTFS, including characterization of the
shutter and development of real time telemetry processing. An area of ongoing
development is Strehl prediction, necessary because of a short but unavoidable delay
in shutter actuation time. We then show the results of laboratory testing of RTFS,
conducted with realistic simulations in the test tower at Arcetri, Italy.
Much of this chapter has appeared in print in (Males et al., 2010) and (Males
et al., 2012a). An important caveat to all of this work, taking advantage of perfect
hindsight, is that it was almost entirely unnecessary for MagAO and VisAO. The
need for Lucky-style imaging was anticipated because, simply put, we just did not
think VisAO would work very well. As shown in detail below, any frame selection
technique involves a trade-off between sensitivity and resolution. Above a certain
image quality (Strehl ratio of, say, about 20%), it is not worth it (at least for point
sources). Despite the effort that went into developing this system, I am perfectly
happy to never need it on-sky — VisAO works really well!
3.2 A Generic Frame Selection Algorithm
Before we can analyze its benefits, we first state what we mean by frame selection.
To do this we will develop a general description of a selection algorithm, leaving
specific details for later.
We begin by collecting a stream of raw data at a time ti , such as AO control
loop telemetry or short exposure science image pixels, with n elements


x1 (ti )


~ i ) =  ...  .
X(t


xn (ti )
70
Next the data is converted to a set of m attributes2 by some operation F


y1 (ti )
 . 
~ i) .
..  = F X(t
Y~ (ti ) = 


ym (ti )
For instance, F may include the calculation of slopes given the raw WFS pixels
or sub-aperture counts. Finally we use a classifier G to determine whether some
image quality metric, say Strehl ratio S, is above some threshold value, say ST . The
classifier uses the previous l samples of the m attributes, possibly with a delay of k
time steps (meaning the classifier is also a predictor):

 0 if S(ti+k ) < ST
G Y~ (ti ), · · · , Y~ (ti−l+1 ) =
 1 if S(t ) ≥ S .
i+k
T
(3.1)
The value of G represents the decision whether to include the data at ti+k in the
final image. We explicitly allow for prediction since this will be necessary for the real
time implementation we discuss later. Finally we note that this formulation does
not require that the actual value of the image quality metric (e.g. S) be calculated.
This opens the door to using, for instance, machine learning classification techniques
without a priori knowledge of relationships between the raw data and image quality.
The standard lucky imaging technique can be described using this algorithm. In
~ i ) is made up of the pixel values of a short exposure
this case, the data vector X(t
image at time ti . The corresponding attribute is just the Strehl Ratio S(ti ), and the
operation F is the reduction pipeline which results in the Strehl ratio measurement.
The classifier G is a simple comparison between the measured S(ti ) and ST . In
standard Lucky imaging only the current time step is used and no prediction is
performed, i.e. k = 0 and l = 1.
Another implementation of this algorithm is RTFS (discussed above), developed
for the Magellan VisAO system, which is used to control a camera shutter in real
time. The primary goal of this technique is to minimize the number of detector
reads, while gaining the benefits of frame selection.
2
It is not necessary that m = n
71
3.2.1 WFS Telemetry Based RTFS
RTFS uses a fast shutter to block moments of bad correction, causing only periods
of high S to be recorded by the science camera. This prevents us from using direct
measurements of S to trigger the shutter. Above we developed a notation to describe
a generic frame selection algorithm, including conventional Lucky imaging. Here we
adapt that algorithm and notation to the specific case of using only WFS telemetry
to reconstruct S.
~ i ). The wavefront
We record a slope vector at time ti with n elements, X(t
is reconstructed by multiplying the slope vector by the reconstructor matrix R
(typically the same one in use in the main AO loop).
~ i ) = RX(t
~ i)
A(t
~ i ) is the vector of reconstructed mode amplitudes at time ti . The orthogwhere A(t
onal KL modal basis is normalized such that each mode has unit variance, so we
can calculate the wavefront variance by summing the amplitudes in quadrature
~ i ) · A(t
~ i)
σ 2 = (4 × 109 )2 A(t
where the factor of 4 accounts for the double pass of the ASM in the test tower,
and 109 converts to nanometers. We then calculate the reconstructed S using the
extended Marechal approximation
2π 2 2
σ
Srec (ti ) = e−( λ )
.
Next we apply an empirical calibration, using two parameters.
Scal (ti ) = aSrec (ti ) + b.
See below for further discussion of this calibration step and the interpretation of
these parameters.
Finally, we apply a finite impulse response (FIR) low-pass filter of order N to
prevent high frequencies from over-driving the shutter.
Sf ilt (ti ) =
k=N
X
k=0
fk Scal (ti−k )
72
where the fk are the filter coefficients. The design of appropriate digital filters is
described below.
We use the reconstructed filtered S to classify each moment as a good or bad
according to whether it is above or below a threshold ST .

 0 if Sf ilt (ti ) < ST
G=
 1 if S (t ) ≥ S .
f ilt i
T
(3.2)
The value of G represents the decision whether to open (G = 1) or close (G = 0)
the shutter.
3.3 The Costs & Benefits of Frame Selection
To asses the benefits of frame selection, we use a simple model of the AO imaging
process to calculate S/N and the output of our CAOS simulations to determine
the resulting resolution. The following development relies heavily on the work of
Racine et al. (1999), and benefits from the work of Law et al. (2009, 2008, 2006)
and Gladysz et al. (2008a,b, 2006).
3.3.1 Signal to Noise Ratio and Duty Cycle
The obvious drawback to frame selection is that only a fraction of the telescope time
allotted to the observation is used in the final result. This fraction can be thought of
as the duty cycle DC. The act of throwing away the fraction (1 − DC) of the signal
can be expected to negatively effect the sensitivity of the observation. It might be
true, however, that by keeping only the “good” frames we can overcome this loss
in signal by reducing the noise in our final image, and this has been demonstrated
on-sky (Gladysz et al., 2008a). In conventional lucky imaging, one always has all
the data available from an observation and so has lost no telescope time. In RTFS,
however, we will irretrievably lose the time when the shutter is closed and so we
must understand the trade-offs with sensitivity for this technique.
To that end, we use a simple model of the S/N in AO imaging, based heavily on
that developed by Racine et al.Racine et al. (1999) with only slight modifications,
73
to determine the net efficiency cost of frame selection. Here we skip most of the
derivation and present the results for the limiting cases most likely to be encountered
in natural guide star (NGS) AO.
Our S/N model is
S/N =
√
Efc DCt
Efc + S̄ P̄(θ)f∗ n + (1 − S̄)H(θ)f∗ n + 0.53τ0 [(1 − S̄)H(θ)f∗ n]2 + (Nsky + Ndet )n
(3.3)
where f∗ and fc are the flux (photons sec−1 ) at the telescope of the central star
and the companion (located at separation θ); E is the total flux enclosed in the
photometric aperture; DC is the duty cycle (discussed above); P̄ is the point spread
function (PSF), ideally an obscured Airy pattern, averaged by tip-tilt; n is the
number of pixels contained in the photometric aperture; H(θ) is the uncorrected
halo flux per pixel; τ0 is the speckle lifetime (Racine et al., 1999); Nsky is the perpixel flux due to sky background (BG); and Ndet is the per-pixel flux due to detector
noise. The quantity S̄ is the mean short exposure Strehl, which we use rather than
the long exposure (tip-tilt degraded) Strehl ratio to account for the guide star’s halo
contribution to the noise as it is what quantifies the relative fraction of flux in the
halo. Using the long exposure Strehl here would make the halo noise too large.
3.3.2 Encircled Energy and Aperture Size
The fraction of incident photons contained in a circular aperture assuming a perfect
obscured-Airy PSF is
Z ρ
1
J1 (t)J1 (ǫt)
2
2
2
EP (ρ) =
(1 + ǫ )(1 − J0 (ρ) − J1 (ρ)) − 4ǫ
dt
1 − ǫ2
t
0
(3.4)
where ǫ is the telescope central obscuration and ρ is the aperture size (see Appendix
A and Mahajan (1986)). Now in an AO corrected image only a fraction S̄ of the
flux is contained in the diffraction limited component of the PSF, and (1 − S̄) is
contained in the halo. Following Racine et al. (1999) we adopt the function
"
2 #−11/6
11
0.488
θ
1+
H(θ) =
.
Wh2
6 Wh
(3.5)
21
74
to describe the uncorrected halo, where Wh is a width parameter.
We can integrate equation (3.5) to calculate the fraction of the incident photons
in the halo encircled by an aperture of size ρ:
EH (ρ) = 1 −
11
1+
6
ρ
Wh
2 !−5/6
.
(3.6)
Racine et al. (1999) argued that the halo contribution to flux could safely be ignored
since its S/N would be comparatively low. While this is likely true for high Strehls,
we expect to employ frame selection with only low to moderate Strehls. At Magellan,
with ǫ = 0.29, the enclosed fraction is EP = 0.747 for ρ = 1.12λ/D (the first Airy
minimum). From simulations we derive a value of Wh = 0.23” at λ = 0.7µm, so
EH = 0.018 . For S = 0.1 then
(1 − S)EH
= 0.18
SEP + (1 − S)EH
is a non-negligible fraction of the total signal collected by the photometric aperture
defined by the first Airy minimum. This means that we must account for the halo
component of the PSF of the science object and so cannot assume that E is simply
proportional to S.
In our simulations we have found that the usual model just employed of a diffraction limited core on top of a partially corrected halo has limited ability to describe
the location of the photons in our image. At low Strehls, imperfect correction causes
the core to broaden, and the PSF tends to elongate in the direction of the prevailing
winds. Even at higher Strehls residual telescope jitter can have the same effect. We
also consider it desirable to avoid relying on an analytic model for the PSF, especially the halo component as this is likely to depend greatly on atmospheric seeing
and guide star brightness. In practice, we find that using elliptical apertures fit to
contours of constant flux will give consistent results from our simulated data.
Now let A = E/n be the average fractional photon flux per pixel in the ellipse
described by ~x = (a, b, φ), which are the semi-major axis, semi-minor axis, and
orientation of the ellipse. If we then define ~x∗ as the aperture which maximizes
75
S/N, then the optimum faint companion detection S/N is
√
A(~x∗ )fc DCtn∗
S/N =
1 .
A(~x∗ )fc + S̄ P̄(θ; ǫ)f∗ + (1 − S̄)H(θ)f∗ + 0.53τ0 [(1 − S̄)H(θ)f∗ ]2 n∗ + Nsky + Ndet 2
(3.7)
where n∗ = πa∗ b∗ . We have gone to this effort because we find that using other
algorithms to estimate S/N, such as peak-pixel or a fixed aperture size, tends to
incorrectly analyze the benefits of frame selection in our simulations in various cases
- especially when the contribution of the companion’s halo component is ignored.
3.3.3 Effective Duty Cycle
Now we can solve Equation (3.7) for the time t it takes to reach a desired S/N:
t=
(S/N )2
(A(~x∗ )fc + S̄ P̄(θ; ǫ)f∗ + (1 − S̄)H(θ)f∗
A2 (~x∗ )n∗ fc2 DC
+0.53τ0 [(1 − S̄)H(θ)f∗ ]2 n∗ + Nsky + Ndet ).
We can then compare two data taking techniques, e.g. frame selection to simple
integration. In order for a technique to provide a S/N advantage then the effective
duty cycle DC eff must satisfy the inequality
DC eff =
to
≥1
t1
(3.8)
where to is the the time needed to reach a S/N goal with simple integration (i.e.
doing nothing), and t1 is the time needed with a particular frame selection technique.
The effective duty cycle concept allows us to compare the trade-offs between
resolution, encircled energy, and efficiency, and then decide the optimal imaging
technique for our AO system and science goals. Now we consider the limiting cases
of equations (3.7) and (3.8) which we expect to routinely encounter with Magellan
AO. By choosing cases where specific sources of noise dominate we can compare
imaging techniques without specifying details such as companion brightness and
separation, or the desired S/N.
76
3.3.4 The Speckle Limited Case
Several differential imaging techniques are in common use to reduce the impact of
the coherent speckle noise in high contrast imaging (cf. ADI, SDI, ASDI (Oppenheimer and Hinkley, 2009)). These techniques each have weaknesses, typically being
less effective close to the guide star and when used on extended objects such as a
circumstellar disk. SDI also requires a strong spectral feature in the companion
when compared to the guide star. In cases where speckle suppression cannot be
achieved and the term 0.53τ0 [(1 − S̄)H(θ)f∗ ]2 n∗ dominates in Equation (3.7), then
Equation (3.8) reduces to
DC sp
ef f
= DC 1
A∗1
1 − S̄1
2 1 − S̄o
A∗o
2
.
(3.9)
It is apparent from this expression that if, through frame selection, we can increase S̄1 and/or A∗1 we will have at least some compensation for the loss of efficiency
represented by DC 1 < 1. Furthermore, given the right conditions, frame selection
has the potential to maintain or even improve sensitivity while delivering the higher
resolution represented by increased S̄ and A∗1 .
3.3.5 The Halo Limited Case
If we are able to suppress the speckles, then when the term (1− S̄)H(θ)f∗ dominates
in equation (3.7) we are in the halo photon-noise limited regime. Equation (3.8) then
becomes
1 − S̄o
(A∗1 )2 n∗1
(3.10)
= DC 1
(A∗o )2 n∗o
1 − S̄1
Once again we see that if we can increase S¯1 and/or A∗1 we have some leeway with
DC hef f
lower DC 1 . It should also be noted that the S/N maximizing aperture will be
different between this case and the speckle limited case above due to the different
dependence on n∗ .
77
3.3.6 Background and Read Noise Limited
The next limiting case that should be considered occurs when the dominate noise
terms are due to sky BG and detector RON. However, the present work is focused
on bright NGS AO. In this regime, we will almost always be limited by halo noise
(photon and speckle) within the FOV of our camera. As such, we will only state
here, without proof, that because RTFS allows arbitrarily long integrations the
detector read-noise performance can be competitive with the current generation of
EMCCDs. When we also consider that RTFS allows us to do this over our entire
detector FOV without windowing, RTFS retains its competitiveness even for wider
separations from faint stars.
3.3.7 Simulated Faint Guide Star Strehl Selection
Now that we have a framework for comparing imaging techniques, we investigate the
performance of an ideal RTFS technique on an observation simulated with CAOS.
The setup of this simulation was nearly identical to that described in Section 2.5,
except seeing was set to the median r0 = 18cm. For an R=10 mag A5V guide
star the loop is stable, but undergoes significant fluctuation in correction quality.
We ran the simulation with this guide star for 5 seconds of observation time, and
extracted the simulated image at the CCD47 at 1 ms intervals and measured Strehl
on each of these short frames. We then applied the same corrections for static and
non-common-path aberrations to the 1ms measurements as in Table 2.3, but do not
use the tip-tilt correction on the 1ms frames.
Next, we establish a threshold ST and stack each 1ms frame which is above
this value. On the combined frame, we then fit elliptical contours at various flux
levels (isophots). For the reasons described in Section 3.3.2 we use these contours
as apertures to calculate the enclosed flux and number of pixels, and then choose
the S/N maximizing aperture for the speckle and halo limited cases. Finally we
measure the FWHM resolution using the 50% peak flux contour. The results of this
algorithm for various thresholds are shown in Figure 3.1.
78
Figure 3.1 Results from Strehl selection on a simulated R = 10 guide star, showing FWHM contours corresponding to
various selection thresholds. The colorbar encodes the threshold St and resultant gross duty cycle DC for each contour,
as well as the resultant mean Strehl S̄ and DC ef f for the speckle and halo limited cases. We see that significant gains
in resolution can be achieved, and compare these gains to those possible with 10 fps lucky imaging. For comparison
the diffraction limits (DL) of the Magellan VisAO system and the Hubble Space Telescope (HST) are plotted.
79
The very competitive design choice for our system would be to use an EMCCD
as the science camera. To study the trade-offs with RTFS, we assume a 1024x1024
array which can be operated at 10fps with negligible read noise. We also assume
a QE penalty of 50% when flux is greater than 1 electron/pixel/read. The same
simulated frames used for RTFS are combined in 100ms exposures, and we then
apply the typical Lucky imaging method of shifting these longer frames before adding
based on ST . In Figure 3.2 we compare this technique to RTFS. When flux is low,
EMCCD based lucky provides a large DC ef f advantage due to the resolution boost
from shift-and-add, however the ultimate resolution achieved is ∼ 10% worse due to
the lower temporal resolution. For brighter objects, or those close to a bright guide
star, the EMCCD based lucky performs worse due to the QE reduction.
An important caveat to this discussion is that we have assumed that the EMCCD “QE reduction”, which is actually due to an increase in photon noise, applies
identically to the speckle noise in the speckle limited case. This is almost certainly
not strictly true, but rather depends on subtle details such as the plate scale and
speckle lifetime. As such, the lower lucky-imaging curves in Figure 3.2 should be
considered merely an illustration of the point, and actual performance in this case
could be better or worse.
A further consideration is the impact of our S/N maximizing apertures. In the
speckle-limited case this is almost always the peak pixel due to the strong dependence on the number of pixels in the aperture. Photometry is seldom conducted
on a single pixel, however, and so the performance of frame selection (whether realtime or conventional lucky) is understated here if one uses a larger aperture. This
is somewhat true in the halo limited case as well, as the optimum aperture tends to
be < 1λ/D in radius, which is probably also smaller than normally used.
Finally we assume a VisAO tip-tilt loop with ∼ 5mas rms control, simulated
by shifting the 1ms images before applying the RTFS algorithm. The correction of
residual atmospheric tip-tilt (∼ 15mas rms) provides a huge improvement in DC ef f .
Interestingly, the achievable resolution is the same without tip-tilt control. This
is because at very high thresholds, only a small fraction of the simulated data is
80
used. This implies that by accepting only the best images, the dominant source
of resolution degradation (Strehl loss) is rejected and residual tip-tilt has a smaller
effect.
The main conclusion of this effort is that RTFS has potential to provide significant gains in resolution and sensitivity - with some trade-offs between the two similar to conventional Lucky imaging. The benefit of RTFS is that these can be
realized over the full FOV of a camera, and with its full QE, using already installed
detectors.
3.4 RTFS Implementation
Having established that RTFS offers significant performance enhancement for the
Magellan VisAO system in a low correction regime, we next report on the implementation of RTFS. We first test the performance limitations of the mechanical shutter,
and then develop algorithms to provide real-time control of the shutter.
3.4.1 Mechanical Shutter Performance
The Magellan VisAO camera uses a Uniblitz VS-25 mechanical shutter. This shutter
has a 25mm aperture, and is capable of operation at up to 40hz. Here we follow
the manufacturer and discuss shutter speed in terms of a complete open and shut
cycle, so 40hz implies 12.5ms exposures if we use a symmetric square wave pulse.
This is equivalent to 80 fps with DC = 0.5, over the full FOV of our 1024x1024
detector. The minimum exposure time of the shutter is ∼ 10ms, and it can be
operated asynchronously. This gives us the time-resolution equivalent to a 100 fps
camera.
We have performed a series of bench tests to determine the accuracy and stability
of the VS-25. Our device has an LED-photosensor synchronization circuit, which is
interrupted by one of the two shutter blades. The state change of this circuit occurs
at 80% shut and 20% open. Figure 3.3 shows the results of one of these tests at
25hz, which is equivalent to 50 fps. We have found the timing of the shutter motion
81
Figure 3.2 Results from Strehl selection on an R=10 guide star, showing the effective
duty cycle vs the resultant resolution for the speckle limited case. Minimum FWHM
(a) corresponds to the semi-minor axis of the elliptical contours shown in Figure 3.1,
and maximum FWHM (b) likewise to the semi-major axis. We compare the results
with those possible with a 10 fps EMCCD (which has a 50% QE penalty for bright
targets). We also show the significant improvement possible with the combination
of a fast tip-tilt loop and RTFS - this system could potentially more than double
observing efficiency in the speckle limited case.
82
Figure 3.3 Performance of the VS-25 shutter. In (a) we present the time to open and
shut while the VS-25 shutter was operated at 25hz continuously (50 fps equivalent,
with DC = 50%). As proxies for full open and shut we use the time to change an
LED-photosensor circuit, which corresponds to 80% open and 20% shut. After a
few minutes of warm up time the device is very stable. We show the histogram of
the 80% shut times after 200 s has elapsed in (b). The standard deviation of this
distribution is σ = 92.5µs, and the open distribution has σ = 11.2µs. For 180,000
cycles, a total exposure of 1 hour, the uncertainty in exposure time will be 55ms, or
0.002%.
83
to be very reliable and stable. If we operated the shutter at 25hz for 2 hours, to
obtain a total exposure of 1 hour, the resulting uncertainty in exposure time would
only be 55ms, or 0.002%.
3.4.2 Telemetry
Our system, based on the LBT architecture, does not have a dedicated real-time
telemetry system built in. For RTFS, WFS slopes are taken from an auxiliary
output of the slope computer (Microgate BCU 39) so as to leave the main AO
loop unaltered. This auxiliary output, a UDP broadcast over standard ethernet, is
normally used to send WFS frames to the AO operator’s workstation. To capture
the slope output in near real-time without requiring any changes to the AO control
software, we use an ethernet bridge. A bridge consists of two ethernet adapters, and
a kernel software module which passes packets from one adapter to the other so as to
be transparent to other devices on the network but allowing one to capture packets.
We thus can transparently intercept slope computer diagnostic frames and extract
the slope vector. The slope vector is then used to reconstruct the wavefront modal
amplitudes as described above. See the schematic in Figure 3.4 which outlines how
data flows from the WFS detector, through the bridge, to the GPU (discussed next),
and finally becomes a command to the shutter.
3.4.3 GPU Based Reconstruction
We have implemented the matrix-vector multiplication step on a GPU. Our current
device is an NVIDIA GeForce GTX 465, which has 352 cores. We used the NVIDIA
CUDA3 basic linear algebra (BLAS) library, cuBLAS, to perform the multiplication
with the SGEMV routine. For comparison, we also implemented the reconstruction
on the CPU using the automatically tuned linear algebra software (ATLAS) package
(Whaley and Petitet, 2005), which was compiled from source to fully optimize for
speed. On the GPU, time to reconstruct a single frame averages 206 µsec, including
3
http://www.nvidia.com/object/cuda_home_new.html
84
Figure 3.4 Schematic showing the flow of data in our system. The blue lines show
the path of visible wavelength light from the telescope. A selectable beam-splitter
sends light to both the PWFS (left) and the VisAO camera (right). The red lines
show the flow of data. The CCD 39 records the pyramid pupil images, which are
processed by the BCU 39 slope computer. The slopes are sent to the ASM via a
custom fast fiber link. A secondary output, for telemetry monitoring, sends the
slopes over standard ethernet which we transparently intercept for use in RTFS.
From there reconstruction occurs on an off the shelf GPU, which produces a realtime measure of Strehl ratio. This is used to determine whether to open or close
the shutter.
85
slope transfer overhead. On the CPU with ATLAS the average time was 314 µsec,
so using the GPU results in a 34% improvement in reconstruction speed.
3.4.4 Digital Filter Design
After reconstruction the Strehl time series is low-pass filtered using a finite impulse
response (FIR) filter. An FIR is used because of its simplicity and guaranteed
stability. Filters appropriate for each loop speed (and telemetry rate) were designed
in Matlab using the filter design and analysis tool, fdatool. A major concern is
keeping the phase lag low to prevent inaccuracy due to filter delay. Good results
have been obtained with a pass frequency of 10 Hz and a stop frequency of 50Hz,
and 20 dB attenuation, using the generalized equiripple minimum order technique.
3.4.5 Reconstructor Calibration
Due to fitting error, which is caused by the finite number of spatial frequencies
sampled by the WFS, and non-common path (NCP) errors (for VisAO primarily
caused by one beam-splitter) we expect our reconstructed Strehl (Srec ) to underpredict true focal plane S. Using the extended Marechal approximation, we expect
the combined fitting and NCP errors to be a multiplicative correction to Srec :
2
2
S = e(−σf it −σN CP ) Srec .
In our tests so far, we have found that this simple assumption is insufficient to fully
describe the S time series. The logical way to proceed using the above relation is
to set the combined fitting and NCP errors to match the mean Srec to the mean
Sf oc measured in the CCD 47 focal plane. However, this technique underestimates
the peak-to-valley variability of the true S significantly, which is unacceptable for
frame-selection. To match both mean and variance, we use a simple two parameter
model
Scal = aSrec + b
86
where we estimate the parameters by
stdev(Sf oc )
stdev(Srec )
b = mean(Srec )a − mean(Sf oc ).
a =
We do not use a fitting procedure as the sampling frequencies are different between
Sf oc and Srec . Sf oc was measured in 32x32 pixel frames taken at 42fps on the CCD
47. The frames were averaged without shifting, and the ratio of this long exposure
peak height to the mean short exposure peak height provided an estimate of S
loss due to image motion. We then calibrated Sf oc so that the long exposure peak
height is equal to the S measured in a long exposure full frame image, and then
the mean short exposure Sf oc was set to match the image-motion corrected mean
Sf oc . This process avoids the difficulties of accurately normalizing S measurements
in small format images. The results of this calibration can be judged in Figure 3.5.
Both the mean value and the peak-to-valley variations are well fit by our calibrated
reconstructed S.
The parameter a retains a simple interpretation as
2
− ln(a) = σf2it + σN
CP .
Interpreting the parameter b is more challenging. We believe it is related to a
phenomenon which has been dubbed the “optical loop gain”, whereby the sensitivity
of the PWFS depends on the size of the spot on the pyramid tip and hence on the
instantaneous quality of correction. That is, the calibration of Srec depends on the
value of S itself. Work is ongoing to understand and calibrate the effect of this
optical loop gain. We also note that performing these calibrations in terms of WFE
instead of S requires a similar parameter.
3.4.6 Strehl Classification Algorithms
We have previously discussed the use of wavefront sensor (WFS) telemetry exclusively to estimate Strehl ratio. We also considered adding a fast tip-tilt control loop
to the VisAO camera. This would have included a small FOV EMCCD providing
87
Figure 3.5 Reconstructed Srec compared to Sf oc measured in the VisAO focal plane,
for our SDSS i’ bandpass.
88
Figure 3.6 Strehl predictions. In part (a) we show a raw time series from the
simulation described in Section 3.3.7, zoomed into a representative section. The
solid black line is the output of the FIR digital filter designed to have a minimal
phase lag. The dashed red line is the “prediction” result of applying the current
filtered Strehl measurement with a 6ms shutter actuation delay. The solid red line
is the prediction output of using an average of two different linear extrapolations.
In (b) we present the classification accuracy of these two prediction strategies vs.
Strehl selection threshold.
89
direct measurements of Strehl. Though the tip-tilt loop has not yet been implemented, here we describe investigations into using such direct measurements. In
future work we will investigate the benefits of combining WFS telemetry with the
direct measurements.
We can place the RTFS problem in the formalism established in section 3.2. In
the simplest case, where we are using the high speed output of our tip-tilt sensor,
~ i ) consists of Strehl measurements, or simply the value of the
the data vector X(t
brightest pixel. To start we can simply use these measurements as input to the
classifier G, with a delay of k time steps set by the mechanical performance of our
shutter. The main problem with this approach is that we suffer errors due to the
delay. We also must deal with noise in a real system, and desire to reject moments
of classification change which are shorter than our shutter actuation times (e.g. a
1ms long dip barely below the threshold should not close the shutter).
As discussed above, it is necessary to condition the Strehl time series. The tiptilt loop will typically be operated at very high frame rates (1-3 khz), faster than
the main AO loop. Simulations indicate that this produces a sawtooth pattern
in the signal, with sharp increases when the latest correction is applied followed
by decreases between corrections. At such short exposure times photon noise may
become important on fainter stars as well. Due to the mechanical limitations of
a shutter (i.e. minimum cycle time and finite response times) we must filter out
these high frequency components of the signal. For this analysis we designed a
filter with a pass frequency of 50 hz and a stop frequency of 75 hz, optimized for a
minimum phase lag. In terms of the generic selection algorithm, this filter serves as
the operator F and the filtered-signal output becomes the input to the classifier G.
Figure 3.6 illustrates the performance of this filter on a simulated Strehl time series.
To accomplish prediction, we have found good performance with simple linear
extrapolation. Our experiments with various fitting intervals indicate that combining the results of various intervals can improve performance, especially near peaks
and valleys in the signal. By interval we mean the number of previous data points
used for fitting. Based on the manufacturer specifications for the VS-25 shutter,
90
we extrapolate 6ms in the future. Figure 3.6 compares the prediction results of
averaging 4 step and 10 step fitting intervals with no prediction.
Figure 3.6 also shows the classification accuracy of these two approaches. From
Equation (3.1) we know that this is a binary problem, which makes it significantly
easier to analyze compared to attempting to calculate the exact value of Strehl
ratio. In the bottom panel of Figure 3.6 it is apparent that with a real time source
of Strehl measurements we can achieve very good classification accuracy. The simple
algorithms we are considering here struggle a little at lower Strehl thresholds (0.05−
0.10). Considering Figure 3.1, where we find that our best resolution is achieved at
thresholds St >∼ 0.15, these simple techniques appear quite sufficient as accuracy
is > 95%.
3.5 Laboratory Demonstration
We conducted a series of experiments in the Arcetri test tower to test our RTFS
architecture, at the conclusion of our integration and testing period there.
3.5.1 Experimental Setup
On bright guide stars the MagAO system performs very well, producing high and
stable S down to at least λ ∼ 0.7µm. In this regime, RTFS will be counterproductive
due to the small variation in S, and the relatively small improvement in signal-to-
noise ratio for any corresponding reduction in total exposure time. We therefore
expect RTFS to be most useful on fainter stars, where the MagAO system no longer
produces such good correction. Due to the way guide star magnitude was controlled
in the test tower, both with a variable brightness lamp and by changing beamsplitters, it was challenging to create a fully realistic faint guide star simulation
for these tests which also allowed enough light to reach the CCD 47 for accurate
measurement of short exposure S. To compensate, we instead used a 9.4 mag guide
star but ran the loop at 500 Hz and intentionally set gains to produce a large
amount of variability in S. As usual, 0.8” turbulence was simulated, with a 15 m/s
91
Figure 3.7 Short exposure S statistics.
wind. Though artificial, this setup provided a good test of our RTFS architecture
due to the large temporal variability of S while allowing accurate short exposure
measurements, and produced the time series shown in Figure 3.5.
The statistics of our S time series are shown in Figure 3.7. Of note, there is
negative skewness in the S probability density function (PDF). As other authors
have demonstrated, we actually expect positive skewness when the mean value of S
is so low (Gladysz et al., 2008b). This discrepancy is likely due to the artificiality
of our test setup.
92
3.5.2 Results
Using the loop setup described above, we set thresholds at the following selection
fractions: 100%, 95%, 90%, 75%, 50%, 25%, 10%, and 5%. For example, the 5%
threshold means we are attempting to select the best 5% of S. We use the term
selection fraction to make it clear that we mean the amount of time the shutter will
be open if it is following S with complete accuracy, or in other words the telescope
duty cycle.
Once a threshold was selected, the RTFS system was activated in closed-loop
while taking data on the CCD 47 in the SDSS i’ filter. To avoid saturation, we took
short exposures which were then summed (after dark subtraction) without shifting
to form a long exposure image. Figure 3.8 shows the resultant images. As we selected
higher and higher thresholds, there was a clear improvement in the resultant S, and
F W HM . Figure 3.9 plots the improvement in these values vs. threshold.
We measured the flux in each long exposure image, and compared the result to
the flux in the 100% selection fraction image. This provides a measure of the net
telescope duty cycle, or shutter open time, for each threshold. This also serves as
a quick-look proxy for total accuracy of our RTFS system, based on how closely
our system follows the y=x line. The system tends to under-select at the higher S
thresholds. The shutter has an actuation delay of a few msec, and we enforced a reactuation time of 35 msec in software as a mechanical safety measure. These delays
should cause the system to miss many peaks which occur close together, though low
pass filtering mitigates this to some extent.
Figure 3.8 Long exposure images obtained with RTFS. Both long exposure S and F W HM improved as the selection
fraction is changed to higher values of S.
93
94
3.6 Conclusion
When we began simulating the performance of MagAO and VisAO, the simulations
indicated that we would have low to moderate Strehl ratios for wavelengths less than
1.0µm. As is typical for such conditions, we saw large fluctuations in correction
quality over short periods of time. To compensate for this we planned to utilize a
novel frame selection technique, which could provide the ability to reliably achieve
the diffraction limit while offering sensitivity and efficiency improvements.
To understand the costs and potential benefits of frame selection, which unavoidably involves discarding valuable telescope time, we have employed a simple
model of S/N in AO imaging. Using this model we developed a simple framework
to compare various imaging strategies, and showed that our new RTFS technique
is very competitive when compared to short-exposure based lucky imaging. This is
especially true in NGS visible AO where the presence of a bright star in our FOV
makes the use of low-RON EMCCDs challenging.
We demonstrated that commercially available mechanical shutters provide the
timing accuracy and precision to support RTFS. It was also shown that with a real
time source of short exposure Strehl ratio measurements we can obtain very accurate
frame selection. The combination of a fast VisAO specific tip-tilt loop and RTFS
would more than double our observing efficiency and consistently provide diffraction
limited images at the 6.5m Magellan Clay telescope.
Finally we demonstrated RTFS in closed-loop for the first time. Using WFS
telemetry, we were able to reconstruct S in real time and use this knowledge to
select moments of good AO correction using a mechanical shutter. This allowed us
to improve S from 16% to 26% under (somewhat artificial) laboratory conditions.
There is room for further improvement in our system, as higher accuracy would
permit more efficient use of telescope time.
As noted in the introduction, MagAO and VisAO are performing much better
than our initial pessimistic estimates. One might say that they are performing as
they should - something not always achieved by new AO systems. In any case, we
95
Figure 3.9 At left we plot achieved S for various selection thresholds, and at right
we plot F W HM . The selection thresholds correspond to the S distribution, that is
a 10% threshold means that the shutter opens only when S is in the best 10%. The
achieved S was lower when at the 5% threshold, compared to the 10% threshold.
The shutter has a finite actuation time of about 10 msec and this drop in S at the
highest threshold is possibly due to this delay compared to the width of peaks of
S above the threshold. If the shutter actuates too slowly to catch the highest S, it
will instead be open during lower S periods.
96
Figure 3.10 Duty cycle for the selection thresholds. Duty cycle was measured photometrically, and serves as a proxy for accuracy. A perfect system would follow
the y=x line. The system is less accurate, and tends to under-select, at the most
selective thresholds. This is likely due to the shutter actuation delay of 10 msec,
and a software safety re-actuation time of 35 msec. These delays cause the system
to miss many peaks which occur close together. Low pass filtering mitigates this to
some extent.
have so far not needed RTFS on sky. I have conducted a few short engineering trials
- mainly to make sure the shutter still works - during our commissioning runs, but
have not obtained a full RTFS data set. For now we use the shutter mainly for
taking darks.
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CHAPTER 4
HIGH CONTRAST IMAGING WITH VISAO: OBSERVATIONS OF β
PICTORIS B
4.1 Introduction
In 1984, Astronomers from the University of Arizona, observing at LCO, spatially
resolved an extended edge-on debris disk around β Pictoris. Smith and Terrile
(1984) hypothesized that the disk, which had been inferred from observations of
the IRAS satellite, indicated the presence of planets around β Pic, either forming
or recently formed. Since this discovery, the star has been observed repeatedly
at many wavelengths. Here we review a small portion of the literature, paying
particular attention to the line of evidence pointing to the presence of at least one
planet orbiting β Pictoris.
4.1.1 Disk Observations and Variability
The β Pic disk, being visible in seeing limited imaging, was subject to many investigations from ground-based telescopes. For instance, it was observed in R band by
Golimowski et al. (1993), using a coronagraph and image stabilizer, also at the 100”
du Pont at LCO. They detected wide asymmetries in the disk. Kalas and Jewitt
(1995) also observed in R band with a coronagraph, and also detected asymmetry.
The asymmetries found were on too large a spatial scale to be associated with planets closer to the star. Using an anti-blooming CCD, rather than a coronagraph,
Lecavelier Des Etangs et al. (1993) obtained BV RIc images with information as
close as 2” from the star and noted that the nature of the disk particles changed
closer to the star, possibly related to planetary formation, and that there were hints
of inhomogeneous dust distributions in the inner regions of the disk.
98
The disk was observed with HST as well, and a warp in the inner disk was
detected (Burrows et al., 1995; Heap et al., 2000; Golimowski et al., 2006). Groundbased AO observations also show the warped inner disk (Mouillet et al., 1997).
Analysis of this warp indicated that it should be unstable, and required the presence
of a perturbing planet to be maintained (Augereau et al., 2001) .
Lagrange-Henri et al. (1988) interpreted spectroscopic variability in metallic absorption lines as the infall of solid bodies — comets — of km size. This lead to
the interpretation that these comets were being disturbed by a planet (Beust et al.,
1990, 1991), possibly at high inclination. A further interesting incident of variability
occurred on 1981 Nov 10, when β Pic was observed to grow rapidly fainter consistent
with a transit by a Jupiter sized object (Lecavelier Des Etangs et al., 1995).
4.1.2 Detection of β Pictoris b
Lagrange et al. (2009) reported the detection of a point source 8 AU from β Pic,
as many expected based on the several lines of circumstantial evidence pointing to
the presence of a planet around the star. These first observations, from 2003, were
followed up and confirmed in the fall of 2009 by Lagrange et al. (2010). In between
the 2003 initial detection and the 2009 confirmation, the planet had orbited to the
opposite side of the star. The planet has since been detected throughout the near
and mid-IR (Quanz et al., 2010; Bonnefoy et al., 2011; Currie et al., 2011b; Chauvin
et al., 2012a; Bonnefoy et al., 2013; Boccaletti et al., 2013).
Though it was reported to be mis-aligned with the warp by Currie et al. (2011b),
dynamical analysis indicates b is most likely the cause of the warp (Dawson et al.,
2011) and later observations of the planet and disk together in the same image
indicate that b is in fact aligned with the warp (Lagrange et al., 2012). In addition
to matching expectations based on disk morphology, the interesting possibility exists
that a transit of β Pic b also explains the Nov 1981 brightness transient (Lecavelier
Des Etangs and Vidal-Madjar, 2009).
99
4.2 High Contrast Observations of β Pictoris with VisAO
Here we present observations of β Pictoris with MagAO/VisAO. To perform these
observations, we used the VisAO near-focal-plane occulting mask coronagraph. We
expect β Pic b to be located under the mask, so we here present the extensive
characterization of the coronagraph we performed in the lab and on-sky. Next we
describe our observations and data reduction, and show the contrast obtained with
VisAO.
4.2.1 The VisAO Coronagraph
The VisAO camera contains a partially transmissive occulting mask, used to prevent saturation of the CCD when observing bright stars. The mask has a radius
equivalent to 0.1”, were it in the focal plane, but it is approximately 60mm out of
focus in an f/52 beam. Consequently it attenuates flux out to ∼ 0.8” in radius.
We calibrated the mask transmission and PSF by scanning an artificial test
source across the mask with the W-unit off the telescope. The source was scanned
along 12 different lines, spaced roughly 30 degrees apart, in the YS filter. For each
scan, we found the best fit center assuming symmetry, and then combined data from
all scans. Transmission is reported here using the ratio of the maximum pixel. As
we will discuss shortly, the PSF changes shape somewhat dramatically under the
mask so peak fitting is unreliable. The results of our laboratory scans are shown in
Figure 4.1. Though the mask itself is not apodized, it is out of focus resulting in
the smooth roll-off of attenuation. The maximum attenuation of the max pixel is
0.0015, that is ND = 2.8.
The profile of the mask is not well described by convenient functions (Gaussian,
Moffatt, polynomials), so we merely re-binned the raw lab data (median) and interpolate between points as needed for analysis. This binned profile is shown in Figure
4.2.
We tested our laboratory calibration on-sky as well. We scanned a star, with
the AO loop closed and the YS filter, across the mask using the same script as used
100
Transmission
1.000
0.100
0.010
0.001
−100
0
Separation (pixels)
100
Figure 4.1 Transmission of the VisAO occulting mask, on a log scale. Shown here
is the ratio of maximum pixel - no peak fitting was applied due to the change in
shaped caused by the mask. Though the chrome mask is not apodized, it is out of
focus resulting in this apodized transmission profile. Maximum attenuation at the
center is 1.5 × 10−3 , or ND= 2.8. The separation of β Pic b is 59 pixels.
101
for the test source along two lines 90 degrees apart. We compare these on-sky scans
to the lab scans in Figure 4.2. We also tested the mask using binary stars on-sky.
The results of these tests are also shown in Figure 4.2.
As we noted, the apodized transmission profile changes the shape of the PSF under the mask. Relevant example PSFs are shown in Figure 4.3. The test source uses
optics designed for the LBT, and so has a smaller PSF. We magnified these images
to match the diffraction limited PSF we measured on-sky, which has a FWHM=4.7
pixels at 0.98µm.
In Figure 4.4 we quantify this change in shape, comparing the FWHM of an
elliptical Gaussian fit to the PSF vs. position, along the semi-major and semi-minor
axes. The PSF is elongated radially, but maintains the diffraction limited FWHM
in the azimuthal direction. In Figure 4.5 we show the ratio of FWHMs and also
show measurements from our on-sky scans.
4.2.2 Observations and Data Reduction
We observed β Pic on the night of 2012 Dec 04 UT, in the YS filter using the
coronagraph. We used the 50/50 beamsplitter. Conditions were photometric, with
variable seeing at the beginning of the observation, but settling down to ∼ 0.5′′ by
the end. Towards the end of the observation we took off-coronagraph calibration
data, which was presented earlier in Section 2.7.3, where we found that Strehl ratio
was 32 ± 2% and that true optical Strehl was 40%. The latter number is important
for high contrast imaging as it sets the flux in the halo as (1 − S).
We used the WFE telemetry recorded in the Fits headers to select images, using
a cut of 130 nm RMS phase. This resulted in a little over 2hrs of data, with an
elapsed time of 4.17 hrs and 116 degrees of rotation. The complete details of the
observation are given in Table 4.1.
Images were bias and dark subtracted, using shutter-closed darks taken at 15
min intervals throughout the observation. To better facilitate data processing, the
3399 selected and dark-subtracted individual exposures were median coadded in 30
second chunks, with a rotation limit of 0.5 degrees. That is, the images were coadded
102
lab
lab re−binned
on−sky scans
on−sky binaries
1.2
Transmission
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Separation (")
0.8
1.0
Figure 4.2 Transmission of the VisAO occulting mask. As before this is the ratio
of maximum pixels. Here we also show the on-sky calibration checks conducted,
including scans of a star across the mask and two binaries compared on and off
the coronagraph. The on-sky scans were binned: the separation error bars are the
standard deviation of the separations in each bin, and the transmission error bars
are the standard deviation of the mean in that bin. The separation of β Pic b was
0.47”.
103
100
(a)
∆Y (mas)
50
0
−50
Off
−100
−100
−50
0
∆X (mas)
50
100
50
100
50
100
100
(b)
∆Y (mas)
50
0
−50
0.3"
−100
−100
−50
0
∆X (mas)
100
(c)
∆y (mas)
50
0
−50
0.5"
−100
−100
−50
0
∆x (mas)
Figure 4.3 Test source calibrations of the PSF through the occulting mask. (a)
shows the PSF of the test source off the mask. (b) shows the PSF at ∼ 0.3” and (c)
shows the PSF at ∼ 0.5” separation from the mask center. The black circle has a
diameter of 4.7 pixels, the FWHM of the un-occulted PSF measured on-sky. Images
are in a linear stretch. The white arrow indicates the direction of the coronagraph
center. The separation of β Pic b was 0.47”.
104
40
semi−maj
semi−min
FWHM (pixels)
30
20
10
0
−100
0
Separation (pixels)
100
Figure 4.4 FWHMs of an elliptical Gaussian fit to the PSF vs. separation from the
mask center. The separation of β Pic b was 59 pixels.
105
3.0
lab
lab re−binned
on−sky
2.5
FWHM Ratio
2.0
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
Separation (")
0.8
1.0
Figure 4.5 Ratio of Gaussian FWHM along the radial direction to the FWHM along
the azimuthal direction under the mask, vs. separation from the mask center. The
occulting mask changes the shape of the PSF, elongating it radially away from the
mask center. The on-sky results are biased due to the slight elongation present in
the PSF due to the wind. This causes the ratio to start > 1, and to not reach the
same peak value. The separation of β Pic b was 0.47”.
106
Table 4.1 Observations of β Pictoris in YS with the coronagraph.
Date
Filter
CCD Speed
CCD Window
Exp. Time
Elapsed Time
Tot. Rotation
WFE1Threshold
No. Images
Tot. Exposure
Seeing FWHM
AO Speed
AO Binning
AO Modes
Mean WFE1
Median WFE1
Long Exp. Strehl
Optical Strehl2
PSF FWHM
1
2
2012 Dec 04 UT
YS (0.984µm)
250 kHz
1024x1024
2.273 s
4.17 hrs
115.97 deg
130.0 nm rms
3399
2.15 hrs
0.5” - 0.7”
990 Hz
1x1
200
125.91 nm rms
128.9 nm rms
32 ± 2%
40%
4.7 pix=37.2 mas
Instantaneous WFE, average over a single exposure.
Corrected for PRF (charge diffusion)
107
until 30 seconds elapsed time or 0.5 degrees of rotation had occurred.
The coadded images were first registered and centered using the beamsplitter
ghost, which has a good astrometric calibration to the center of the star (cf. Section
2.7.2). The coronagraph is partially transmissive (ND≈ 2.8) in the core, so on a
bright star we are able to use the star itself for centering. After registering with
the ghost, we then located the center of rotational symmetry of the attenuated star
using cross correlation. This procedure finds the center of rotational symmetry to
better than 0.05 pixels.
We then median combined the registered images, forming our master PSF under
the mask. This is shown in Figure 4.6. Using this master PSF, we then carried out
a standard median ADI (MADI) data reduction: the master PSF was subtracted
from individual coadds, and then each was derotated and the images were median
combined. No radial profile subtraction or subtraction of nearby images was applied.
The resulting image is shown in Figure 4.7. We masked the central 200 pixels in
this image, where the residuals are high. Outside the mask, the well known disk is
clearly visible extending to the NE and SW. Next we describe our reduction of the
central region with principle component analysis.
Closer to the star, within ∼ 1.5′′ , MADI does not provide good speckle subtrac-
tion. Inside 1” the mask modulates speckles in a position dependent way, and combined with the small drift that occurred due to flexure, the speckle pattern changed
over the course of the observations. We therefore employed principle component
analysis (PCA), implementing the Karhunen-Loève Image Processing (KLIP) algorithm of Soummer et al. (2012).
We employed search areas, applying KLIP to these regions individually. This is
similar to the optimization and subtraction regions employed in LOCI (Lafrenière
et al., 2007b), though in this reduction our optimization and subtraction regions were
the same. For each image, the reference PSFs were taken to be any of the remaining
images where at least one F W HM = 4.7 pixels of rotation had occured at the inner
edge of the region being reduced. We then applied PCA to the reference PSFs,
forming a KL basis set. The optimum PSF was then calculated by determining
108
1.5
1.0
∆ y(")
0.5
0.0
−0.5
−1.0
−1.5
−1.5 −1.0 −0.5 0.0 0.5
∆ x(")
1.0
1.5
Figure 4.6 VisAO YS master coronagraphic PSF. Noteworthy features include the
beamsplitter ghost to the right, which has Airy rings, and the six short diffraction
spikes at ∼ 1.2′′ due to the six-fold symmetry of the ASM actuators. The flare-like
structure extending to the upper left from the central star is characteristic of slight
misalignment with the center of the mask.
109
∆ DEC(")
2
0
−2
−2
0
∆ RA(")
2
Figure 4.7 Median-ADI reduction of β Pictoris. The large central mask corresponds
to the region reduced with PCA. The disk is detected, though we do no analysis of
it here.
110
the coefficients to apply to each basis image, and summing. The optimum PSF for
each image was subtracted, and the resulting images where de-rotated and mediancombined. The result is shown in Figure 4.8(a).
Next we apply three spatial filters, the parameters of which were determined
using fake planet injection described later. The images reduced with PCA have
azimuthal structure, as is common in ADI reductions. To remove this, we apply an
azimuthal unsharp mask whereby a smoothed image is constructed using a kernel
with a Gaussian profile in azimuth and a boxcar profile in radius. The Gaussian
has angular width F W HMθ = 10 degrees, and the boxcar has radial width F Wr =
0.5 pixels. This azimuthally smoothed image is subtracted to remove the residual
azimuthal structure, the result of which is shown in in Figure 4.8(b). We then
apply a symmetric Gaussian unsharp mask to high-pass filter the image, with a
F W HM = 4.7 pixels (Figure 4.8(c)). This removes most features that are wider
than the PSF. Finally, we smooth the images (low-pass filter) with a Gaussian kernel
of F W HM = 2 pixels, which effectively Nyquist samples the 4.7 pixel PSF. The
final result is shown in Figure 4.8(d).
To aid in determining the optimal values for various parameters (including the
number of KLIP modes, the radial and azimuthal size of the search reagions, and
the smoothing filter parameters), we injected fake planets of various contrasts using
the measured coronagraphic PSF at 0.47′′ (the expected separation of β Pic b) at
21 position angles spaced 9 degrees apart, in the 180 degrees opposite the location
of the planet. Images with the fake planets were reduced with PCA and filtered as
described. We tried various combinations of region sizes and spatial filter parameters. For each set of parameters, we conducted aperture photometry on these fake
planets. To estimate the noise in the aperture photometry we also tested apertures
at the same radius where there was no fake or (known) real planet. This allowed an
estimate of S/N at each contrast level, which we used along with visual inspection
of the results to determine the best parameters.
We found that choice of region size, in both radial extent and angular width,
affected throughput. In general, having fewer pixels in the search region decreased
111
(a)
(b)
(c)
(d)
0.4
0.2
0.0
∆ RA [arcsec]
−0.2
−0.4
0.4
0.2
0.0
−0.2
−0.4
0.4
0.2
0.0 −0.2 −0.4
0.4
0.2
0.0 −0.2 −0.4
∆ DEC [arcsec]
Figure 4.8 Here we show the step-by-step results of the 3 spatial filters we applied.
In (a) we show the raw results of our KLIP/PCA reduction. (b) shows the image
after applying the azimuthal unsharp mask. (c) shows the data after the symmetric
unsharp mask, and (d) shows the final image after gaussian-smoothing by 2 pixels.
In each panel the arrow highlights the detection of β Pic b.
112
throughput. Conversely, minimizing the size of the region allowed better speckle
subtraction. These competing effects caused us to vary the search region size with
radius. KLIP has the advantage that throughput can be modeled at any location
in the image, even if a real astronomical source is there. This is done by projecting
a model of the signal onto the same KL modes, and reducing the model as before.
This “forward-modeling” (Soummer et al., 2012) is subtly distinct from fake planet
injection, in that we are not injecting the model images into the data. After applying
PCA we apply the same spatial filters as is done to the actual images. Throughput is estimated by comparing the heights of fitted peaks. Though photometry of
β Pic b was calibrated with the fake planet injection, we used such throughput
measurements to determine our detection limits as described next.
4.2.3 VisAO YS Contrast Limits
To determine the detection limits of this observation, we first quantified the fundamental noise floor. We use the master PSF from the MADI reduction to calculate
a radial profile of the PSF. This was converted from ADU/image to total photons
by multiplying by gain and the total exposure time, and the halo photon noise at
each pixel is then the square root of this quantity. We next divided the 1σ noise
by the coronagraph transmission profile. This limit in photons is converted into
contrast by using the beamsplitter ghost and the calibration of ghost-peak to PSFpeak described in Section 2.7.2. The RON limit was calculated similarly, assuming
4.5e− per readout (see Table 2.1). Note that the RON contrast limit is not constant,
as it too is divided by the coronagraph transmission. Next, the halo photon noise
and RON were added in quadrature, and then normalized for coronagraph and PSF
peak. This then gives the fundamental detection limit of our observation. We do
not expect to be photon noise limited, however, instead speckles will set our floor.
Next we calculated the standard deviation in 4 pixel annuli for both the MADI
and the PCA reductions. This was chosen as it corresponds to the 2 pixel radius
aperture we used for photometry. These noise profiles were converted to electrons,
contrast relative to the peak, and corrected for coronagraph transmission. The PCA
113
limit was also corrected for throughput determined by forward modeling. Since the
disk is detected in the MADI image, we mask out the disk PA±15 degrees.
All of these contrast curves are shown in Figure 4.9, as the 3σ detectability
contrast limits. We use 3σ in this analysis because we have a very strong prior on
the location of the planet.
4.3 Detection of β Pictoris b with VisAO
As noted hinted above, there is a point-source-like signal in our PCA reduction at
the expected location of β Pic b. In Figure 4.10(a) we show the reduced data. In
Figure 4.10(b) we show the S/N map, which is the image divided by the radial noise
profile. In both images there is a clear point source at or near the expected position
of the planet (separation ≈ 0.47′′ , PA ≈ 211).
We observed this target simultaneously with Clio, where we had much higher
S/N from 3-5µm, thus providing us a position for the planet. On the same night
as these VisAO observations, we obtained a high S/N detection of the planet in the
M ′ bandpass, at separation 0.496 ± 0.025′′ and PA 212.0 ± 2.0 degrees (Morzinski
et al., 2013, in prep), noting that these measurements are preliminary pending a
refined distortion solution for Clio. We used the fake planets to calibrate our VisAO
astrometry by measuring their position after reduction. We found that even at this
low SNR, Gaussian centroiding produced unbiased results on the fake planets. The
estimated position uncertainty from this analysis is 0.65 pixels. In tests on a binary
in ADI mode using the coronagraph, we found an additional 1 degree systematic
error in PA which is possibly due to the coronagraphic mask. We add this error
directly to the statistical uncertainty estimated from fake planets. We did not find a
similar systematic error in separation. We measured a separation of 0.4676±0.0059′′
and PA of 210.4 ± 1.65 degrees. Our astrometry is summarized in Table 4.3.
To further determine the significance of our detection, we conducted aperture
photometry along circles of constant radius, with a spacing of 1 FWHM, using
apertures 2 pixels in radius. We formed an estimate of the local sky at 5 pixels
114
10−4
All curves 3σ
10
PCA
3σ Contrast
b
−5
MA
DI
10−6
RON+Photon Noise Limit
RON
10−7
0.0
PSF 1/2
0.5
1.0
1.5
Sep(")
2.0
2.5
3.0
Figure 4.9 Here we show the 3σ detection limits, in terms of contrast ratio, for
∼ 2 hrs of integration on β Pic at YS . The readout noise (RON) assumes 4.5 e−
per pixel. The PSF limit is derived from the median-PSF calculated as part of
ADI processing. The radial profile of the median-PSF was multiplied by gain and
4.2. RON and
divided by the coronagraph transmission profile shown in Figure
√
PSF limits were added in quadrature to determine the basic N limit. This sets
the fundamental noise limit of this observation. We then show the 3σ contrast
curves, calculated as standard deviation in 4 pixel annuli, for median ADI (MADI)
with the disk masked, and for principle component analysis (PCA). PCA shows
significant
improvement over MADI, and past ∼ 1.0′′ is rapidly converging to the
√
N photon-noise limit. We also show our detection of β Pic b, at 0.47′′ .
Table 4.2 Astrometry of β Pictoris b
Clio M ′ µm
VisAO YS :
Sep = 0.496 ± 0.025′′
PA = 212.0 ± 2.0 deg
Sep = 0.4676 ± 0.0059′′
PA = 210.4 ± 1.65 deg
Morzinski et al, in prep
(preliminary)
This work
115
(a)
(b)
∆ RA [arcsec]
0.4
0.2
0.0
−0.2
−0.4
0.4
0.2
0.0
−0.2
−0.4
0.4
0.2
∆ DEC [arcsec]
Figure 4.10 (a) Final reduction. (b) S/N map.
0.0
−0.2
−0.4
116
0.6
4
Probability Density
0.5
S/N
2
0
−2
0.4
0.3
0.2
0.1
−4
0.0
0
100
200
Position Angle
300
−4
−2
0
S/N
2
4
Figure 4.11 (a) Aperture S/N vs. position angle. The aperture containing β Pic
b, which was excluded from the standard deviation, is shown as the red star. (b)
Histogram of the results. The location of the planet is highlighted in red. The solid
curve is a normal distribution with σ = 1.
radius, with a width of 1 pixel. We did this at 4 radii, separated by 1 FWHM
each. The results for each radius were normalized by the standard deviation of
aperture fluxes on that radius, and we excluded the aperture containing the known
planet from the calculation of standard deviation. We show the results of this test
in Figure 4.11. The statistics appear to be Gaussian, and β Pictoris b is detected
with S/N ∼ 4.4. This gives a false alarm probability of ∼ 5 × 10−6 .
We also used the fake planets to calibrate our photometry in the reduced image.
This results in an estimate of YS contrast of (3.0±0.7)×10−5 , or ∆YS = 11.30±0.25
117
mags. Mitchell and Johnson (1969) observed β Pic in the 99 filter of the 13-color
system. The central wavelength of our YS filter and the 99 filter are nearly identical,
so we use their measurement of 3.561 ± 0.035 mag as the brightness of β Pic A in
YS . We take into account the following sources of uncertainty:
• Detection S/N: 23%
• Coronagraph centering (±5 pixels): 16%
• Ghost calibration: 2.4%
• β Pic A Photometry: 3.5%
• β Pic A distance modulus: 0.005%
Our estimate for the apparent magnitude of β Pic b is then 14.87 ± 0.31, and
13.43 ± 0.31 for the absolute magnitude.
4.4 Prior Measurements of β Pic b photometry in J, H, and KS
β Pic b has been detected at other wavelengths by other observers. At J band, it was
detected with NACO by Bonnefoy et al. (2013). This data was re-reduced by Currie
et al. (2013) with slightly higher reported S/N. As these are reductions of the same
data with different algorithms, we do not treat them as statistically independent
results, rather here we adopt the higher S/N measurement of Currie et al. (2013).
For the H band detection of NACO, we likewise choose the reported higher S/N
measurement of Currie et al. (2013) over Bonnefoy et al. (2013). Currie et al. (2013)
did conduct new observations of β Pic b with NICI at H band. Since there are slight
differences in these two bandpasses, we do not average these results. In KS band we
have the NACO measurement of Bonnefoy et al. (2011) and the NICI measurement
of Currie et al. (2013). There is also an unpublished NICI measurement provided by
Mike Liu (private communication). We average the two NICI measurements. The
YS JHKS photometry of β Pic b to-date is collected in Table 4.3.
118
Table 4.3 Photometry of β Pictoris b
Filter
Instrument
Date
Apparent
Magnitude
14.87 ± 0.31
Absolute
Magnitude
13.43 ± 0.31
YS
VisAO
2012/12/04
J
NACO
H
KS
Notes
2011/12/16
14.11 ± 0.21
12.68 ± 0.21
[2]
NACO
NICI
2012/01/01
2013/01/09
13.32 ± 0.14
13.25 ± 0.18
11.89 ± 0.14
11.82 ± 0.18
[2]
[2]
NACO
NICI
NICI
NICI mean
2010/04/10
2012/12/15
2013/01/09
12.6 ± 0.1
12.37 ± 0.13
12.47 ± 0.13
12.42 ± 0.09
11.2 ± 0.1
10.93 ± 0.13
11.04 ± 0.13
10.98 ± 0.09
[3]
[4]
[2]
[1]
[1]
Notes: [1] this work, [2] Currie et al. (2013), [3] Bonnefoy et al. (2011)
[4] Mike Liu, private communication.
4.5 Prior Exoplanet Photometry in the Y Band
This is the first ground-based direct-detection of an exoplanet in the optical. Other
efforts have pushed into the Y band on the HR8799 planets. Currie et al. (2011a)
detected HR8799 b at 1.04µm in the unfortunately labeled z filter. From here on
we, follow Liu et al. (2012) and refer to this filter as z1.1 . See further discussion in
Appendix B.
Oppenheimer et al. (2013) have the ability to work down to 0.995µm with Project
1640, and reported low significance detections of HR8799 b and HR8799 c at 1.05µm.
At 0.986µm, our detection of β Pic b further pushes our ability to probe exoplanet
atmospheres blue-ward.
Another planet-mass object which has been observed at similar wavelengths is
2M1207b, which was observed with the Hubble Space Telescope by Mohanty et al.
(2007). For both 2M1207b and HR8799b we would like to directly compare our
results in the optical and near-IR. To do so, we must convert these measurements
into our YS bandpass and the NACO filters. Though we show how this can be done
119
Table 4.4 Estimated YS and NACO photometry of 2M1207b and HR 8799b
Filter
λ0
µm
Abs. Magnitude
Measured
Estimated
References
2M1207b
F090M
0.905 18.86±0.25
—
YS
0.986
—
18.2±0.26
Y
1.032
—
17.79±0.26
z1.1
1.039
—
17.73±0.26
F110M
1.102 17.01±0.16
—
J2M ASS
1.241 16.40±0.21
—
JN ACO
1.256
—
16.34±0.21
H2M ASS
1.651 14.49±0.21
—
HN ACO
1.656
—
14.52±0.22
KS,2M ASS 2.166 13.33±0.12
—
KS,N ACO 2.160
—
13.38±0.13
HR 8799b
YS
0.986
—
18.84±0.29
Y
1.032
—
18.31±0.29
z1.1
1.039 18.24±0.29
—
JM KO
1.249 16.30±0.16
—
JN ACO
1.256
—
16.52±0.17
HM KO
1.634 14.87±0.17
—
HN ACO
1.656
—
14.92±0.17
KS,M KO
2.156 14.05±0.08
—
KS,N ACO 2.160
—
14.17±0.09
Notes: [1] Song et al. (2006), [2] this work,
[3] Mohanty et al. (2007), [4] Currie et al. (2011a),
[5] Marois et al. (2008b)
[1]
[2]
[2]
[2]
[1]
[3]
[2]
[3]
[2]
[3]
[2]
[2]
[2]
[4]
[5]
[2]
[5]
[2]
[5]
[2]
for normal brown dwarf spectral types in Appendix B, these two objects do not
correspond to any known brown dwarf. Instead we turn to published best-fit model
spectra. For 2M1207b we use the model of Barman et al. (2011), and for HR8799b
we use the best-fit model from Madhusudhan et al. (2011). We use the models
to calculate a ∆mag between the filters with actual photometry and our desired
bandpasses. The estimates for the photometry in other bands are then formed by
applying this ∆mag to the actual measurement. We illustrate this in Figure 4.12
and summarize the results in Table 4.4.
[10−13 ergs cm−2 sec−1 µm−1]
120
10
2M1207b
1
F090M
YS
Y z1.1
F110M
J
10
Fλ at 10 pcs
HR 8799b
Measured
Estimated
Model
1
0.9
1.0
1.1
λ [µm]
1.2
Figure 4.12 Optical and near-IR photometry and models of 2M1207b and HR 8799b.
To estimate photometry in the Y atmospheric window and in the NACO filters
we used the models to extrapolate or interpolate from the measured photometry.
Measured photometry is indicated by filled circles, and estimated photometry is
indicated by asterisks. The 2M1207b model is from Barman et al. (2011), and the
HR 8799b model is from Madhusudhan et al. (2011). See also table 4.4
121
4.6 Discussion
It is interesting to compare β Pictoris b with other planetary mass objects, as well as
with field brown dwarfs. We discussed 2M1207b and HR8799b above. For the field
dwarfs, we collected YJHK spectra of 497 objects. 441 of these are from the SpeX
Prism Spectral libraries maintained by Adam Burgasser1 (from various sources), 23
are WISE brown dwarfs from Kirkpatrick et al. (2011), and 33 are from Allers and
Liu (2013). We correlated 91 of these with parallax measurements, either listed
in the SpeX Library (from various sources) or from Dupuy and Liu (2012). We
conducted synthetic photometry on these spectra as described in Appendix B.
In Figure 4.13 we compare β Pic b to the field dwarfs in color-color plots, and
include HR 8799b and 2M1207b. We also highlight the location of 2M0355, a young
low-gravity object identifiedy by Faherty et al. (2013) as having colors similar to
the young, dusty planets. Two things are evident from the color-color plots. First,
β Pic b is very different from the other planets. The other HR 8799 planets (c,d,e)
can, based on their near-IR colors, be expected to fall in regions similar to the
three comparison planets and planet-like objects we show. Furthermore, though YS
appears somewhat brighter than expected, β Pictoris b has colors consistent with
those of early L dwarfs. We note that age alone can not explain the differences
here, as 2M1207 (∼ 8 Myr) is younger than β Pic (∼ 12 Myr), and both are likely
younger than HR8799 (∼ 30 Myr).
Based on this observation, we next attempted to fit the YJHK photometry of β
Pic b to our collection of brown dwarf spectra. We conducted synthetic photometry
on the spectra, as described in Appendix B, in each of the filters: VisAO YS , NACO
J, NACO H, NICI H, NACO KS , and NICI KS . For each spectrum, we then found
the magnitude offset that minimized χ2 between these synthetic measurements and
the measurements of β Pic b (see Table 4.3). The best five fitting objects are shown
in Figure 4.14. Of note, the very best fitting spectra is a medium surface gravity
(β) L1 dwarf.
1
http://pono.ucsd.edu/~adam/browndwarfs/spexprism/
122
3.0
β Pic b
HR 8799 b
2M1207 b
2M0355
2.5
YS−JNACO
2.0
1.5
1.0
0.5
M
L0−L5
L5−L9
T0−T5
T5−T9
0.0
−1.0 −0.5
3
0.0
0.5 1.0
JNACO−HNACO
1.5
2.0
2.5
β Pic b
HR 8799 b
2M1207 b
2M0355
YS−JNACO
2
1
M
L0−L5
L5−L9
T0−T5
T5−T9
0
0
5
1
2
JNACO−KS,NACO
3
β Pic b
HR 8799 b
2M1207 b
2M0355
YS−KS,NACO
4
3
2
1
0
−2
M
L0−L5
L5−L9
T0−T5
T5−T9
−1
0
1
JNACO−HNACO
2
3
Figure 4.13 β Pic b color-color plots, comparing β Pic b to the field brown dwarfs, as
well as the planets HR 8799b and 2M1207b and the low-gravity dusty brown dwarf
2M0355. β Pic b has colors consistent with a field L dwarf, or perhaps an early T
dwarf. This is quite different from other directly imaged young giant planets.
Apparent Fλ [10−12 ergs/s/cm2/µm]
123
2MASSJ17111353+2326333
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
10
8
6
4
2
L1.0β
SDSSJ162255.27+115924.1
L6.0
SDSSJ085834.42+325627.7
T1.0
2MASSJ15575011−2952431
M9.0
2MASSJ00332386−1521309
L1.0
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
λ [µm]
Figure 4.14 The field brown dwarfs which best match the photometry of β Pic b.
124
χ2ν
10
L9.5 ± 5
1
L2 ± 1.5
M0
2
4
6
8
L0
2 4 6 8 T0
Spectral Type
2
4
6
8
Y0
Figure 4.15 β Pic b spectral type. The red points are individual field dwarfs, and
the black crosses with error bars show the median and standard deviation in each
half spectral type. We fit parabolas to the two apparent minima to find the best-fit
spectral type.
We collated the results of these fits by spectral type (to 0.5 types), shown in
Figure 4.15. The median χ2ν for each half spectral type is also shown, with error
bars determined by the standard deviation in each type. There are two minimums,
one for early L and one for late L/early T. We fit each of these with a parabola.
The results are L1.8±1.2 and L9.5±4.8. The L2 minimum is a better fit, so we
adopt L2±1.5 as the best fit spectral type. This is consistent with L2γ±2 adopted
by Bonnefoy et al. (2013).
To test the effect that each filter has on the spectral type fit, we repeated the fit
with one bandpass excluded. These results are shown in Figure 4.16. It is evident
125
χ2ν
10.0
1.0
w/out YS
w/out J
0.1
w/out KS
χ2ν
10.0
1.0
w/out H
0.1
M0 4 8 L0 4 8 T0 4
Spectral Type
8 M0 4
8 L0 4 8 T0 4
Spectral Type
8 Y0
Figure 4.16 β Pic b spectral type without various filters. This shows that our YS
measurement pushes the fit to earlier L types.
that our YS result is pushing the fit to earlier spectral types. Dropping either YS or
KS results in a dramatically lower χ2ν . Excluding either J or H does not significantly
change the results. So we conclude that the best-fit spectral type is primarily being
determined by YS and KS .
Finally, we use our best-fit spectral type to place β Pic b on YS , J, and H colormagnitude diagrams. We show absolute magnitude in these filters vs. both X − KS
color spectral type in Figure 4.17. As in the color-color plots, β Pic b is consistent
with an early L dwarf. We also show the same three planet/planet-like comparison
objects. We placed HR 8799b and 2M1207b on the spectral type diagram using
their best fit spectral temperatures from Madhusudhan et al. (2011) and Barman
126
et al. (2011), respectively, and the spectral type to temperature relationships given
by Stephens et al. (2009). These plots once again illustrate the wide diversity in the
directly imaged exoplanets. Despite similar ages these objects have very different
colors and luminosities
4.7 Conclusion and Future Work
We have presented the first ground-based detection of an exoplanet with a CCD.
With its groundbreaking VisAO camera, the MagAO system detected β Pictoris b at
at 0.986µm, with a contrast of 3.0 × 10−5 . This is certainly the shortest wavelength
direct image of an exoplanet from the ground, and given the latest results indicating
Fomalhaut b may not be a true planet, this could be the bluest image of an exoplanet
to date. This results represents a new frontier in exoplanet science as we push into
the visible.
We compared the YS JHKS photometry of β Pictoris b with field brown dwarfs.
In color-color and color-magnitude plots, β Pic b is consistent with being an early
type L dwarf. Using nearly five hundred objects with Y through K spectroscopy,
we found a best-fit spectral type of L2±1.5. We also compared these results to the
other directly imaged exoplanets with Y photometry HR 8799 b, 2M1207b. These
objects are remarkably different from β Pictoris b at these wavelengths.
We made full use of MagAO’s unique O/IR wavelength coverage, observing this
exoplanet from 0.98µm to 5µm. Our YS photometry is brighter than expected for a
typical L dwarf given prior measurements. There are a few more verifications that
we plan to conduct, but this result appears to be robust. Though we do not address
it here, there are other, soon-to-be published, measurements in the near-IR using
the NICI camera which are also bright compared to the others (Mike Liu, private
communication). There may be more to this story, such as variability. We leave a
comprehensive multi-spectral modeling effort to Morzinski et al. (2013, in prep).
For now, we have shown the power of blue-wavelength imaging of exoplanets.
127
12
L0−L5
L5−L9
T0−T5
T5−T9
Abs. YS
14
16
18
L5
1100K
L0
1300K
1600K
β Pic b
HR 8799 b
2M1207 b
2M0355
2250K
20
22
1
2
3 4
Ys−KS
5
T0
Sp. Type
T5
L0−L5
L5−L9
T0−T5
T5−T9
12
Abs. J
14
−1
0
1
2
J−KS
3
L5
T0
Sp. Type
1100K
L0
1300K
β Pic b
HR 8799 b
2M1207 b
2M0355
1600K
18
2250K
16
T5
10
L0−L5
L5−L9
T0−T5
T5−T9
Abs. H
12
14
−1
0
1
H−KS
2
L5
T0
Sp. Type
1100K
L0
1300K
β Pic b
HR 8799 b
2M1207 b
2M0355
1600K
18
2250K
16
T5
Figure 4.17 Color-magnitude diagrams. YS photometry, NACO photometry, and
temperature equivalent spectral type for HR 8799b and 2M1207b estimated as described in the text.
128
CHAPTER 5
DETECTABILITY OF EGPS IN THE HZ
In this chapter we begin to consider what comes next. The unique thermal-IR and
visible wavelength coverage of the high order Magellan and LBT adaptive optics
systems allows the first direct imaging search of the habitable zone (HZ) of very
nearby stars, where Kepler hints that planets are common.
Typical direct imaging searches can be characterized as searching for young, selfluminous, giant planets at wide separations. With the unique wavelength coverage
offered by MagAO and the LBTAO systems, we can search nearby old stars at close
separations, moving the hunt for EGPs into the HZ. Extrasolar gas-giant planets
(EGPs) are roughly the same radius regardless of mass, and in the HZ irradiation will
set the minimum planet temperature, so minimum HZ EGP thermal luminosity is
nearly independent of mass and age. Similar logic applies to reflected visible light. In
short, EGPs should be very detectable in the HZs of nearby stars. A search for such
planets directly addresses the goals of Astro2010/New Worlds (Blandford, et al.,
2010), and developing the ability to spectrophotometrically characterize HZ planets
is of paramount importance to the search for life—the primary goal of NASA’s
Exoplanet Exploration Program. The next few years should be very exciting.
5.1 The Habitable Zone
The HZ is generally defined as the region around a star where liquid water can exist
on a planet’s surface. Though this is a simple statement, determining the location of
this region is difficult as it depends on many factors such as the composition of the
atmosphere, the level of plate tectonics and volcanism, and the time history of the
star’s luminosity. In any case, it seems obvious that the most important quantity
defining whether water is liquid will be the temperature of the planet. As a simplified
129
starting point we can assume that this is set by the equilibrium temperature
1/4
1/4 r −1/2
L
1 − AB
(5.1)
278.5K
Teq =
f
L⊙
1AU
where AB is the bond albedo and f is the fraction of the surface area where the
heat is uniformly distributed. AB is defined as the amount of incoming radiation
reflected by the planet, over all wavelengths. L is the luminosity of the star in solar
units, and r is the distance of the planet from the star. Rearranging we have a
convenient scaling of distance for a given temperature and stellar luminosity
2 s !1/2
1/2 r(Teq )
1 − AB
278.5K
L∗
=
(5.2)
1AU
f
Teq
L⊙
and most simply
rTeq ∝
p
L∗ .
(5.3)
As a first guess at defining the HZ we can calculate the distance from a 1L⊙ star
at which water boils at one Earth atmosphere of pressure is (T = 373K)
rboil = 0.56 AU
for AB = 0 and f = 1. The distance from a 1L⊙ star at which water freezes
(T = 273K) is
rf reeze = 1.04 AU
It is of course more complicated than this. The seminal work on defining the location
of the HZ is Kasting et al. (1993), who modeled an Earth-like atmosphere orbiting a
Sun-like star. They argued that the inner edge of the HZ is set by water loss through
the process of photodissociation of H2 O and the subsequent escape of H2 to space.
In this model the outer edge was set by the formation of CO2 clouds in the planet
atmosphere, which have a cooling effect. A major consideration within the HZ is
the presence of CO2 and its impact on temperature through the greenhouse effect.
CO2 concentration is modulated by weather, volcanism, and by temperature itself.
Kasting et al. (1993) give a “conservative” HZ of 0.95-1.37 AU, quite different from
the blackbody boiling-freezing guess above.
130
A further consideration is that stellar luminosity is not constant with time. Taking this into account, and considering conditions on Venus in the distant past (when
it may have been wet), and Mars in the distant past (when it may also have had
standing water), Kasting et al. (1993) give the “early-Venus” and “early-Mars” HZ
estimate of 0.75-1.77 AU.
The Kasting et al. (1993) HZ model has been updated and adapted by many
authors, but was most recently updated in Kopparapu et al. (2013), using essentially
the same model but with a new H2 O and CO2 line list. The new conservative HZ
estimate is 0.99 - 1.70 AU, placing Earth at the inner edge. Another recent analysis
by Zsom et al. (2013) argues that for a planet with low relative humidity, what they
call a desert world, the inner edge of the HZ could be as close as 0.5 AU. Zsom
et al. (2013) also provocatively argue (as have others before) that the outer edge of
the HZ is effectively infinite, as other processes such as tidal heating can generate
enough heat to keep water liquid even without a main sequence star.
For this analysis we will assume the “wide HZ” of (Traub, 2012), with separation
r = 0.72-2.0AU for stellar luminosity L∗ = 1L⊙ . This very optimistic HZ definition,
which is actually due to Kasting, was designed to ensure that NASA’s Kepler mission
does not miss any potentially habitable worlds (Traub, 2012). We show this “wide
HZ” for a sample of 12 nearby stars in Figure 5.1. These stars were chosen because
part or all of their HZs project to & 300 mas, making them accessible to MagAO
and LBTAO.
5.2 Are there planets in the HZ?
Having agreed on a definition of the HZ, we might then ask the question “but are
there planets in the HZs of other stars?”. One way to answer this question is to
calculate the fraction of stars in the sky with a planet in the HZ. If this question
is narrowed to consider only Earth-like planets, this quantity is frequently called
eta-Earth, η⊕ . Traub (2012) extrapolated from the first 136 days of Kepler data
131
Figure 5.1 Projected HZs of select nearby stars. For these stars, the projected
separation of the HZ makes it accessible with the high order LBT & MagAO systems
in the thermal-IR and the visible. MagAO/Clio2/VisAO and LBTI can credibly
search nearby HZs for EGPs with mass as low as ∼ 0.1MJup .
132
that the frequency of earth-like planets around sun-like stars is
η⊕ = 0.34.
Though this should be treated with caution since it is such a wide extrapolation,
it stands as one of our best estimates of η⊕ to date. More recent updates to the
Kepler candidate catalog have been generally consistent with this analysis.
Now if we extend Traub (2012)’s analysis to all planet sizes, we find that
ηplanet = 1.2.
In other words most stars have at least 1 planet in the HZ1 . For EGPs, with RP >
8R⊕ , ηEGP = 0.11, so ∼ 1 in 10 stars will have an EGP in the HZ. This result is
broadly consistent with radial velocity (RV) studies (Wittenmyer et al., 2011a,b;
Mayor et al., 2011). Star-by-star RV completeness was given by Wittenmyer et al.
(2011b), e.g., for α Cen A they are 50% complete to 0.12MJup and 90% complete
√
to 0.26MJup – nearly the mass of Saturn – at 1.5 L AU. Similar survey-wide limits
were given by Mayor et al. (2011). Planets should be common in the HZ of nearby
stars, yet RV has not ruled out planets of nearly the mass of Saturn at 1.5AU around
nearby stars.
The recently discovered ∼1M⊕ planet α Cen Bb (Dumusque et al., 2012), though
not in the HZ, has exciting implications—it begins to address remaining questions
about the formation and stability of planets around binary stars (cf. Eggl et al.
(2013) and references), and it is likely that there are multiple planets in the system
(Lissauer et al., 2011). α Cen Bb makes a search of the HZ of α Cen A&B and other
nearby stars highly compelling.
5.3 The Radius and Temperature of a Giant Planet
Old EGPs should be easily detectable in the HZ in the thermal-IR (3–5µm). The key
result leading to this assertion is that EGPs with masses ranging from ∼0.1MJup to
1
For a completely different way to arrive at this estimate, Bovaird and Lineweaver (2013) claim
that the Generalized Titius-Bode rule predicts that the average number of planets in the HZ should
be 1 to 2
133
10MJup are the same size to within 20%. At higher planetary masses, M & 3MJup ,
electron degeneracy pressure supports the internal structure of the planet. Below
3MJup , coulomb pressure supports the planet’s atmosphere. The combination of
these two effects means that the radius of the planet depends only weakly on the
1/10
planet’s mass. A useful scaling for M . 3MJup is RP ∝ MP
, were RP is planet
radius and MP is mass (Fortney et al., 2011).
The total luminosity of an EGP will closely vary as
LP ∝ RP2 TP4 .
Where TP is the planet temperature. Extrasolar planet direct-imaging search we
have typically looked for young planets, still cooling. Their effective temperature,
Tef f , is then set by their age and mass as they radiate the gravitational potential
energy from formation. In addition to age, then, mass also plays an important role
in setting temperature. Combined with the constraints imposed by the limitations
of current generation high-contrast imagers, the planets imaged to-date have been
young, massive (∼ 10MJup ), and at wide physical separations.
Closer to the star, however, the situation is somewhat different. Here the radiation from the star also plays a role in setting the planet temperature. The minimum
temperature is set by Equation (5.1) regardless of mass and age, so once the planet
cools to the point that Tef f ≤ Teq , its luminosity will be set by Teq and RP . Now
since RP only weakly depends on mass, in this regime LP itself only weakly depends on mass. In the HZ the minimum EGP thermal luminosity is nearly
independent of mass and age.
Armed with this result, and an imaging system capable of high enough contrast
in the HZ of a star, we should be able to detect EGPs of very low masses. It is then
interesting to consider how low the mass-radius relationship for giant planets extends. This was recently addressed by Batygin and Stevenson (2013), who analyzed
the possible composition of Kepler -30d, an 8.8 ± 0.5R⊕ planet orbiting at a distance
such that Teq = 364K. They conclude that with a sufficiently large core (3 − 5M⊕ ),
EGPs with H/He dominated atmospheres are stable under moderate irradiation
134
(as in the HZ) down to even a few Earth masses. Their models indicate EGPs will
have RP > 8R⊕ down to MP ∼ 10M⊕ = 0.03MJup . An important implication of
this result is that planets with Radii in the RP ∼ 8R⊕ regime could have very low
masses, and such planets — based on current Kepler results — might be common.
5.4 Thermal Infrared Brightness of EGPs
To determine how bright an EGP is in the HZ, we can use the non-irradiated COND
models (few, if any, other model grids extend to low enough temperatures). Our
goal is to calculate the flux in a certain bandpass as a function of distance from
the star, allowing temperature to vary with separation until Teq < Tef f , Now the
typically cited “cooling curves” or isochrones of Baraffe et al. (2003) can’t be used
as is. At young ages, the planets are still contracting so their radii are inflated
compared to a planet of the same mass at an older age. This means that we can’t
simply interpolate magnitudes across Tef f on the grid of isochrones at a given mass,
as the brightness will be too high due to the larger radius.
We downloaded the COND spectra, corresponding to the AMES-2000 line list2 .
These are parameterized by Tef f and surface gravity log(g). The first step is then
to use the isochrones of Baraffe et al. (2003) to find the expected radius of a planet
of a given mass and age. For planets with mass lower than the lowest mass given
1/10
in the isochrone, we extrapolate RP ∝ MP
. We can then use radius to find the
surface gravity of the planet through
2
MP
1RJup
g = 2478.50
[cgs].
1MJup
RP
Next, at a given separation from the star we calculate Teq , assuming AB = 0.34
(typical of planets in our solar system) and f = 1. We interpolate on the grid of
spectra with log(g) and setting Tef f = Teq , and apply the dilution factor correction
to determine the flux measured at 10 pc. We then convolve the resulting spectrum
with the M ′ bandpass of Clio (MKO M ′ ). We also convolve the Vega spectrum
2
http://phoenix.ens-lyon.fr/Grids/AMES-Cond/
135
of Bohlin (2007) with M ′ , and so determine the absolute magnitude in M ′ for the
planet.
The final step is to apply the distance modulus for the star being considered.
We show the results of these calculations for α Cen A in Figure 5.2 and for Sirius in
Figure 5.3. Though we have very recently observed these stars at M ′ with MagAO,
we have not yet derived a contrast curve. Instead, we use a contrast curve measured
at the LBT with LMIRCAM3 , and scale it for the smaller diameter Magellan Clay
primary. The resulting 1, 5, and 10 hour detection limits are over-plotted in the
figures.
With MagAO, and with LBTAO, we should be sensitive to HZ EGPs with
M &0.1MJup . It is worth noting that JHK imaging (e.g. GPI, Project 1640) cannot
√
detect such planets. The major caveat is that we assumed photon-noise N scaling
√
for both D and exposure time. Due to speckle-noise, achieving N scaling over
10hrs is challenging. It is one of the main goals of my future work to test the limits
√
of N scaling, and to develop active techniques to suppress speckles in this regime.
An additional question that should be addressed regards the choice of M ′ vs
L′ . An important consideration is the impact that Methane absorption has on L′
brightness of EGPs. Exoplanets detected to date have generally been brighter than
expected in bandpasses where methane should make them faint, but these results
are for much warmer atmospheres than we consider here. The COND models predict
(roughly) that these low-mass EGPs will be approximately 2 magnitudes fainter at
L′ than at M ′ . At the contrasts needed, around such bright stars, we do not expect
to be background limited at these tight separations. That means that we should
seek to maximize Strehl ratio to minimize speckle noise, and should maximize the
number of photons collected to maximize signal-to-noise ratio. Taken together, these
arguments favor M ′ despite the higher thermal background. For an example of AO
imaging with high thermal backgrounds, see Appendix C.
3
provided by Vanessa Bailey
136
Separation (AU)
2
1
10
3
17.0
αCen A
15.8
8
6
∆ M’
Mass (MJ)
14.7
13.5
4
12.3
2
11.2
0
10.0
0.5
1.0
1.5
2.0
Separation (")
2.5
3.0
Figure 5.2 The contrast of EGPs around α Cen A using the COND spectra and our
assumptions about Teq . The calculations were cut off at an arbitrary 0.1MJup . The
contrast curves are for 1, 5, and 10 hrs with MagAO/Clio. The required ∆M ′ ≈ 14
required to detect very low mass planets is very achievable.
137
Separation (AU)
4
2
6
10
17.0
Sirius
15.8
8
6
∆ M’
Mass (MJ)
14.7
13.5
4
12.3
2
11.2
0
10.0
0.5
1.0
1.5
2.0
Separation (")
2.5
3.0
Figure 5.3 The contrast of EGPs around Sirius using the COND spectra and our
assumptions about Teq . The calculations were cut off at an arbitrary 0.1MJup . The
5σ contrast curves are for 1, 5, and 10 hrs with MagAO/Clio.
138
5.5 Habitable Zone EGPs in the Visible
Next we consider the brightness of EGPs in the visible (0.5–1.0µm), where reflected
starlight will be the dominant source of photons. The reflected flux from a planet,
Fp , relative to the flux from its star, F∗ , is
Fp
= Ag
F∗
Rp
r
2
Φ(α)
where Ag is the geometric albedo, Rp is the planet radius, r is the distance of the
planet from the star, Φ is the phase function, and α is the phase angle. Putting in
the appropriate constants gives
Fp
= 1.818 × 10−9 Ag
F∗
1 AU
Rp
×
1R⊕
rp
2
Φ(α)
(5.4)
Cahoy et al. (2010) modeled the atmospheres of Jupiter and Neptune-like planets,
and present the resulting geometric albedos for such planets at a range of separations
from a star. EGPs should have high geometric albedo near r ≈ 2AU due to water
clouds, but these will evaporate closer to the star. The competing effects in Equation
(5.4) of 1/r2 and Ag increasing with r cause a peak in EGP contrast to occur between
1 and 2 AU. EGP reflectivity peaks in the HZ, with only weak mass dependence.
That is, the same low-mass EGPs we discussed above should be at their brightest
in the HZ.
Assuming that the main driver of changes in Ag as separation changes is the
change in Teq , we can adapt the models of Cahoy et al. (2010) to stars of various
luminosities. We show the contrast of EGPs orbiting α Cen A&B and τ Cet in
Fig. 5.4, based on Ag from Cahoy et al. (2010), and predicted contrast for ǫ Eri b
using its astrometric orbit (Benedict et al., 2006) (periastron in early 2014). These
calculations fully include the effects of orbital phase modeled by Cahoy et al. (2010),
rather than the simplified Lambert phase function.
√
In Figure 5.4 we plot the halo-photon-noise ( N ) contrast limit for Ma-
gAO/VisAO at i’ derived from our test-tower PSF measurements. We also show
√
the N limit derived from the PCA reduction of the β Pic observations described
139
earlier. In both of these cases we have made the following assumptions: 10 hours
of open-shutter time on a -0.5 mag star, with a broadband r′ i′ z ′ filter, in the 950
beamsplitter (meaning all blue photons go to the CCD-47). The scaling of the β
Pic contrast curve assumed a factor of 10 increase in system throughput compared
to YS . In all cases these assumptions were applied to the measurements assuming
√
N scaling.
Achieving such high contrasts will be very difficult, even at wide (> 20λ/D)
separations. These observations will not be photon-noise limited! Rather, we ex√
pect to reach a speckle noise limit before reaching the N limit. However, this
regime (30-50% visible Strehl ratio (SR) on a 6.5m telescope) is completely new and
unexplored: the nearest sun-like stars have not been imaged at close separations in
visible light. Testing the limits of AO corrected high-contrast imaging in the visible
is a major focus of my future research.
5.6 Blazing The Trail
In the next few years will use MagAO and LBTI to perform the first credible search
for EGPs in the HZ of nearby stars. Our thermal-IR observations may lead to the
first images of an exoplanet in the HZ. Even with no detections, we will provide
constraints on HZ planets in parameter space not yet reached by RV. Our VisAO
observations will be an important step towards detecting exoplanets in reflected
light. This search has already begun: during MagAO commissioning run 2 we
observed both Sirius and α Cen A in i′ and M ′ .
The observations discussed here are limited to a handful of very nearby, bright
stars, and will be sensitive only to EGPs with RP ∼ 8R⊕ . However, on the next
generation of giant telescopes D2 will improve our sensitivity from RP ≈ 8R⊕ to
RP ≤ 2R⊕ , allowing detection and characterization of rocky, potentially habitable,
planets. While probing the HZ of these nearby stars we will develop and test ExAO
control strategies for both the thermal-IR and visible wavelength regimes, using
MagAO and LBTAO. This work is an important precursor to future ground-based
140
Figure 5.4 Visible reflected light contrasts for hypothetical EGPs on circular orbits
around α Cen A&B and τ Cet, and ǫ Eri b contrast based on the astrometric orbit
(Benedict et al., 2006). Predictions include effects of separation and orbital phase
1/10
(Cahoy et al., 2010). Radius was scaled by RP ∝ MP , and mass was set by RV
50% completeness.
141
searches for rocky habitable planets such as that proposed by Guyon et al. (2012).
142
CHAPTER 6
DIRECT IMAGING IN THE HABITABLE ZONE AND THE PROBLEM OF
ORBITAL MOTION
6.1 Introduction
In this chapter we turn to the far future, and consider the problem of detecting
planets orbiting within the HZ using the next generation of giant telescopes. This
chapter has previously been published in the Astrophysical Journal as Males et al.
(2013).
Orbital motion (Kepler, 1609) has been used in one fashion or another to detect
planets around stars other than our Sun in large numbers. The radial velocity (RV)
technique monitors the Doppler shift of a stellar spectrum as the star itself orbits
the planet-star center of mass, thus allowing us to infer the presence of a planet.
Similarly, the astrometry technique monitors the motion of the star on the sky and
likewise infers the presence of a planet. The transit technique monitors the reduction
in brightness of the star as the orbiting planet temporarily crosses the line of sight
between the telescope and the star.
Unlike these indirect techniques, direct imaging detects light from the planet
itself and spatially resolves it from the light of the star (Traub and Oppenheimer,
2011). The extreme difference in brightness between star and planet at small projected separations has generally limited direct imaging efforts to wide separations
where orbital motion is ignorable. The next generation of large telescopes will move
us into a new regime of direct imaging, moving closer to the star. We will even
be able to begin probing the liquid water habitable zone (HZ). Here we point out
that at these tight separations orbital motion will no longer be negligible in direct
imaging. As we will show the motion of planets in the HZ (and closer), during the
required integration times, will be large enough to limit our sensitivity unless we
143
take action to correct it.
In Section 6.2 we present our motivation for this study and briefly review some of
the related prior work. In Section 6.3 we develop the basic tools needed to analyze
this problem, including the expected speed of orbital motion in the focal plane and
the effect it has on signal-to-noise ratio (SN R). In Section 6.4 we analyze the impact
orbital motion will have on a search of α Cen A by the Giant Magellan Telescope
(GMT) working at 10µm, and propose a method to mitigate this impact by deorbiting a sequence of observations. Then in Section 6.5 we treat the more favorable
case of a cued search, where we have prior information from an RV detection. To do
so we analyze the case of the potentially habitable planet Gl 581d being observed
by the planned European Extremely Large Telescope (E-ELT). Finally, in Section
6.6, we present our conclusions and prospects for future work.
6.2 Motivation and Related Work
Moving the hunt for exoplanets into the HZ of nearby stars marks a departure from
prior efforts. Here we briefly discuss the definition of the HZ, review direct imaging
results to date, discuss the differences between them and and future efforts, and
finally review some closely related prior work.
6.2.1 Nearby Habitable Zones
The HZ is generally agreed to be the region around a star where a planet can
have liquid water on its surface. This is far from simply related to the blackbody
equilibrium temperature, as it depends on atmospheric composition and the action
of the greenhouse effect (Kasting et al., 1993; Kopparapu et al., 2013), among other
factors. For our purposes it is enough to assume that the HZ is generally located at
about one AU from a star, scaled by the star’s luminosity
p
aHZ ≈ L ∗ /L⊙ AU.
(6.1)
Traub (2012) provided three widths for the HZ based on various considerations,
and then used the first 136 days of data from the Kepler mission to estimate that
144
the fraction of sun-like stars (spectral types FGK) with an earth-like planet in the
HZ is η⊕ ≈ 0.34. More generally, this analysis indicates that ηplanet ≈ 1.2, implying
that every sun-like star is likely to have a planet in its HZ, and some will have more
than one. While this exciting result is based on a very large extrapolation from the
earliest Kepler results, it is currently one of our best estimates of planet frequency
in the HZ.
This topic was recently brought to the fore with the announcement of α Cen Bb
by Dumusque et al. (2012). Discovered using the RV technique, α Cen Bb is an
m sin i = 1.13M⊕ planet orbiting a K1 star at 0.04 AU. While certainly not in the
HZ, this discovery has exciting implications for the presence of planets in the HZ of
the nearest two sun-like stars.
The above arguments hint that planets will be common in the HZ of sun-like
stars. We are about to enter a new era of exoplanet direct imaging. With the next
generation of giant telescopes and high-performance spaced-based coronagraphs we
will be searching for planets in this scientifically important region around nearby
stars.
6.2.2 A Different Regime
The typical search for exoplanets with direct imaging has used 2.4m (Hubble Space
Telescope, HST) to 10m (Keck) telescopes. These surveys have mostly concentrated
on young giant planets, which are expected to be self-luminous as they dissipate heat
from their formation. This allows them to be detected at wider separations from
their host stars, where reflected starlight would be too faint. This has also caused
planet searches to typically work at H band (∼ 1.6µm), with exposure times of ∼ 1
hr. Examples conforming to these survey archetypes include Lowrance et al. (2005)
using HST/NICMOS; the Gemini Deep Planet Search (Lafrenière et al., 2007a);
the Simultaneous Differential Imaging survey using the Very Large Telescope and
MMT (Biller et al., 2007); the Lyot Project at the Advanced Electro-Optical System
telescope (Leconte et al., 2010); the International Deep Planet Survey (Vigan et al.,
2012); and the Near Infrared Coronagraphic Imager at Gemini South (Liu et al.,
145
2010).
These searches have had some success. Examples include the 4 planets orbiting
the A5V star HR 8799 (Marois et al., 2008b, 2010), with projected separations of 68,
38, 24, and ∼ 15 AU. These correspond to orbital periods of ∼ 460, ∼ 190, ∼ 100,
and ∼ 50 years, respectively. The A5V star β Pic also has a planet (Lagrange et al.,
2010) orbiting at ∼ 8.5 AU with a period of ∼ 20 years (Chauvin et al., 2012b).
Another A star, Fomalhaut, has a candidate planet on an 872 year (115 AU) orbit
(Kalas et al., 2008). At these wide separations it takes months, or even years, to
notice orbital motion.
In the much closer HZ, however, orbital periods will be on the order of one
year. We show in some detail that this is fast enough to yield projected motions of
significant fractions of the point spread function (PSF) full width at half maximum
(FWHM) over the course of an integration. The resulting smeared out image of the
planet will have a lower SN R, making our observations less sensitive.
6.2.3 Long Integration Times
In addition to HZ planets having higher orbital speeds than the current generation
of imaged exoplanets, integration times required to detect them will be much longer.
Direct imaging surveys to date have mostly worked in the infrared while attempting
to detect young planets still cooling after formation. The coming campaigns to
image planets in the HZ of nearby stars will focus on older planets, which will be
less luminous in the near infrared. In the HZ, starlight reflected from the planet will
be more important. The result is integration times required to detect such planets
will be tens of hours, rather than the ∼ 1 hour characteristic of current campaigns.
Consider the Exoplanet Imaging Camera and Spectrograph (EPICS), an instru-
ment proposed for the E-ELT. Kasper et al. (2010) predicted that EPICS will be
able to image the RV detected planet Gl 581d, which has a semi-major axis of 0.22
AU with a period of ∼ 67 days (Forveille et al., 2011; Vogt et al., 2012). This orbit
places it on the outer edge of the HZ of its M2.5V star (von Braun et al., 2011).
EPICS will be able to detect Gl 581d, at a planet/star contrast of 2.5 × 10−8 , in 20
146
hrs with SN R = 5 (Kasper et al., 2010). Since this is a ground based instrument,
a 20 hour integration will be broken up over at least 2 nights. Plausible observing
scenarios could extend this to several nights, taking into account such things as the
need for sky rotation. As we will show, the planet will move several FWHM on the
EPICS detector during a multi-day observation.
More generally, Cavarroc et al. (2006) showed that when realistic non-common
path wavefront errors are taken into account, the integration times required to
achieve the 10−9 to 10−10 contrast necessary to detect an earth-like planet around
a sun-like star approach 100 hours on the ground, even on a 100m telescope with
extreme-AO and a perfect coronagraph. One of several concerns about the feasibility of a 100 hour observation from the ground is that such a long observation will
be broken up over many nights.
With net exposure times of 20 to 100 hrs, and total elapsed times for ground
based observations of several to tens of days, HZ planets will move significantly over
the course of a detection attempt. The focus of this investigation is the impact of
the orbital motion of a potentially detectable planet on sensitivity.
6.2.4 Related Work
Though it has not yet been a significant issue in direct imaging of exoplanets, orbital
motion has been considered in several closely related contexts. Here we briefly
review a select portion of the literature. A very similar problem has been addressed
in the context of searching for objects in our solar system, such as Kuiper Belt
objects (KBOs), which can have proper motions on the order of 1” to 6” per hour
(Chiang and Brown, 1999). Blinking images to look for moving objects by eye is
a well established technique. A more computationally intensive form of blinking
images proceeds by shifting-and-adding a series of short exposures along trial paths,
usually assumed to be linear. This “digital tracking” makes it possible to detect
KBOs too faint to appear in a single exposure. This has been done both from the
ground (Chiang and Brown, 1999; Yamamoto et al., 2008) and from space with HST
(Bernstein et al., 2004). More recently Parker and Kavelaars (2010) have taken into
147
account nonlinear motion and optimized selection of the search space, especially
important given the large data sets that facilities such as the Large Synoptic Survey
Telescope will produce.
Orbital motion is an important consideration when planning coronagraphic surveys of the HZs of nearby stars. Brown (2005) treats the problem of completeness
extensively. Large parts of the HZ will be within the inner working angle of a Terrestrial Planet Finder-Coronagraph (TPF-C) type mission, and so undetectable during
a single observation. Also discussed in Brown (2005) is photometric completeness that is how long the TPF-C must integrate on a given star to detect an earth-like
planet in the HZ. Other work on this topic includes Brown and Soummer (2010) and
Brown (2004). These analyses consider orbital motion only between observations,
not during a single observation as we do here. In general, the scenarios considered
for these studies involved space-based high-performance coronagraphs on medium
to large telescopes. In such cases exposure times were short enough and continuous
so that orbital motion should be negligible during a single observation.
The work most similar to our analysis here is the detection of Sirius B at 10µm by
Skemer and Close (2011), in fact, it was part of our motivation for the present study.
Skemer and Close (2011) used the well known orbit of the white dwarf companion
to Sirius to de-orbit 4 years worth of images. Before accounting for orbital motion,
Sirius B appeared as only a low SN R streak, but after shifting based on its orbit
it appears as a higher SN R point source from which photometry can be extracted.
Similar to this method, we will analyze the prospects for de-orbiting sequences of
images, only we consider the case with no prior information at all, and with orbital
elements with significant uncertainties.
6.3 Quantifying The Problem
In this section we will quantify the effects of orbital motion on an attempt to detect
an exoplanet. Our first step will be to determine how fast planets move when
projected on the focal plane of a telescope. Then we will illustrate the impact this
148
motion will have on the SN R and the statistical sensitivity of an observation.
6.3.1 Basic Equations
We begin by considering a focal plane detector working at a wavelength λ in µm.
The FWHM of the PSF for a telescope of diameter D in m, neglecting the central
obscuration, is
λ
arcsec.
(6.2)
D
If we are observing a planet in a face-on circular (FOC) orbit with a semi-major
FWHM = 0.2063
axis of a in AU at distance d in pc, its angular separation will be a/d arcsec. At the
focal plane the projected separation will then be
ρ = 4.847
aD
in FWHM.
λd
(6.3)
We note that it will occasionally be convenient to specify ρ in AU instead of FWHM.
When it is not clear from the context we will use the notation ρau to denote this.
p
The orbital period is P = 365.25 a3 /M∗ days around a star of mass M∗ in M⊙ .
In one period, the planet will move a distance equal to the circumference of its orbit,
2πρ, so the speed of the motion in a FOC orbit will be1
s
1AU
1µm
1pc
D
M∗
in FWHM day−1 .
vF OC = 0.0834
1m
λ
d
1M⊙
a
(6.4)
In the general case, the equations of motion in the focal plane are
r
1 h
ẋ = vF OC
e sin(f ) (cos(Ω) cos(ω + f ) − sin(Ω) sin(ω + f ) cos(i))
1 − e2
i
−(1 + e cos(f )) (cos(Ω) sin(ω + f ) + sin(Ω) cos(ω + f ) cos(i))
r
1 h
ẏ = vF OC
e sin (f ) (sin (Ω) cos(ω + f ) + cos(Ω) sin(ω + f ) cos(i))
(6.5)
1 − e2
i
−(1 + e cos(f )) (sin(Ω) sin(ω + f ) − cos(Ω) cos(ω + f ) cos(i))
p
ẋ2 + ẏ 2
vom =
1
This result is equivalent to defining the gravitational constant in the focal plane as G =
q
∗
(0.0834D/(λd))2 and using the equation for speed in a circular orbit vcirc = GM
a .
149
where Ω is the longitude of the ascending node, ω is the argument of pericenter, i is
the inclination, and the true anomaly f depends on a, e, and the time of pericenter
passage τ through Kepler’s equation (Murray and Correia, 2010).
In Figure 6.1 we show the variation in projected orbital speed for both circular
orbits at several inclinations, and face-on eccentric orbits (i = 0), for a planet
orbiting a 1M⊙ star at 1 AU. In the plots we normalized speed to 1, and provide
vF OC for several interesting cases. These various scenarios produce projected orbital
speeds of appreciable fractions of a FWHM per day. We will later show that,
especially for ground based imaging, this causes a significant degradation in our
sensitivity.
Our main focus here is on planets in the HZ. Our simple definition of the HZ
√
results in aHZ ∝ L∗ . Now, on the main sequence mass and luminosity approximately follow scaling laws of the form L∗ ∝ M∗b , where b > 2 except for very massive
stars. So according to Equation (6.4) we expect vF OC in the HZ to increase as M∗
decreases, i.e. M stars will have faster HZ planets than G stars. For example, a
planet in the HZ of α Cen B (M∗ = 0.9M⊙ , L∗ = 0.5L⊙ ) will be moving roughly
20% faster than a planet in the HZ of α Cen A (M∗ = 1.1M⊙ , L∗ = 1.5L⊙ ) (stellar
parameters from Bruntt et al. (2010)).
To provide a more concrete example we return to the 20 hour observation of Gl
581d by the E-ELT/EPICS proposed by Kasper et al. (2010). Using a wavelength
of 0.75µm with Equation (6.4) we find vF OC = 0.82 FWHM per day, or a total of
0.68 FWHM for a continuous 20 hour observation. Since this is a ground based
observation the actual amount of motion to consider is ∼ 1.15 FWHM over the
∼ 1.4 days minimum it would take to integrate for 20 hours. Were this a face-on
orbit, an eccentricity of 0.25 (Forveille et al., 2011) would increase the maximum
orbital speed to as much as 1.05 FWHM per day, or 1.47 FWHM minimum for a 20
hour ground based observation.
150
(a)
Normalized Projected Speed (vFOC)
1.0
i=0 (face−on)
i=30
0.8
0.6
Scaling Factors for 1 MO, 1 AU:
D (m) λ (µm) d (pc) vFOC(FWHM/day)
6.5
VisAO:
0.75
1.34
0.54
8.1
GPI:
1.6
1.34
0.32
SPHERE: 8.2
0.6
1.34
0.85
24.5
GMT:
10.0
1.34
0.15
24.5
1.6
10
0.13
24.5
0.5
10
0.41
E−ELT: 39.0
0.75
10
0.43
i=60
0.4
0.2
0.0
0
i=90 (edge−on)
50
e=0 for each curve
100
True Anomaly (degrees)
150
2.5
(b)
Normalized Projected Speed (vFOC)
e=0.7
e=0.6
2.0
e=0.4
1.5
e=0.1
1.0
e=0
0.5
i=0 (face−on) for each curve
0.0
0
50
100
True Anomaly (degrees)
150
Figure 6.1 Magnitude of projected orbital speed, normalized to 1 FWHM day−1 ,
for 1 AU orbits around a 1M⊙ star. In (a) we show the orbital speeds for circular
orbits at various inclinations, and in (b) we show the speeds for face-on orbits at
various eccentricities. We give scaling factors in (a) for MagAO/VisAO (Close et al.,
2012b), GPI (Macintosh et al., 2012), SPHERE/ZIMPOL (Roelfsema et al., 2010),
GMT (Johns et al., 2012), and E-ELT/EPICS (Kasper et al., 2010). These scalings
can be applied to the y-axis of either plot for various scenarios. These cases can
also be scaled for different semi-major
axes, telescopes, wavelengths, star masses
q
D
M∗
and distances, by vF OC ∝ λd
. See the text for the general equations of motion
a
for arbitrarily oriented eccentric orbits.
151
6.3.2 Impact on Signal-to-Noise Ratio
So what does the orbital motion calculated above do to our observations? To find
out we consider a simple model of aperture photometry. Let us assume that we are
conducting aperture photometry with a fixed radius rap , that the PSF is Gaussian,
and that we are limited by Poisson noise from a photon flux N per unit area.
With these assumptions, the optimum rap is 0.7 FWHM, but taking into account
centroiding uncertainty rap ≈ 1 FWHM is typical. We will approximate orbital
motion at speed vom by substituting x → x − vom t − x0 . Orbits are of course
not linear, but this will be approximately valid over short periods of time. The
parameter x0 allows us to optimize the placement of the aperture to obtain the
maximum signal, i.e. centering the aperture in the planet’s smeared out flux. Note
that with the exception of this centering parameter, this model appears quite naive
in that we are not adapting the aperture radius and are pretending that we won’t
notice a smeared out streak in our images.
Now the SN R in the fixed-size aperture after time ∆t will be
Z rap Z 2π Z ∆t
2
2
2
I0 e(−4 ln 2((r cos θ−vom t−x0 ) +r sin θ)) dtdθrdr.
0
0
p
SN Rf ix = 0
2 ∆t
N πrap
int
(6.6)
where I0 is the peak value of the PSF. In the case of no orbital motion vom = 0 and
aperture rap = 1 FWHM, so we have
√
0.6I0 ∆t
√
.
(6.7)
SN Ro =
N
As a simple alternative to a fixed size aperture, we also consider allowing our photometric aperture to expand along with the motion of the planet. This aperture
will collect the same signal as in SN Ro , but the noise increases with the area as
2rap vom ∆t, so we have
SN Rexp = p
√
0.6I0 ∆t
.
(6.8)
N (1 + (2/π)vom ∆t)
√
A convenient scaling is to multiply top and bottom by vom and work in normalized
√
SN R units of Io / N vom . This puts time in terms of FWHM of motion, ǫ = vom ∆t,
and allows comparisons without specifying vom .
152
1.4
No Orbital Motion
Orbital Motion, Fixed Ap.
Orbital Motion, Expanding Ap.
1/2
∝ t
SNR (Io / (Nvom)1/2)
1.2
1.0
0.8
0.6
∝ t −1/2
0.4
0.2
0.0
0
1
2
3
Time (FWHM of motion)
4
5
4
5
1.0
0.9
SNR / SNRo
0.8
0.7
0.6
0.5
0.4
0.3
0
Orbital Motion, Fixed Ap.
Orbital Motion, Expanding Ap.
1
2
3
Orbital Motion (FWHM)
Figure 6.2 Top panel: SN R of a Gaussian PSF with and without orbital motion,
in normalized
√ units with time given as FWHM of motion. With no orbital motion
SN Ro ∝ t. Equation (6.6) was used to calculate the SN R with orbital motion.
After ∼ 2 FWHM of movement, a maximum is reached and the observation can only
be degraded by integrating further. Note
√ that the fixed-aperture orbital motion case
eventually goes down as SN R ∝ 1/ t. For comparison we also show the results
with an aperture expanding with the moving planet, which eventually reaches a
limit of 0.75. In the bottom panel we show the fractional reduction in SN R due to
orbital motion for the fixed radius photometric aperture.
153
In Figure 6.2 we plot the normalized SN R vs. time (measured in terms of
FWHM of motion) with and without orbital motion and for both the fixed and
expanding aperture cases. For the fixed aperture, after ∼ 2 FWHM of orbital
motion a maximum of 0.69 is reached, and from there noise is added faster than
signal. This means that further integration only degrades the observation.
The expanding aperture SN Rexp exceeds the maximum of SN Rf ix after about
8 FWHM of motion, and
√
x
r
π
≈ 0.75.
2
(6.9)
1 + (2/π)x
So if we integrate 4 times longer, adjusting the aperture size would allow us to
lim 0.6 p
x→∞
= 0.6
gather a little more SN R, but only to a point. Given this large increase in telescope
time for a relatively small improvement in SN R (only ∼ 9% even if we integrate
forever), and its better performance for smaller amounts of motion, the fixed-radius
aperture will be our baseline for further analysis – keeping in mind that in some
cases it may not be the true optimum.
The peak in SN Rf ix (equation 6.6) sets the maximum nominal integration time
before orbital motion will prevent us from achieving the science goal. That is
∆tmax = (SN Rmax /0.6)2 . If the observation of a stationary planet would require
an integration time longer than ∆tmax , then we can’t achieve the desired SN R on
an orbiting planet. This also sets the maximum orbital motion ǫmax = vom ∆tmax .
From Figure 6.2 we find that ǫmax = 1.3 FWHM. If more than 1.3 FWHM of motion
occurs during an observation, we will not achieve the required SN R.
We also show the fractional reduction in SN R in Figure 6.2. Almost no degradation occurs until after ∼ 0.2 FWHM of motion has occurred. SN R is reduced by
∼ 1% after 0.5 FWHM of motion, ∼ 5% after 1.0 FWHM, and by ∼ 19% after 2.0
FWHM of motion. We must now decide how much SN R loss we can accept in our
observation.
The above analysis assumes a continuous integration. On a ground-based telescope one must consider that the maximum continuous integration time is . 12
hours, and in practice will likely be much shorter when performing high contrast
154
1.0
SNR (Io/N1/2)
0.8
vom
vom
vom
vom
vom
vom
=
=
=
=
=
=
0.0
1.0, continuous
1.0, ∆t = 12 hrs
1.0, ∆t = 4 hrs
0.5, ∆t = 4 hrs
0.15, ∆t = 4 hrs
0.6
0.4
0.2
0.0
0
20
40
60
Net Integration Time ∆tint (hrs)
Figure 6.3 Here we show the impact of orbital motion when combined with finite
nightly integration times. The SN R of a Gaussian PSF with and without orbital
motion is plotted in arbitrary units vs ∆tint . The orbital speed vom is given in
FWHM day−1 .
155
AO corrected imaging. For instance, an exposure of 20 hours might have to be
broken up over 4 or 5 or more nights, when considering the vagaries of seeing (required AO performance), airmass (either through transmission or r0 requirements),
rotation rate (for ADI), and weather. We can adapt the calculations for a ground
based integration as follows
Z rap Z 2π "j=M
XZ
SN Rgnd =
0
0
j=1
tj +∆tj
I0 e(−4 ln 2((r cos θ−vom t−x0
)2 +r 2
sin2
θ))
#
dt dθrdr.
tj
p
2 ∆t
N πrap
int
(6.10)
In this expression we have broken the observation up into M integration sets which
j=M
X
∆tj
start at times tj and have lengths ∆tj . The total integration time is ∆tint =
j=1
and the total elapsed time of the observation is ∆ttot = tM + ∆tM − t1 .
We plot the results for a few ground-based scenarios in Figure 6.3. As one
can see, observations of planets with orbital motion will be significantly degraded
from the ground. This problem, which has been negligible in the high contrast
planet searches to date, only becomes worse as we consider larger telescopes and
improvements in AO technology which allow searches at shorter wavelengths. We
next analyze how this reduction in SN R will affect our ability to detect exoplanets
by increasing the rate at which spurious detections occur.
6.3.3 Impact on Statistical Sensitivity
Now we turn to the problem of detecting a planet of a given brightness. A planet
is considered detected if its flux is above some threshold SN Rt , which is chosen for
statistical significance. The goal in choosing this threshold is to detect faint planets
while minimizing the number of false alarms. For the purposes of this analysis we
assume Gaussian statistics, in which case the false alarm probability (PF A ) per trial
is
PF A
1
= erfc
2
SN R
√
2
(6.11)
156
Typically, planet hunters use a threshold of SN R = 5, which gives PF A = 2.9×10−7 .
The number of false alarms per star, the false alarm rate (F AR), is then
F AR = PF A × Ntrials .
(6.12)
where Ntrials is the number of statistical trials per star. Following Marois et al.
(2008a), for a stationary planet Ntrials is just the number of photometric apertures
in the image. A typical Nyquist sampled detector of size 1024x1024 pixels has
Ntrials ∼ 8 × 104 . Thus, an SN R = 5 threshold will result in F AR ∼ 0.02 – about 1
false alarm for every 50 observations. In the speckle limited case with non-Gaussian
statistics, F AR will be worse than this for the same SN R (Marois et al., 2008a).
In any case, the F AR is the statistic which determines the efficiency of a search for
exoplanets with direct imaging. A high F AR will cause us to waste telescope time
following up spurious detections, while raising the SN R threshold to counter this
limits the number of real planets we will detect.
The reduction of SN R caused by orbital motion confronts us with three options.
Option I is to maintain the detection threshold constant and accept the loss of
sensitivity. Option II is to lower the detection threshold to maintain sensitivity,
accepting the increase in FAR. Option III is to correct for orbital motion, which as
we will show also causes an increase in FAR.
Option I: Do Nothing
The default option is to do nothing, keeping our detection threshold set as if orbital
motion is not significant. The drawback to this is that we will detect fewer planets.
To quantify this we use the concept of completeness, that is the fraction of planets
of a given brightness we detect. For Gaussian statistics and detection threshold
SN Rt = 5, the search completeness is given by
1
SN R(ǫ) − 5
√
C(ǫ) = 1 − erfc
.
2
2
(6.13)
where ǫ = vom ∆t is the amount of motion. In Figure 6.4 (top) we show the impact of
orbital motion on search completeness. Maintaining the detection threshold lowers
157
1.0
7.
75
6.
0.8
Completeness
σ
65
σ
5.
47
σ
0.6
5σ
0.4
0.2
0.0
0
Option I − Lower Completeness
1
2
3
Orbital Motion ε (FWHM)
4
5
100
p(
aε
)
2σ
∝
10−2
1σ
)
b/ε
c(
erf
3σ
ex
10−4
∝
PFA per aperture
Option II − Higher PFA
4σ
10−6
5σ
Threshold required to maintain completeness
PFA at required threshold
−8
10
0
2
4
6
Orbital Motion (FWHM)
8
10
Figure 6.4 Top panel: completeness as a function of orbital motion if we maintain
our detection threshold at 5σ. Planet brightness is expressed as the SN R at which
we would be 50%(5σ), 68%(5.47σ), 95%(6.65σ), and 99.7% (7.75σ) complete with
no orbital motion. Bottom panel: the increase in false alarm probability (PF A ) if we
lower the detection threshold to maintain 50% completeness for an orbiting planet
that would have a brightness of 5σ were it stationary. After ∼ 1 FWHM of motion
PF A increases exponentially until ∼ 4 FWHM where it becomes asymptotic to 0.5.
158
completeness. How much depends on the completeness level, with brighter planets
being less affected. For planets bright enough to yield 95% completeness with no
motion, significant reduction in the number of detections begins after ∼ 1 FWHM of
motion. For 99.7% completeness the impact becomes significant after ∼ 1.5 FWHM.
Option II: Lower Threshold
Once orbital motion is recognized to be significant, a simple countermeasure would
be to lower the detection SN R threshold in order to maintain completeness. The
drawback to this option is that we have more false alarms, which must then be
followed up using more telescope time. This results in a less efficient search. In
Figure 6.4 (bottom) we show PF A as a function of orbital motion, and denote the
detection threshold we must use to maintain 50% completeness for a planet bright
enough to give SN R = 5 were it stationary. Note that PF A begins to increase exponentially after ∼ 1 FWHM of motion. After ∼ 4 FWHM PF A begins approaching
0.5 asymptotically. Once ǫ ≈ 2 FWHM the number of false alarms per 1024x1024
image approaches 1.
Option III: De-orbit
Option III is to correct for orbital motion, hoping to maintain sensitivity while
limiting the increase in PF A . The essence of any such technique will be calculating
the position of the planet during the observation, and de-orbiting in some way,
say shift-and-add (SAA) on a sequence of images. The drawback of this approach
is that it will produce more false alarms per observed star due to the increased
number of trials, similar to lowering the detection threshold. If the orbit were
precisely known, we could proceed with almost no impact on F AR. However, in
the presence of uncertainties in orbital parameters or in a completely blind search
we will have to consider many trial orbits. For now we can perform a “back-of-theenvelope” estimate of the number of possible orbits to understand how much F AR
will increase. To do so, we begin by placing bounds on the problem.
159
We can first establish where on the detector we must consider orbital motion.
At any separation r from the star, the slowest un-bound orbit will have the escape
velocity. Since we know that physical separation is greater than or equal to projected
separation, r ≥ ρ, and that maximum projected speed will occur for inclination
i = 0, we know that
√
vesc =
2vF OC (a → ρ)
(6.14)
sets the upper limit on the projected focal plane speed of an object in a bound orbit.
We can also set an upper limit on the amount of motion ǫmax we can tolerate over
the duration ∆ttot of the observation based on the SN R degradation it would cause.
So we only need consider orbital motion when
√
2vF OC (ρ)∆ttot > ǫmax .
(6.15)
From here we determine the upper limit on projected separation from the star for
considering this problem:
ρmax = 0.0136M∗
D ∆ttot
λd ǫmax
2
AU.
(6.16)
By the same logic, for any point closer than ρmax the maximum possible change in
position is
∆ρmax ≈
√
2vF OC (ρ)∆ttot in FWHM.
(6.17)
Then we must evaluate possible orbits ending anywhere in an area of π(∆ρmax )2
FWHM2 around an initial position.
These two limits set the statistical sensitivity of an attempt to de-orbit an observation. The number of different orbits, Norb , will be determined by the area of the
detector where orbital motion is non-negligible, and the size of the region around
each point that we consider. That is
Norb ∝
so
Norb ∝
Z
ρmax
0
M∗
ǫ
∆ρ2max ρdρ.
2 D
λd
4
∆t4tot .
(6.18)
(6.19)
160
In general Ntrials ∝ Norb , so F AR ∝ PF A × Norb . Larger D, shorter λ, closer d,
and smaller acceptable orbital motion ǫ will then all increase F AR2 . Perhaps the
most important feature of this result is that Norb ∝ ∆t4tot – increasing integration
time rapidly increases the F AR of a blind search. Note that this is still less
severe than the exponential increase in PF A found for merely lowering the thresh-
old. In the next section we will test these relationships after fully applying orbital
mechanics, and see that they hold.
6.4 Blind Search: Recovering SNR after Orbital Motion
In this section we consider in detail a blind search, i.e. an observation of a star for
which we have no prior knowledge of exoplanet orbits. We showed above that the
problem is well constrained. Here we derive several ways to further limit the number
of trial orbits we must consider. After that, we describe an algorithm for determining
the orbital elements that must be considered and then discuss the results. Finally,
we use this algorithm to de-orbit a sequence of simulated images and analyze the
impact of correlations between trial orbits on F AR.
To provide numerical illustrations throughout this section we consider the problem of a 20 hour observation of α Cen A using the GMT at 10µm. This scenario is
loosely based on performance predictions made for the proposed TIGER instrument,
a mid-IR diffraction limited imager for the GMT (Hinz et al., 2012). The details
of these predictions are not important for our purposes, so we will only assert that
this is a plausible case. There are other examples in the literature with similar
integration times, such as the EPICS prediction we discussed earlier.
We assume that this 20 hr observation is broken up into five ∆t = 4 hr exposures,
spread over 7 nights or ∆ttot = 6.2 elapsed days from start to finish. The choice of
∆t is essentially arbitrary, but we have good reasons to expect it to be shorter than
an entire night. An important consideration is the planned use of ADI, and the
2
Assuming background limited photometry with a diffraction limited PSF, we expect ∆t ∝
1/D4 (Hardy, 1998). All else being equal, larger telescopes are better when considering this
problem
161
attendant need to obtain sufficient field rotation in a short enough time to provide
good PSF calibration while avoiding self-subtraction (Marois et al., 2006). The
effect of airmass on seeing through r0 ∝ cos(z)3/5 , where z is the zenith angle, and
hence on AO system performance, could also cause us to observe as near transit
as possible. Efficiency will be affected by chopping and nodding, necessary for
background subtraction at 10µm. This will limit the net exposure time obtainable
in one night..
Few ground-based astronomers would object to an assertion that we loose 2
nights out of 7 to weather. We could be observing in queue mode, such that these
observations are only attempted when seeing is at least some minimal value, or
precipitable water vapor is low. One can even imagine the opposite case at 10µm,
such that nights of the very best seeing are devoted to shorter wavelength programs.
While this scenario may be somewhat contrived, we feel that it is both plausible and
realistic. We now proceed to describe a technique that would mitigate the effects
of orbital motion for our GMT example and should be applicable to other long
exposure cases.
6.4.1 Limiting Trial Orbits
Here we derive limits on the semi-major axis and eccentricity of trial orbits to
consider. These limits are based only on the amount of orbital motion tolerable for
the science case, and do not represent physical limits on possible orbits around the
star.
It is always true that r ≥ ρ. This implies that, for any orbit, the separation of
apocenter must obey ra ≥ ρ. This allows us to set a lower bound on a, amin , given
a choice of e through
ρau ≤ amin (1 + e)
(6.20)
which gives
amin = 0.2063
λdρ
.
D(1 + e)
(6.21)
The fastest speed in a bound planet’s orbit will occur at pericenter, and using
162
the maximum tolerable motion ǫmax during our observation of total elapsed time
∆ttot we can set an upper bound on a by noting that
r
1+e
∆ttot ≤ ǫmax
vF OC (amax )
1−e
which leads to
amax =
D
0.0834
λd
2
1+e
M∗
1−e
∆ttot
ǫmax
(6.22)
2
.
(6.23)
Using the GMT example: for e = 0.0, amax = 3.9 AU; and for e = 0.5, amax =
11.8 AU. Using Equation 6.16 we have a projected separation limit of ρmax = 7.7
AU, so it is possible for these definitions to produce amax < amin for certain choices
of e at a given ρ. This condition tells us that at such a value of e no orbits can
move fast enough to warrant consideration. Thus we can set a lower limit on e at
projected separation ρ
emin =
1p 2
ξ
ξ + 8ξ − 1 −
2
2
(6.24)
where we have simplified by pulling out
3
ρ ǫ 2 λd
ξ = 29.66
.
M∗ ∆t
D
(6.25)
In practice, we might consider eccentricity ranges with emax less than 1, thus
improving our sensitivity. Inputs to our choice of emax could include some prior
distribution of eccentricities, or dynamical stability considerations in binary star
systems and systems with known outer companions.
6.4.2 Choosing Orbital Elements
Now we describe an algorithm for sampling the possible trial orbits over a set of M
sequential images. For now, we assume no prior knowledge of orbital parameters. We
will employ a simple grid search through the parameter space bounded as described
above.
1. Determine the region around the star to consider using Eq. (6.16).
163
2. Identify regions of interest. In the best cases the orbital motion will be small
enough that we will be able stack the images and search the result for regions
with higher SN R (e.g. SN R > 4) and limit further analysis to those areas. In
the worst cases orbital motion will be large enough that we will need to blindly
apply this algorithm at each pixel within the bounding region identified in the
previous step. In the present GMT-αCen example we are in the former case.
3. For each region, choose a size, perhaps based on vesc (as in Eq. 6.17).
4. Chose a starting point (x1 , y1 ), with ρ1 =
p
x21 + y12 . If we are proceeding pixel
by pixel, then (x1 , y1 ) describes the current pixel.
5. Choose e ∈ emin (ρ1 ) . . . emax using Equation (6.24) and assumptions about
emax .
6. Choose a ∈ amin (ρ1 , e) . . . amax (e) using Equations (6.21) and (6.23).
7. Choose time of pericenter τ ∈ t1 − P (M∗ , a) . . . t1 where P is the orbital
period and t1 is the time of the first image. Now calculate the true anomaly
f (t1 ; a, e, τ, P ) using Kepler ’s equation and physical separation using:
r=
a(1 − e)
1 + e cos(f )
(6.26)
8. if e 6= 0: Choose ω ∈ 0 . . . 2π
if e = 0: set ω = 0.
9. if sin(ω + f ) > 0:
(a) Given e, a, τ , f , and ω, calculate
q
2
± ρr2 − cos2 (ω + f )
cos i =
sin(ω + f )
sin Ω =
y cos(ω + f ) − x sin(ω + f ) cos i
r(cos2 (ω + f ) + sin2 (ω + f ) cos2 i)
(6.27)
(6.28)
164
cos Ω =
y sin(ω + f ) cos i + x cos(ω + f )
r(cos2 (ω + f ) + sin2 (ω + f ) cos2 i)
(6.29)
where Ω should be determined in the correct quadrant.
(b) We now have a complete set of elements, and so can SAA the sequence of
images based on these orbits (one for each i). Doing so requires calculating the true anomaly fj at the time of each image, and then calculating
the projected orbital position of the prospective companion in each image.
10. if sin(ω + f ) = 0, we do not have a unique solution for inclination. This is the
special case where the planet is passing through the plane of the sky.
(a) for ω + f = 0 calculate Ω:
sin Ω =
y
r
(6.30)
cos Ω =
x
r
(6.31)
sin Ω =
−y
r
(6.32)
cos Ω =
−x
r
(6.33)
or for ω + f = π calculate Ω:
determining Ω in the correct quadrant.
(b) Choose i ∈ 0 . . . π
(c) We now have a complete set of elements, and so can SAA as in step 9b
above.
(d) Repeat steps 10b to 10c until all i chosen.
11. Repeat the above steps until the parameters ω, τ , a, and e are sufficiently
sampled for each starting point.
165
6.4.3 De-orbiting: Unique Sequences of Whole-Pixel Shifts
The algorithm just described will produce a large number of trial orbits, many of
which will be very similar. The information content of our image is set by the
resolution of the telescope, so we can take advantage of this similarity to greatly
reduce the number of statistical trials. This is done by grouping similar orbits into
sequences of whole-pixel shift sequences, where the pixels are at least as small as
FWHM/2. As we will see, we typically will want to oversample, to say FWHM/3,
to ensure adequate SN R recovery.
We calculate the pixel-shift sequence for each orbit by determining which pixel
the trial planet (or rather, the center of its PSF) lands on at each time step. Many
orbits end up producing the same sequences of pixel-shifts, and we will keep only
the unique ones for use in de-orbiting the observation. In Figure 6.5 we illustrate
the outcome of the pixel-shift algorithm, showing two unique sequences and a few
of the orbits that produced them.
To test the above algorithm and the pixel-shift technique, we used our GMT α
Cen A example and determined the trial orbits for various separations and ∆ts. We
set ǫmax = 0.5 based on our earlier analysis of SN R. The results are summarized
in Figure 6.6. The problem is generally well constrained in that we only have a
finite search space for any initial point. The data used to construct Figure 6.6 are
provided in Table 6.1. Comparing Norb to Nshif ts , note the large reduction in the
number of trials (∼ 108 to ∼ 102 ) due to combining similar orbits.
6.4.4 Norb Scalings
In Figure 6.7 we plot the area of the detector which contains the possible trial orbits
at ρ1 = 1.0 AU vs. the total elapsed time ∆ttot . We conclude from this plot that
the area around a given starting point is proportional to ∆t2tot . Also in Figure 6.7
we plot area vs separation from the star, and conclude that area is proportional
to 1/ρ1 . Taken together these results give confidence that the Norb ∝ ∆t4tot scaling
derived earlier holds when we fully apply orbital mechanics rather than the escape
166
0.65
0.60
4
0.55
3
4
y (")
5
5
3
2 1 2
0.50
0.45
0.40
0.40
0.45
0.50
x (")
0.55
0.60
Figure 6.5 Two sequences of whole pixel-shifts, one in red and one in blue. We
also show a few of the many orbits that produce these shift sequences. Once these
shifts are determined, a set of 5 images can be de-orbited by shifting the images by
the indicated sequence 5-4-3-2-1, that is the pixel containing the orbit in image 2 is
is shifted and added to the pixel containing the orbit in image 1, and likewise for
images 3, 4, and 5. Of course, the entire image is shifted, not just single pixels.
167
1.0
0.8
∆t
∆t
∆t
∆t
=
=
=
=
α Cen A
GMT 10µm
4.2 days
6.2 days
8.2 days
10.2 days
FWHM
arcsec
ρ1 = 1.5 AU
0.6
ρ1 = 1.0 AU
0.4
0.2
0.0
0.0
ρ1 = 0.5 AU
0.2
0.4
0.6
arcsec
0.8
1.0
Figure 6.6 Example trial orbits for the GMT, working at 10µm, observing αCen A.
Plotted are the end points of orbits calculated using the algorithm given in Section
6.4.2 for the given initial projected planet separations ρ1 and elapsed observation
times ∆ttot . The red points show the effect of changing initial separation for a
constant elapsed time. At 1 AU initial separation the colors correspond to different
elapsed times as indicated in the legend. We further analyze these relationships in
Table 6.1 and Figure 6.7. The results of the algorithm appear more complicated
than the simple escape-velocity circle analysis in Section 6.3.3. The end-point clouds
are not circularly symmetric about the starting point, and have some azimuthal
structure. For instance there is a triangle extending azimuthally corresponding to
face-on high-e orbits, and there are gaps along the radius from the star corresponding
to i very near 90o . These structures are consequences of the chosen grid resolution.
168
Table 6.1 Results of applying the algorithm detailed in Section 6.4.2 for various
separations and elapsed observation times. See also Figure 6.7. Note the dramatic
reduction in the number of trials (Norb vs. Nshif ts ) after combining similar orbits
into whole-pixel shift sequences.
ρ1 (AU)
0.5
1.0
1.0
1.0
1.0
1.5
1.0
1.0
1.0
1.0
∆ttot (days)
6.0
2.0
4.0
6.0
8.0
6.0
2.0
4.0
6.0
8.0
No. Obs.
5
5
5
5
5
5
3
5
7
9
Norb
2.7 × 108
4.1 × 108
4.1 × 108
4.1 × 108
4.1 × 108
5.2 × 108
4.1 × 108
4.1 × 108
4.1 × 108
4.1 × 108
Nshif ts
285
14
76
134
253
90
10
78
292
815
169
velocity approximation.
Things are a bit more complicated when we consider the scaling of the number
of whole-pixel shift sequences. We conducted two sets of trials at ρ1 = 1.0 AU. In
the first, the number of observations and their relative spacing was held constant
regardless of ∆ttot . In the second set, the number of observations scaled with ∆ttot .
As shown in Figure 6.7, when the number of observations is constant, the number
of shifts scales as ∆t2tot , but when the number of observations grows with ∆ttot the
number of shifts scales as roughly ∆t3.6
tot . Figure 6.7d shows that the number of shifts
scales as 1/ρ1 . Taken together, we see that for a constant number of observations
the pixel-shift technique will follow the Norb ∝ ∆t4tot scaling. However, if the number
of observations also scales with ∆ttot , then our results imply that Norb ∝ ∆t5.6
tot . The
value of the exponent likely depends on the details of the observation sequence, but
this has important implications for observation planning.
6.4.5 Recovering SNR
We next consider whether de-orbiting by whole-pixels adequately recovers SN R. To
test this we “orbited” a Gaussian PSF on face-on orbits with various eccentricities,
starting from pericenter. We then calculated shifts for detector samplings of 2, 3, and
4 pixels/FWHM, and then de-orbited by these shifts. The results are summarized in
Table 6.2. On a critically sampled detector we only recover a 5σ planet to ∼ 4.9σ,
a 2% loss of SN R. At 3 pixels/FWHM we do much better, recovering SN R to
4.97 for low eccentricities, and 4.95 for higher eccentricities. Performance for 4
pixels/FHWM sampling is similar. A 2% loss of SN R nearly doubles PF A , so it
appears that we should oversample to at least 3 pixels/FWHM, either optically or
by re-sampling images during data reduction. In our analysis we have assumed that
the limiting noise source is background photons (PSF halo or sky), so we ignore the
increased readout noise expected from oversampling.
Area (Apertures)
170
10 (a)
(b)
1/ρ
1
2
ot
∆t t
1
ρ1 = 1.0 AU
(c)
∆ttot = 6.2 days
(d)
# Shifts
1000
6
3. t
to
∆t
1/ρ1
2
t
∆t to
100
No. Obs. const
No. Obs.∝∆ttot
4
∆ttot (days)
10
0.5
1
ρ1 (AU)
Figure 6.7 Scaling of the number of orbits and the number of resulting whole-pixel
shifts with observation elapsed time and with distance from the star. These results
demonstrate that the number of trial orbits Norb ∝ ∆t4tot scaling that we derived
using the escape velocity holds when we rigorously apply orbital mechanics. Note
though that the situation is more complicated with the number of shifts – if the
number of observations increases with elapsed time then the number of shifts grows
faster than ∆t2tot , implying that Norb will increase faster than ∆t4tot . These scalings
lead to one of our main, if seemingly obvious, conclusions: one must limit the elapsed
time of an observation as much as possible when orbital motion is significant.
2
171
Table 6.2 SNR recovered after de-orbiting with whole-pixel shifts for various samplings.
Sampling
(pix/FWHM)
2
3
4
e=0.0
4.89
4.97
4.97
e=0.1
4.89
4.96
4.97
SN R Recovered
e=0.2 e=0.3 e=0.5
4.89
4.88
4.86
4.95
4.94
4.94
4.97
4.97
4.94
e=0.7
4.86
4.95
4.92
e=0.9
4.86
4.95
4.92
172
6.4.6 Correlations And The True Impact On PF A
As we have noted several times, the main impact of orbital motion is to reduce
SN R, which in turn reduces our statistical sensitivity. If we attempt to de-orbit an
observation in order to recover SN R, we do so at the cost of a large increase in the
number of trials. Worst case, this results in a proportional increase in F AR since
nominally F AR = PF A × Norb . However, we expect significant correlation between
trials of neighboring orbits and whole-pixel shifts. To investigate this, we performed
a series of monte carlo experiments. A sequence of images with Gaussian noise was
generated, and first stacked without shifting, hereafter called the naive-add. The
same sequence was then shifted by each possible whole-pixel shift, assuming a 1AU
initial separation around α Cen A. This experiment was conducted for observations
with total elapsed times ∆ttot of 4.2, 6.2, 8.2, and 10.2 days, with samplings of 2, 3,
and 4 pixels/FWHM.
We performed several tests on each sequence. The first was a simple threshold
test on the naive-add, with the threshold set for the worst case orbital motion given
by Equation 6.10 with vom = vesc . We performed simple aperture photometry, with
a rap = 1 FHWM. As expected the resultant PF A1 is as predicted by Equation
6.11. The next test was to apply a 5σ threshold after de-orbiting by whole-pixel
shifts and adding. If all shifts were completely uncorrelated, then we would expect
F AR = (2.9 × 10−7 ) × Nshif ts , but as we predicted, shifts are correlated and PF A2
is lower than this.
The final test performed was to apply both thresholds in sequence, such that a
detection is made only if the naive-add results in SN R greater than the threshold
for worst case orbital motion, and the de-orbited SAA results in SN R > 5. This
PF A3 is lower than either PF A1 or PF A2 , but still higher than if no orbital motion
occurred.
The results of each trial are present in Table 6.3. Applying both threshold tests
results in significant improvement over the naive-add in terms of F AR. Another
interesting result is that sampling has only a minor impact on PF A3 . This makes
173
Table 6.3 False alarm probabilities after de-orbiting Gaussian noise images.
∆ttot (days)1 SN Rt 2 Nshif ts 3
PF A1 4
PF A2 5
PF A3 6
64
122
231
364
1.74 × 10−6
1.24 × 10−5
4.40 × 10−4
4.33 × 10−3
7.65 × 10−6
1.52 × 10−5
2.71 × 10−5
4.03 × 10−5
8.06 × 10−7
2.70 × 10−6
9.93 × 10−6
2.17 × 10−5
108
285
496
741
2.11 × 10−6
1.21 × 10−5
4.31 × 10−4
4.34 × 10−3
1.37 × 10−5
3.39 × 10−5
5.64 × 10−5
8.15 × 10−5
4.80 × 10−7
2.04 × 10−6
9.96 × 10−6
2.67 × 10−5
217
487
844
1315
1.78 × 10−6
1.24 × 10−5
4.35 × 10−4
4.32 × 10−3
2.64 × 10−5
5.61 × 10−5
9.19 × 10−5
1.41 × 10−4
4.44 × 10−7
1.48 × 10−6
1.14 × 10−5
3.15 × 10−5
2 pixels/FWHM
4.2
6.2
8.2
10.2
4.635
4.220
3.330
2.625
3 pixels/FWHM
4.2
6.2
8.2
10.2
4.635
4.220
3.330
2.625
4 pixels/FWHM
4.2
6.2
8.2
10.2
4.635
4.220
3.330
2.625
1
Elapsed time of the observation.
√
SN R threshold from Equation 6.10, using vorb = 2vF OC .
3
Number of unique whole-pixel shifts required to de-orbit.
4
False alarm probability for the naive-add, from MC experiment results. Expected values given by
Equation 6.11.
5
False alarm probability after de-orbiting with whole-pixel shifts.
6
False alarm probability after testing both the naive-add and de-orbiting.
2
some sense as we expect the correlation of neighboring shifts to be set by the FWHM,
not the sampling. So even though the accuracy of SN R recovery is improved, and
quite a few more shifts are required, these shifts remain correlated across the same
spatial scale resulting in little change in the overall F AR.
6.4.7 Impact on Completeness of the Double Test
There is still an impact on completeness, however, because we are now conducting
two trials instead of one. This lowers the true positive probability (PT P ). Consider a
174
5σ planet on the worst case fastest possible orbit, for the 10.2 day elapsed time case.
The threshold for the naive add is 2.625. We have a 50% probability of detecting
this planet after the naive add. If it is detected on the first test, there is then some
probability PT P < 1 of detecting at SN R ≥ 5 after de-orbiting. Worst case, this
will be 50%, resulting in a net PT P of 25%. In reality, it will be better than this as
the two trials will be strongly correlated.
Even if this worst case of 25% were realized this is still significant improvement
over Option I. A 2.6σ signal would only be detected 10% of the time with a 5σ
threshold. Given the reduction in PF A from 4.3 × 10−3 to 2.2 × 10−5 , likewise an
improvement over Option II at 2.6σ, it is clear that de-orbiting by whole-pixel shifts
does improve our ability to detect an orbiting planet. The situation will be even
better for slower planets, and most of the area searched will not be subject to the
worst case orbital speed. We leave a complete analysis of the impact on search
completeness for future work. One can also imagine adjusting the thresholds to
optimize completeness at the expense of worse PF A .
6.4.8 Tractability of a Blind Search
We end this section by concluding that a blind search when orbital motion is significant is tractable. Orbital motion will make such a search less sensitive, both in
terms of number of false alarms and in terms of completeness, but Keplerian mechanics gives us enough tools to bound the problem. As we have shown de-orbiting
a sequence of observations can recover SN R to its nominal value, and we can do so
while controlling the impact on statistical sensitivity. For the ∆ttot = 6.2 day obser-
vation, PF A3 was roughly a factor of 10 higher than if no orbital motion occurred.
This increase only occurs over a bounded region around the star, so the net effect on
F AR will be contained. Using this factor of 10 as the mean value over the 7.7 AU
= 69.1 FWHM radius region around α Cen A where orbital motion is significant,
the F AR in this area will have gone from ∼ 1/1000 to ∼ 1/100 in our GMT/10µm
example. The key, though, appears to be to limit the elapsed time of the observation
as the number of trials increases — decreasing sensitivity – proportionally to at least
175
Table 6.4 Orbital parameters for Gl 581d used in this analysis. We derived the
values reported here from other parameters where necessary. Only the uncertainty
in t0 impacts our analysis. In both models the orbital period is 66.6 days.
Model
Forveille et al. (2011)
Vogt et al. (2012)
a (AU)
0.218 ± 0.005
0.218 ± 0.005
e
0.25 ± 0.09
0.0 ± 0.0
ω (deg)
356.0 ± 19.0
0.0 ± 0.0
σt0 (days)
±3.4
±7.45
∆t4tot in a blind search.
The main caveat at this point in our analysis is that we have drawn the conclusion
of tractability using Gaussian statistics. It is well known that speckle noise, which
will often be the limiting noise source for high contrast imaging in the HZ, is not
Gaussian and results in much higher PF A for a given SNR (Marois et al., 2008a).
Future work on this problem will need to take this into account.
Next we consider a more strongly bounded scenario, where we have significant
prior information about the orbit of the planet from radial velocity surveys.
6.5 Cued Search: Using RV Priors
The situation is greatly improved if we have prior information, such as orbit parameters from RV or astrometry. Here we consider the case of Gliese 581d, and
the previously discussed future observation of this planet by EPICS at the E-ELT
(Kasper et al., 2010). There is some controversy surrounding the solution to the RV
signal, and whether planet d even exists (Forveille et al., 2011; Vogt et al., 2012;
Baluev, 2012). We show results for both the floating eccentricity Keplerian fits of
Forveille et al. (2011)[hereafter F11], and the all circular interacting model of Vogt
et al. (2012)[hereafter V12]. Doing so allows us to illustrate the impact of eccentricity on the analysis, and prevents us having to take a stand in a currently raging
debate. The parameters used herein are listed in Table 6.4.
Instead of a grid search, we use a monte carlo (MC) method. The RV technique
provides the parameters a, e, ω and t0 or their equivalents. We can take the results of
176
fitting orbits to the RV signal, and the associated uncertainties, as prior distributions
which we sample to form trial orbits. We will assume that all uncertainties are
uncorrelated and are from Gaussian distributions.
We assume that the 20 hr integration is broken up over 6.2 nights based on the
same logic discussed in Section 6.4. Kasper et al. (2010) actually assumed 20 × 1
hr observations based on the amount of rotation needed, but did not consider the
effects of orbital motion over 20 days of a 67 day period (M. Kasper, personal
communication (2012)).
6.5.1 Constraints
In order to minimize the number of trial orbits to consider, we can apply various
constraints taking advantage of the information we have from the RV detection.
In the case of a multi-planet system dynamical analysis can place constraints
on the inclination based on system stability. For Gl 581, Mayor et al. (2009) found
the system was stable for i > 30. We can also make use of the geometric prior
for inclination, where we expect Pi = sin(i) in a population of randomly oriented
systems.
Since this is a reflected light observation, the orbital phase and its impact on the
brightness of the planet must be considered. The planet’s reflected flux is given by
2
Rp
Fp (α) = F∗
Ag (λ)Φ(α)
(6.34)
r
where F∗ is the stellar flux, Rp is the planet’s radius, r its separation, Ag (λ) is the
wavelength dependent geometric albedo, and Φ is the phase function at phase angle
α. The phase angle is given by
cos(α) = sin(f + ω) sin(i).
(6.35)
In general, determining the quantity Ag (λ)Φ(α) requires atmospheric modeling (Cahoy et al., 2010). For now, we assume that Φ follows the Lambert phase function
Φ(α) =
1
[sin(α) + (π − α) cos(α)]
π
(6.36)
177
We assume that the prediction of Kasper et al. (2010) was made for the planet at
quadrature, α = π/2, where Φ = 0.318. We then require that the mean value of Φ
during the observation be greater than this value - that is the planet is as bright or
brighter than it is at quadrature.
6.5.2 Initial Detection
An important consideration in an RV-cued observation will be when to begin. As
a first approximation, we assume that maximizing planet-star separation will maximize our sensitivity. This may not be true when working in reflected light due to the
phase and separation dependent brightness of the planet in this regime. Proceeding
with the approximation for now, we expect to plan this observation to be as close to
apocenter as possible. In this case we will begin integrating 3.1 days before t0 +P/2.
To understand the area where we will be searching for Gl 581d, we first conducted
an MC experiment to calculate the possible positions of the planet at t = t0 + P/2 −
3.1 days. To do so, we drew random values of a, e, w, and t0 from Gaussian
distributions with the parameters of Table 6.4. We drew a random value of i from
the sin(i) distribution, and rejected any value of i ≤ 30 based on the dynamical
prior. Finally Ω was drawn from a uniform distribution in 0 . . . 2π. This process
was repeated 109 times, and the frequency at which starting points occur in the
area around the star was recorded. The results are shown in Figure 6.8 for the V12
circular model and for the F11 eccentric model. The Figure shows the area which
must be searched to obtain various completeness. For instance, if we desire 95%
completeness in the V12 model, we must consider an area of 71 apertures. Since
this SN R = 5 detection is broken up into 5 distinct integrations, our first attempt
will have SN R = 2.24, giving a F AR = 0.89 for the first 4 hr integration. In other
words, we should expect a false alarm in addition to a real detection.
178
0.018
0.06
FWHM
0.015
0.04
arcsec
0.00
0.009
−0.02
0.006
−0.04
0.003
−0.06
68.3% = 48.5 ap
95.5% =109.6 ap
99.7% =164.0 ap
−0.06 −0.04 −0.02 0.00 0.02
arcsec
0.04
probability per aperture
0.012
0.02
0.000
0.06
0.038
0.06
FWHM
0.032
0.04
arcsec
0.00
0.019
−0.02
0.013
−0.04
0.006
−0.06
68.3% = 32.0 ap
95.5% = 72.9 ap
99.7% = 85.3 ap
−0.06 −0.04 −0.02 0.00 0.02
arcsec
0.04
probability per aperture
0.026
0.02
0.000
0.06
Figure 6.8 Possible starting points for Gl 581d, observed near apocenter. Top: using
the parameters of Forveille et al. (2011)’s eccentric model. Bottom: assuming the
parameters of Vogt et al. (2012)’s circular interacting model. The color shading is
in units of probability per aperture (each aperture has area πFWHM2 ). The legend
indicates the color which encloses the given completeness intervals, and the enclosed
area in apertures, which can be directly related to the false alarm rate as discussed
in the text.
179
6.5.3 Calculating Orbits and Shifts
Now we assume that we have an initial detection at SN R ∼ 2.24 within the highest
probability regions3 . In order to follow-up this detection over subsequent nights, we
must determine the possible locations of the planet, constrained by the RV-derived
orbital elements.
We proceed by choosing a, e, ω, and t0 from Gaussian distributions as above.
Now as long as r > ρ we will have a unique solution for i and Ω given the randomly
chosen parameters (see the blind search algorithm above). We take into account
dynamical stability by rejecting any orbit which has i ≤ 30. The orbit determined
in this fashion was then projected 6.2 days into the future and the frequency of
these final points was recorded. We show the result for the V11 model in Figure 6.9,
top panel. Using the RV determined parameters and their uncertainties allows us
to determine the probability density of orbit endpoints, and determine how much of
the search space we must consider for a given completeness. The whole-pixel shifts
were also calculated using a sampling of FWHM/3, and are shown in the legend. We
also applied the blind search algorithm to this observation from the same starting
point, and show the results for comparison in the bottom panel of Figure 6.9. As
expected the RV priors significantly reduce the search space - we have 942 trial
shift-sequences to consider instead of 12000.
Another important consideration here is that our initial 2.24σ detection will
have a large position uncertainty, which we estimate by σρ0 = F W HM/SN R. We
added a random draw for the starting position, and repeated the MC experiment
for F11 and also conducted a run for the V12 parameters. The results are shown in
Figure 6.10. The number of shift sequences is much higher due to the uncertainty
in the starting position caused by our low SN R initial detection, but we expect
correlations to come to the rescue as in our α Cen example. To compare to Figure
6.9 keep in mind that the blind search would have to be applied to all 5500 pixels
in the search space indicated by Figure 6.8.
3
For the purposes of this analysis, we calculated initial separation ρ1 using the mean parameters
for each model and an inclination i = 60
180
0.06
0.05
0.08
FWHM
0.04
arcsec
0.07
0.03
0.05
0.02
0.03
0.01
probability per aperture
Gl 581d
E−ELT
0.75µm
0.10
68.3% (1.0 ap, 234 shifts)
95.5% (2.9 ap, 650 shifts)
99.7% (4.6 ap, 942 shifts)
0.02
0.00
−0.01
−0.01 0.00
RV cued (F11)
0.01
0.02 0.03
arcsec
0.04
0.05
0.00
0.06
0.06
0.05
Gl 581d
E−ELT
0.75µm
FWHM
arcsec
0.04
0.03
0.02
0.01
0.00
blind search
−0.01
−0.01 0.00
0.01
0.02 0.03
arcsec
0.04
0.05
0.06
Figure 6.9 Trial orbits for Gl 581d, observed near maximum elongation. In the
top panel we use the parameters of Forveille et al. (2011)’s eccentric model. The
bottom panel shows the results for a blind search from the same starting point. The
red cross shows the starting point, and the star is located at the origin. The top
panel color shading is in units of probability per aperture (each aperture has area
πFWHM2 ). The legend indicates the color which encloses the given completeness
intervals, the enclosed area in apertures, and the number of unique whole-pixel shift
sequences which must be tried in order to de-orbit the observation. The number of
shift sequences is directly related to the false alarm rate, and hence the sensitivity.
For comparison, the blind search algorithm produced ∼ 12000 shifts. RV cueing
greatly improves our sensitivity in the presence of orbital motion.
181
As in the GMT/α Cen example, we leave for future work a complete analysis
of sensitivity and completeness. The large number of trial shifts calculated when
we include uncertainty in the starting position motivates us to suggest that we will
ultimately turn this analysis over to a much more robust optimization strategy, such
as a Markov Chain Monte Carlo (MCMC) routine. Once an area of the image was
identified with a high post-shift SN R, a MCMC analysis could determine the very
best orbit and assign robust measures of significance to the result.
We also note that these results likely overestimate the number of trial orbits
since we have assumed uncorrelated errors. In reality the RV best fit parameters
are likely strongly correlated, which should act to reduce the number of orbits to
consider.
6.6 Conclusions
In the coming campaigns to directly image planets in the HZs of nearby stars, orbital
motion will be large enough to degrade our sensitivity. This effect has been ignorable
in direct imaging campaigns to date, which have typically looked for wide separation
planets. We have analyzed this issue in some detail, and shown that applying basic
Keplerian orbital mechanics allows us to bound the problem sufficiently that we
believe direct imaging in the HZ to be a tractable problem. Our main conclusions
are:
(1) When projected onto the focal plane, a planet in a face-on circular orbit
moves with speed given by
vF OC = 0.0834
D
λd
r
M∗
FWHM day−1 .
a
(6.37)
In the HZ of nearby stars, especially when considering giant telescopes, speeds are
high enough that planets will move significant fractions of a PSF FWHM during a
single observation. This smears out the planet’s flux resulting in a lower SN R.
(2) In background limited photometry, an SN R maximum is reached after about
∼ 2 FWHM of motion has occurred on the focal plane. From there, integrating
182
0.06
0.05
0.10
68.3% (1.9 ap, 73244 shifts)
95.5% (5.1 ap, 173578 shifts)
99.7% (8.4 ap, 242407 shifts)
0.08
FWHM
0.04
arcsec
0.07
0.03
0.05
0.02
0.03
0.01
probability per aperture
Gl 581d
E−ELT
0.75µm
0.02
0.00
−0.01
−0.01 0.00
RV cued (F11)
0.01
0.02 0.03
arcsec
0.04
0.05
0.06
0.06
0.05
0.10
68.3% (2.7 ap, 69575 shifts)
95.5% (9.4 ap, 191809 shifts)
99.7% (16.0 ap, 276875 shifts)
0.08
FWHM
0.04
arcsec
0.07
0.03
0.05
0.02
0.03
0.01
probability per aperture
Gl 581d
E−ELT
0.75µm
0.00
0.02
0.00
−0.01
−0.01 0.00
RV cued (V12)
0.01
0.02 0.03
arcsec
0.04
0.05
0.00
0.06
Figure 6.10 Trial orbits for Gl 581d, observed near maximum elongation, assuming
the parameters of (top) Forveille et al. (2011)’s Keplerian eccentric model and (bottom) Vogt et al. (2012)’s circular interacting model. In this simulation we allowed
the initial position to vary with standard deviation σx,y = F W HM/SN R. The red
cross shows the starting point, and the star is located at the origin. The color shading is in units of probability per aperture (each aperture has area πFWHM2 ). The
legend indicates the color which encloses the given completeness intervals, the enclosed area in apertures, and the number of unique whole-pixel shift sequences which
must be tried in order to de-orbit the observation. The number of shift sequences
is directly related to the false alarm rate, and hence the sensitivity.
183
longer offers no improvement with a fixed-size aperture. Adapting the aperture
could mitigate this to some extent, but at the cost of significantly longer exposure
times.
(3) When SN R is reduced by orbital motion, we have three options. Option
I is to do nothing, and accept the loss of completeness due to planets appearing
fainter. Option II is to adjust our detection threshold at the cost of more false
alarm detections. Option III is to de-orbit an observation, recovering SN R to its
nominal value, but also at the cost of more false alarms.
(4) For exposure times of 10s of hours, we expect an observation to extend over
several days under realistic assumptions about ground based observing. If we naively
attempt to de-orbit such an observation, the false alarm rate per star will increase
by at least F AR ∝ ∆t4tot , where ∆ttot is the total elapsed time of the observation.
(5) De-orbiting a sequence of shorter exposures is possible, and tractable. Taking
advantage of strong correlations between trial orbits, we will realize increases in the
F AR on the order of a factor of 10 in the region around a star where orbital motion
matters. Since this will be a small, bounded region, this increase in F AR appears
to be acceptable.
(6) Cueing from another detection method, such as RV, provides significant
benefit. It allows us to initiate our search at the optimum time, and significantly
reduces the size of the search space. Having prior distributions for some of the
orbital elements will allow us to efficiently determine where and how to search to
optimize completeness.
184
CHAPTER 7
CONCLUSION
In this dissertation we have explored the development and on-sky performance of the
world’s newest AO system, MagAO, and its unique ability to contribute to exoplanet
science. We started by introducing the MagAO system, and its visible wavelength
science camera VisAO. VisAO is the first long-exposure diffraction-limited imager
on a large telescope. MagAO is a near clone of the LBTAO systems, and was
put through an extensive laboratory integration and testing period based on the
LBT process. VisAO was used as the camera for all of these tests, and so was well
characterized and a fully integrated part of the AO system by the end of this period.
Once deployed at LCO, MagAO and VisAO proceeded to take the highest resolution
filled-aperture image ever taken, splitting the 31 mas binary θ1 Ori C in the Orion
Trapezium Cluster for the first time.
Despite our optimism about the prospects for visible wavelength science, we were
aware that AO systems frequently under-perform when they reach the telescope.
Early in the development of VisAO, the LBTAO systems had not yet been proven
on-sky. To prepare for possible disappointment, we developed our own version of
Lucky imaging, called Real-Time Frame Selection (RTFS). Here we presented the
theoretical justification of this technique, showing that any frame selection technique
trades resolution for sensitivity. We then demonstrated the viability of RTFS using a
fast shutter, both in simulations and in the laboratory. Luckily, MagAO and VisAO
work at least as well as we had hoped, and so we ultimately do not use RTFS on
sky.
VisAO’s detection of β Pictoris b, a 10 MJup exoplanet, demonstrates the high
performance of this system. We achieved a contrast of 1.7 × 10−5 at only 0.47′′ .
This high contrast, close separation detection was made possible by the stable 40%
optical Strehl ratio PSF in median seeing at LCO. This is the first detection of an
185
exoplanet from the ground with a CCD. Using our photometry, we can analyze new
regions of the exoplanet’s atmosphere.
MagAO’s contributions to exoplanet science have only just begun. With its
unique O/IR wavelength coverage and stable high-contrast PSF, we will be able to
use MagAO to probe the Habitable Zones of select nearby stars for the first time. In
the thermal-IR, we are sensitive to gas-giant exoplanets with very low masses — as
small as 0.03 MJup . With VisAO, we will take the first high-resolution, high-contrast
images of the close surroundings of these stars in visible light. While searching for
planets, these observations will teach us many lessons about the challenges of long
exposures in this regime. We are “blazing the trail” for the next generation of giant
telescopes.
We closed with an analysis of one problem that the giant telescope planet-hunters
will have to deal with: orbital motion. As we begin to probe the HZ, we will find
that planets move enough over the course of a single observation that they smear,
resulting in reduced S/N. This problem is correctable, but not without some work.
We showed that Keplerian mechanics can be used to bound the problem, and recover
most of the lost sensitivity.
When I started graduate school in the Fall of 2008, the number of known exoplanets was counted in the tens, and the imaging of the HR8799, Fomalhaut, and
β Pic planets had not yet been announced. In the last 5 years the number of exoplanets has grown to over 3000, mainly thanks to Kepler, and we have had some
success with direct imaging. It is an exciting time in exoplanet science, and as we
continue to improve our instruments it will continue to be so.
186
APPENDIX A
POINT SPREAD FUNCTION RADIOMETRY AND PHOTOMETRY
Here I present a collection of derivations useful for analyzing AO corrected point
spread functions (PSFs). These are generally straightforward and can be found in
one form or another in various textbooks. They are given here to provide a common
notation and common units.
A.1 PSF Modeling
The obscured Airy pattern is
Io
I(x) =
(1 − ǫ2 )2
2J1 (πx) 2ǫJ1 (ǫπx)
−
πx
πx
2
.
(A.1)
where ǫ is the obscuration fraction and x is the radial coordinate in units of λ/D.
The quantity represented by I is the irradiance, and has units of energy per time per
area, or power per area. For the purpose of modeling the performance of photondetecting arrays of pixels at the focus of a telescope, the natural unit for power is
photons/sec/(λ/D)2 . Here we are using λ/D as the unit of length in the focal plane.
Expanding Equation (A.1) gives us
"
2
2 #
4Io
J1 (πx)J1 (πǫx)
J
(πǫx)
J1 (πx)
1
I(x) = 2
− 2ǫ
.
+ ǫ2
2
2
2
π (1 − ǫ )
x
x
x
which we can integrate to find the power enclosed by the Airy pattern at radius x′
#
"Z ′ 2
2
Z x′ Z x′
x
J
(πǫx)
J
(πx)
J
(πx)J
(πǫx)
8I
1
1
1
1
o
xdx + ǫ2
xdx − 2ǫ
dx
Penc (x′ ) =
π(1 − ǫ2 )2 0
x
x
x
0
0
which simplifies to
"
#
Z x′
4I
J
(πx)J
(ǫπx)
o
1
1
Penc (x′ ) =
Pc (πx) + ǫ2 Pc (ǫπx) − 4ǫ
dx
2
2
π(1 − ǫ )
x
0
(A.2)
187
where we have followed Mahajan (1986) in defining
Pc (y) = 1 − J02 (y) − J12 (y).
Now if we let x′ → ∞ this becomes
Ptot
so
Z ∞
4Io
J1 (x)J1 (ǫx)
2
=
1 + ǫ − 4ǫ
dx
π(1 − ǫ2 )2
x
0
Ptot =
4Io
π(1 − ǫ2 )
Now we have the peak of the Airy pattern in terms of Ptot .
Io =
πPtot (1 − ǫ2 )
4
(A.3)
Ptot is conveniently expressed as the photon flux from a star in a given bandpass:
π
Ptot = F0 10−0.4m D2 (1 − ǫ2 )
4
where F0 is the flux, in photons m−2 sec−1 , of a 0 magnitude star taking into account
filter transmission, QE, etc.
Another useful quantity when applying the above expressions is the plate-scale of
the detector. Each pixel has a fixed projected angular size, measured in arcseconds,
which we denote here with ps. The area of a pixel, in λ/D units, is just
Apix =
psD
0.2063λ
2
where λ is in µm and D is in m. For VisAO ps ≈ 0.00791 so
AVpixisAO =
0.249
.
λ2
A.2 Characterizing the PSF
Several quantities are used to characterize the PSF, including the full-width at half
maximum (F W HM ), the radius of the first minimum, and the fraction of the total
188
Quantity
F W HM
1st Min.
1st Max.
I(1st Max.)/ Io
EP (F W HM/2)
EP (1st Min.)
ǫ=0
1.03 λ/D
1.22 λ/D
1.63 λ/D
0.0175
0.475
0.838
ǫ = 0.11
1.02 λ/D
1.20 λ/D
1.63 λ/D
0.0212
0.467
0.824
ǫ = 0.29
0.98 λ/D
1.12 λ/D
1.62 λ/D
0.0455
0.432
0.747
Table A.1 Quantities typically used to characterize a PSF. For comparison, the
values for an unobscured aperture, and for ǫ = 0.11 (LBT & MMT) and ǫ = 0.29
(MagAO) are given.
power contained within various radii (EP (r)). These quantities depend on the central
obscuration. Using Equations (A.1) and (A.2) yields the values in Table A.1.
It is also convenient to introduce the notation
F W HM = κ
λ
D
where κ is the coefficient in the first row of Table A.1. While typically negligible,
on the MagAO system where the central obscuration ǫ = 0.29, there is actually a
5%change in the F W HM of the Airy pattern - a detectable difference of, e.g., 0.2
pixels at 1 micron on VisAO. In Section A.3 below we will see other ways that κ
should be taken into account.
A.3 Tip & Tilt Errors, FWHM, and Strehl Ratio
If we have residual tip & tilt (TT) errors in the focal plane after AO correction, the
result will be a smeared out PSF. We can model TT errors (jitter) as a displacement in the position of the PSF center, described by a 2D Gaussian probability
distribution
pT T (r) =
1
2
2
e−r /(2σT T )
2
2πσT T
where σT T is the RMS displacement of the PSF center. Now we can assume that
the PSF is itself a Gaussian, with F W HM = κλ/D (κ defined above), which means
189
a Gaussian width parameter (a.k.a. standard deviation) of
F W HM
σP SF = p
.
2 2 ln(2)
The resulting smeared out image will just be the convolution of the TT probability
distribution and the PSF. As such it will have a width parameter given by σ 2 =
σP2 SF + σT2 T . This yields the following estimate for the FWHM of a PSF with TT
errors
s
2
λ
κ
F W HMT T =
+ 8 ln(2)σT2 T .
(A.4)
D
TT errors will also be evident as a lower peak height, i.e. a lower Strehl ratio.
The degraded peak height can be estimated by calculating
Z ∞
1
2
2
2
2
Io,T T =
Io e−r /(2σP SF ) e−r /(2σT T ) rdrdθ.
2
2πσT T 0
Now ST T = Io,T T /Io so
ST T =
1+
1
8 ln(2)
κ2
σT T
λ/D
2
(A.5)
.
It is worth noting that these two expressions are slightly different than others
that have appeared in the literature. Some of the difference can be explained by
other authors (e.g. Tyson (2011), Hardy (1998)) using 1.22λ/D as the FWHM this is actually the radius of the first Airy minimum for an unobscured aperture.
(Hardy, 1998) gives 5.17 instead of 8 ln(2)/1.032 , which appears to just be a rounding
difference. Another subtle difference is the constant 8 ln(2) vs π 2 /2 given by Sandler
et al. (1994). These are numerically somewhat similar, 5.5 compared to 4.9. I have
so far been unable to find an explanation for this discrepancy.
Again we note the importance of κ for MagAO. In Equation (A.5) it enters as a
square, and so has over a 10% impact - MagAO is more sensitive to tip-tilt errors
than an unobscured aperture.
A.4 Gaussian PSF Photometry
We use the “CCD equation” to write the signal to noise ratio
Itot
SN R = √
Ntot
190
Where Itot is the total signal collected, and Ntot is the variance of the measurement.
For a Gaussian PSF, the SN R, in an aperture of radius x, is
Z x
r2
2πIo
exp − 2 rdr
SN R = √
2σ
πx2 N 0
where Io is the peak of the Gaussian, N is the variance per unit area, and we have
already integrated over the polar angle θ. The width parameter σ (a.k.a. standard
deviation) is related to the full-width-at-half-maximum as
F W HM
σ= p
2 2 ln(2)
Integrating gives
√
π F W HM 2
√
SN R =
4 ln(2) x N
1 − exp
−4 ln(2)x2
F W HM 2
Io
Differentiating with respect to aperture radius x leads to the transcendental equation
1
−4 ln 2 2
exp
x =
8
2
F W HM
1 + F Wln(2)
x2
HM 2
which has a minimum at x = 0 and a maximum at x ≈ 0.7F W HM .
If we set x = F W HM we have
SN R = 0.599
F W HM
√
Io .
N
√
It is convenient to note that in the peak pixel SN Rpk = Io / N , so
SN Rap = 0.599F W HM × SN Rpk
is the correction from peak pixel to the full aperture SN Rap .
A.5 Propagation of Errors
A.5.1 Absolute Magnitude
The absolute magnitude is given by
M∗ = m∗ + 5 log(dpc ) − 5
191
where dpc is the distance of the star in parsecs. Propagation of errors for this quantity
yields
2
σM
∗
=
2
σm
∗
+
5
ln(10)
2
σd2pc
d2pc
A.5.2 Physical Photometry
The flux-density of a star in a given bandpass is
F∗ = F0 10−m∗ /2.5
where m∗ is the apparent magnitude of the star in the bandpass and F0 is the flux
of an m∗ = 0 mag star in the bandpass (the zero-point). Propagation of errors for
this quantity gives
σF2 ∗
=
The partial derivatives are
∂F∗
∂F0
2
σF2 0
+
∂F∗
∂m∗
2
2
.
σm
∗
∂F∗
= 10−m∗ /2.5
∂F0
∂F∗
− ln(10) −m∗ /2.5
10
F0
=
∂m∗
2.5
so
"
σF2 ∗ = σF2 0 +
or
ln(10)
2.5
2
#
2
10−2m∗ /2.5
F02 σm
∗
"
#1/2
2
σF2 0
ln(10)
σF∗
2
=
+
σm∗
.
F∗
F02
2.5
Similarly, if F∗ is known the magnitude of a star is
F∗
m∗ = −2.5 log10
.
F0
Propagation of errors gives
2
σm
∗
=
∂m∗
∂F∗
σF2 ∗
+
∂m∗
∂F0
σF2 0
(A.6)
192
and the partial derivatives are
−2.5
∂m∗
=
∂F∗
F0 ln(10)
∂m∗
2.5
=
∂F0
F∗ ln(10)
so we have
2
=
σm
∗
2.5
ln(10)
2 "
σF∗
F∗
2
+
σF0
F0
2 #
.
(A.7)
193
APPENDIX B
SYNTHETIC PHOTOMETRY AND CONVERSIONS
In this appendix we provide details of our synthetic photometry. The primary
purpose of this analysis is to verify the methodology used for our analysis of β Pic
b, but we also determine transformations between various filter systems used in
brown dwarf and exoplanet imaging which may be useful to others.
B.1 Filters
Here we describe the process by which we assembled synthetic filter profiles for
this analysis. In general, we obtained a transmission profile, and determined an
atmospheric transmission profile appropriate for the site. Table B.1 summarizes the
atmosphere assumptions and models used. We finally converted to photon-weighted
“relative spectral response” (RSR) curves, using the following equation (Bessell,
2000)
T (λ) =
1
λT0 (λ)
hc
(B.1)
where T0 is the raw energy-weighted profile.
In the following subsections we describe details particular to the different photometric systems and passbands. Comparisons of the filters in each band bass are
shown in Figures B.1, B.2, B.3 and B.4.
B.1.1 The Y Band
The Y band was first defined in Hillenbrand et al. (2002). We follow Liu et al.
(2012) and assume that the UKIDSS Y filter defines the MKO system passband,
as the largest number of published observations in this passband are from there
(cf. Burningham et al. (2013)). This is a slightly narrow version of the filter. The
194
Table B.1 Atmospheres.
System
Model
Airmass PWV (mm) Notes
VisAO
ATRAN, Cerro Pachon
1.0
2.3
1,2
2MASS
PLEXUS
1.0
5.0
3
MKO
ATRAN, Mauna Kea
1.0
1.6
1
UKIDSS
1.3
1.0
4
NACO
Paranal-like
1.0
2.3
5
NICI
ATRAN, Cerro Pachon
1.0
2.3
1
Notes:
[1] Lord (1992)
[2] C. Manqui elevation is 2380 m, C. Pachon is 2700 m.
[3] Cohen et al. (2003)
[4] Hewett et al. (2006)
[5] 0.4-6.0 µm atmospheric transmission for Paranal from ESO.
UKIDSS Y RSR curve is provided in Hewett et al. (2006), which is already photonormalized and includes an atmosphere appropriate for Mauna Kea.
We also consider the the unfortunately named Z filter used at Subaru/IRCS and
Keck/NIRC2, which is actually in the Y window rather than in the traditionally
optical Z/z band. To add to the confusion the filter has been labeled with a lowercase z, which is how it is referred to in Currie et al. (2011a), but the scanned filter
curves and Alan Tokunaga’s website1 indicate that it was meant to be capital Z.
In any case, it is a narrow version of the Y filter of Hillenbrand et al. (2002). Here
we follow Liu et al. (2012) and refer to it as z1.1 to emphasize its location in the Y
window. We used the same atmospheric assumptions as for the MKO system (see
below).
The VisAO YS (Y-short) passband is defined by a Melles-Griot long-pass dichroic
filter at ∼ 950µm (LPF-950) on the blue side, and limited by CCD QE (∼ 1.1µm)
on the red side. This places the YS filter on the blue edge of the Y atmospheric
window. We convolved the transmission curve from the manufacturer catalog with
the quantum efficiency (QE) for our EEV CCD47-20 with near-IR coating, and
1
http://www.ifa.hawaii.edu/~tokunaga/MKO-NIR_filter_set.html
195
included the effects of 3 Al reflections. We used the ATRAN model atmosphere
(Lord, 1992), provided by Gemini Observatory 2 , for Cerro Pachon with 2.3 mm
precipitable water vapor (PWV). Cerro Pachon, ∼ 2700m, is slightly higher than
the Magellan site at Cerro Manqui, ∼ 2380m (D. Osip, private communication), so
this will somewhat underestimate atmospheric absorption.
B.1.2 The 2MASS System
The 2MASS J, H, and KS transmission and RSR profiles were collected from the
2MASS website3 . The RSR profiles are from Cohen et al. (2003). They used an
atmosphere based on the PLEXUS model for 1.0 airmass. This model does not use
a parameterization corresponding directly to PWV, but according to the website it
is equivalent to 5.0 mm PWV.
B.1.3 The MKO System
We used the Mauna Kea filter profiles provided by the NSFCam website4 for the
MKO J, H, KS , and K passbands. According to Alan Tokunaga’s website these
correspond to the 1998 production run of these filters. We again used the ATRAN
model atmosphere from Gemini, now for Mauna Kea with 1.6 mm precipitable water
vapor (PWV) at 1.0 airmass.
B.1.4 The NACO System
We obtained transmission profiles for NACO from the instrument website5 . We used
the “Paranal-like” atmosphere provided by ESO6 , which is for 1.0 airmass and 2.3
mm PWV. The NACO filters are close to the 2MASS system. As shown in Figures
B.2 through B.4 there are subtle differences, which are somewhat more pronounced
once the atmosphere appropriate for each site is included.
2
http://www.gemini.edu/?q=node/10789
http://www.ipac.caltech.edu/2mass/releases/allsky/doc/sec6_4a.html
4
http://irtfweb.ifa.hawaii.edu/~nsfcam/filters.html
5
http://www.eso.org/sci/facilities/paranal/instruments/naco/inst/filters.html
6
http://www.eso.org/sci/facilities/eelt/science/drm/tech_data/data/atm_abs/
3
196
Rel. Spectral Response
Norm. Transmission
1.0
Y
IRCS z1.1
VisAO YS
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
0.8
0.9
1.0
λ [µm]
1.1
1.2
Figure B.1 Comparison of filters in the Y atmospheric window. The top panel shows
the curves prior to applying the atmosphere and photo-normalizing. The Y curve in
the top panel is from Hillenbrand et al. (2002). The bottom panel shows the curves
after being multiplied by atmospheric transmission and converted to RSR, and in
the case of Y itself this is the UKIDSS curve from Hewett et al. (2006).
B.1.5 The NICI System
Profiles for the NICI filters were obtained from the instrument websites for NICI7
and NIRI8 . The Cerro Pachon ATRAN atmosphere was used, with 1.0 airmass
and 2.3 mm PWV. The NICI J, H, and KS bandpasses are intended to be in the
MKO system, but due to differences in the altitude and transmission between Cerro
Pachon and Mauna Kea, as well as subtle differences between the filter profiles we
used, there are noticeable differences in the filters. As we will see these can be
appreciable for cool brown dwarfs.
7
8
http://www.gemini.edu/sciops/instruments/nici/
http://www.gemini.edu/sciops/instruments/niri/
197
Rel. Spectral Response
Norm. Transmission
1.0
2MASS
MKO
NACO
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
1.1
1.2
λ [µm]
1.3
1.4
1.5
Figure B.2 Comparison of filters in the J atmospheric window. The top panel shows
raw transmission profiles, and the bottom shows our final RSR curves.
Rel. Spectral Response
Norm. Transmission
1.0
2MASS
MKO
NACO
NICI
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.4
1.5
1.6
1.7
λ [µm]
1.8
1.9
2.0
Figure B.3 Comparison of filters in the H atmospheric window. The top panel shows
raw transmission profiles, and the bottom shows our final RSR curves.
198
Rel. Spectral Response
Norm. Transmission
1.0
2MASS
MKO
NACO
NICI
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.9
2.0
2.1
λ [µm]
2.2
2.3
2.4
Figure B.4 Comparison of filters in the K atmospheric window. The top panel shows
raw transmission profiles, and the bottom shows our final RSR curves.
B.2 Synthetic Photometry
Having collected or synthesized RSR profiles for each bandpass, we next proceed to
calculate various quantities of interest, and ultimately fluxes, in each. The effective
wavelength λ0 of each filter is calculated as
R∞
λR(λ)dλ
λ0 = R0 ∞
R(λ)dλ
0
where T (λ) is filter RSR. The effective width ∆λ, such that
Z ∞
Fλ (λ)R(λ)dλ
Fλ (λ0 )∆λ =
0
was also calculated, where Fλ is the flux in the bandpass. Finally we integrated
the filter profiles with the HST CALSPEC spectrum of Vega from Bohlin (2007) to
determine the flux densities of a 0 mag star in each filter. These calculations are
summarized in Table B.2.
Now to calculate the magnitude of some object with a spectrum given by Fλ, obj
199
Table B.2 Synthetic Photometric System Characteristics
Filter
Y Band
VisAO YS
MKO Y
IRCS z1.1
J Band
2MASS J
MKO J
NACO J
H Band
NICI CH4,1%S
MKO H
2MASS H
NACO H
NICI H
K Band
MKO KS
NACO KS
2MASS KS
NICI KS
MKO K
NICI Kcont
λ0
(µm)
∆λ
( µm)
0 mag Fλ
(10−6 ergs/s/cm2 /µm)
0.986
1.032
1.039
0.087
0.101
0.049
6.91
5.99
5.89
1.241
1.249
1.256
0.163
0.145
0.192
3.23
3.11
3.1
1.584
1.634
1.651
1.656
1.658
0.017
0.277
0.251
0.308
0.270
1.31
1.22
1.18
1.18
1.18
2.156
2.160
2.166
2.176
2.206
2.272
0.272
0.323
0.262
0.268
0.293
0.038
0.45
0.45
0.443
0.436
0.414
0.366
200
we calculate
R∞
R(λ)Fλ, obj dλ
0
m = −2.5 log R ∞
R(λ)Fλ, vega dλ
0
(B.2)
using the Vega spectrum of Bohlin (2007).
B.3 Photometric Conversions
To quantify the differences between these systems, and to accurately compare results for objects with measured in the different systems, we used the library of brown
dwarf spectra we compiled from various sources (described in Chapter 4). We calculated the magnitudes in each of the various filters and then fit a 4th or 5th order
polynomial to the results. Our notation is
m1 − m2 = c0 + c1 SpT + c2 SpT 2 + c3 SpT 3 + c4 SpT 4 + c5 SpT 5 .
(B.3)
where SpT is the spectral type given by
SpT = 0...9, for M 0...M 9
SpT = 10...19, for L0...L9
SpT = 20...29, for T 0...T 9
We provide the coefficients determined in this manner for a variety of transformations in Table B.3. Next we discuss some of the results.
B.3.1 Converting 2MASS to MKO
To begin with, we consider the conversions from 2MASS to MKO. There are many
objects with measurements in both systems, which allows us to directly compare
our synthetic photometry to actual measurements. We here use the compilation
of Dupuy and Liu (2012). This also allows a comparison to the previous work of
Stephens and Leggett (2004), who employed similar methodology to ours but with
201
fewer objects. The results are shown graphically in Figure B.5. In all three bands
our synthetic photometry and fit appear to be a good match to the measurements.
In J our results appear to be an improvement over Stephens and Leggett (2004),
and in H and K either fit appears to be reasonable. These results give confidence
that our synthetic photometry reproduces the variations in these systems reasonably
well.
B.3.2 Y Band Conversions
We analyze the variation with spectral type of between the YM KO and the VisAO
YS and IRCS/NIRC2 z1.1 filters. In our analysis we did not use these conversions,
but provide them here to further characterize the bandpasses.
B.3.3 J Band Conversions
We present the relationship between the JM KO and the JN ACO bandpasses in Figure
B.7. Note that the differences are quite significant for later brown dwarf spectral
types.
B.3.4 H Band Conversions
The shifts in the various H bandpasses are presented in Figure B.8. These shifts
are generally small, and within the errors of typical exoplanet photometry. Note,
however, the large shift for later spectral types between the narrow band CH41%S
filter of NICI.
B.3.5 K Band Conversions
We show the differences in the various KS bandpasses in Figure B.9. These conversions result in small shifts for the M and L dwarfs, but there are more noticeable
differences for T dwarfs.
202
0.5
0.2
Measured
Binned−Measured
Synthetic
Poly Fit
Stephens & Leggett 04
0.4
Measured
Binned−Measured
Synthetic
Poly Fit
Stephens & Leggett 04
0.1
H2M−HMKO
J2M−JMKO
0.3
0.2
0.1
0.0
−0.1
∆(H2M−HMKO)
∆(J2M−JMKO)
0.0
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
−0.2
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
4
6
8 T0
Spectral Type
2
4
6
8
Y0
0.2
Measured
Binned−Measured
Synthetic
Poly Fit
Stephens & Leggett 04
KS,2M−KMKO
0.1
0.0
∆(KS,2M−KMKO)
−0.1
−0.2
0.05
0.00
−0.05
M2
4
6
8
L0
2
Figure B.5 2MASS to MKO Conversions. Here we show our synthetic photometry
(red points) in the 2MASS and MKO systems and compare to the measurements
made in the 2 systems (crosses, from Dupuy and Liu (2012)). We also plot the binned
median of the measurements. Our polynomial fit is shown as the solid black line.
For comparison we show the fit determined by Stephens and Leggett (2004), who
also used synthetic photometry, albeit with fewer objects. Our fit to the synthetic
photometry appears to be a better match to the actual measurements in J. In the H
and K bands both fits appear to be acceptable, with Stephens and Leggett (2004)
being somewhat better for M and L dwarfs in H. The coefficients of our fits are given
in Table B.3. These results give confidence in our synthetic photometry.
−0.0
0.25
−0.2
0.20
−0.4
0.15
YMKO−z1.1
YMKO−YS
203
−0.6
0.05
−1.0
0.00
−1.2
0.25
−0.05
∆(YMKO−z1.1)
∆(YMKO−YS)
−0.8
0.10
0.00
−0.25
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
Figure B.6 Here we show the relationships between the YM KO and the VisAO YS
and IRCS/NIRC2 z1.1 filters. The coefficients of our fits are given in Table B.3.
JNACO−JMKO
0.3
0.2
0.1
∆(JNACO−JMKO)
0.0
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
Figure B.7 Here we show the relationship between the JM KO and the JN ACO bandpasses. The coefficients of our fit are given in Table B.3.
0.02
0.10
0.00
HNICI−HMKO
0.15
0.05
−0.02
0.00
−0.04
−0.05
−0.06
∆(HNICI−HMKO)
∆(HNACO−HMKO)
HNACO−HMKO
204
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
0.05
0.00
−0.05
Y0
M2
0.15
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
1.2
1.0
0.10
HNICI−CH4,1%S
HNACO−HNICI
0.8
0.05
0.00
0.6
0.4
0.2
∆(HNACO−HNICI)
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
∆(HNICI−CH4,1%S)
0.0
−0.05
−0.2
0.05
0.00
−0.05
M2
Figure B.8 Here we show the relationship between the HM KO , HN ACO , and HN ICI
bandpasses. These conversions are generally small, and within the errors of typical
exoplanet photometry. We also compare the HN ICI filter and NICI’s CH4,1%S narrow
band filter, which can have dramatic shifts for the T dwarfs. The coefficients of our
fits are given in Table B.3.
205
0.10
−0.00
KS,MKO−KS,NACO
KS,2M−KS,mko
0.05
0.00
−0.05
−0.10
−0.10
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
∆(KS,MKO−KS,NACO)
∆(KS,2M−KS,MKO)
−0.05
−0.15
0.05
0.00
−0.05
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
M2
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
4
6
8 T0
Spectral Type
2
4
6
8
Y0
0.12
0.04
0.10
0.08
KS,NACO−KS,NICI
KS,MKO−KS,NICI
0.02
0.00
−0.02
0.00
0.05
0.00
−0.05
4
6
8
L0
2
4
6
8 T0
Spectral Type
2
4
6
8
Y0
4
6
8
L0
2
∆(KS,NACO−KS,NICI)
∆(KS,MKO−KS,NACO)
0.04
0.02
−0.04
M2
0.06
−0.02
0.05
0.00
−0.05
KS,NICI−Kcont
0.0
−0.5
−1.0
∆(KS,NICI−Kcont)
−1.5
−2.0
0.05
0.00
−0.05
M2
Figure B.9 Here we show the relationship between the KS,2M ASS , KS,M KO , KS,N ACO ,
and KS,N ICI bandpasses. These corrections are generally small, but for later T
dwarfs begin to be significant. We also compare the KS,N ICI filter and NICI’s Kcont
narrow band filter. Note, the large shift for later spectral types in this filter is in
the opposite direction (brighter) than for the CH41%S filter (fainter) of NICI. The
coefficients of our fits are given in Table B.3.
Table B.3 Photometric conversion coefficients.
Filters
YM KO − YS
Y − z1.1
J2M − JM KO
JN ACO − JM KO
H2M − HM KO
HN ACO − HM KO
HN ICI − HM KO
HN ACO − HN ICI
HN ICI − CH4,1%S
KS,2M − KM KO
KS,2M − KS,M KO
KS,M KO − KS,N ACO
KS,M KO − KS,N ICI
KS,N ACO − KS,N ICI
KS,N ICI − Kcont
c0
0.0664
0.00226
-0.0281
-0.0866
0.00165
-0.0553
-0.0172
-0.0381
-1.23
-0.313
0.027
-0.0433
-0.0371
0.00619
1.05
c1
−0.0671
0.00727
0.02
0.0334
-0.00858
0.0157
0.000395
0.0153
0.671
0.145
-0.0154
0.0211
0.0214
0.00025
-0.517
c2
0.00423
−0.000671
-0.00159
-0.0032
0.000398
-0.00184
-0.000389
-0.00145
-0.147
-0.0227
0.00226
-0.00424
-0.00294
0.00131
0.107
c3
−4.19 × 10−5
2.37 × 10−5
6.16 × 10−5
0.00014
−1.02 × 10−5
8.61 × 10−5
2.25 × 10−5
6.36 × 10−5
0.0159
0.00167
-0.00017
0.00034
0.000214
-0.000125
-0.00988
c4
−4.88 × 10−6
−7.09 × 10−8
−5.51 × 10−7
−1.78 × 10−6
1.68 × 10−7
−1.24 × 10−6
−3.14 × 10−7
−9.23 × 10−7
-0.000908
−5.79 × 10−5
6.08 × 10−6
−1.23 × 10−5
−7.65 × 10−6
4.6 × 10−6
0.000424
c5
8.48 × 10−8
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
7.41 × 10−7
−7.75 × 10−8
1.59 × 10−7
9.92 × 10−8
−6 × 10−8
−6.91 × 10−6
σ
0.048
0.012
0.012
0.015
0.008
0.012
0.008
0.007
0.037
0.013
0.006
0.007
0.005
0.007
0.057
206
207
APPENDIX C
FOUR DECADES OF IRC +10216: EVOLUTION OF A CARBON RICH DUST
SHELL RESOLVED AT 10µM WITH MMT ADAPTIVE OPTICS AND
MIRAC4
C.1 Introduction
This appendix has previously been published in the Astrophysical Journal (Males
et al., 2012b). This research formed part of my 2nd year project. It is included here
mainly to demonstrate that AO works at thermal wavelengths, and that we have
experience working with challenging thermal backgrounds.
C.1.1 The carbon star IRC +10216
When stars of low to intermediate mass are in the last stages of nuclear burning on
the asymptotic giant branch (AGB) of the Hertzsprung-Russel (HR) diagram, they
are typically characterized by high luminosity, which varies with long periods (1 −
2yrs), and mass loss. The high mass loss rates, up to Ṁ ∼ 10−4 M⊙ yr−1 , ultimately
lead to the termination of nuclear burning and produce dusty, often optically thick,
circumstellar envelopes (CSEs) which provide one of the key observational features
of AGB stars. Of particular concern here, the CSE is often the dominant source of
light in the near and mid-infrared (IR) and contains much information about the
evolution and mass loss history of the enshrouded star. For thorough treatments of
AGB stars and their evolution see Habing and Olofsson (2003) and Herwig (2005),
and references therein.
The carbon star IRC +10216 (CW Leo) is perhaps the best studied example of
an AGB star. Since its discovery by the 2.2 µm survey in 1969 (Becklin et al., 1969),
IRC +10216 has been recognized as a star enshrouded by a thick CSE. It exhibits
large (> 2X) changes in luminosity over its 649 day cycle (Le Bertre, 1992) and is
208
extremely bright in the mid-IR (> 104 Jy). IRC +10216 is classified as a carbon
star (Herbig and Zappala, 1970), implying that the ratio of carbon to oxygen in its
photosphere is greater than 1. It is believed to be in the final transitional stage
between the thermal pulse (TP) AGB and the post-AGB/planetary nebula stage
(Skinner et al., 1998; Osterbart et al., 2000). More recently Melnick et al. (2001)
reported the detection of warm water vapor in the CSE of IRC +10216, and Decin
et al. (2010) have reported the detection of many water lines in the CSE by the
Herschel satellite (Pilbratt et al., 2010).
IRC +10216 is clearly a fascinating and well studied object, and it is impossible
to fully review the extensive literature on it here. As such we focus mainly on the
N band atmospheric window, which is bounded by water vapor at λ . 8µm and
CO2 at λ & 14µm, and on high-spatial resolution imaging and interferometry of the
CSE. In carbon stars, the N-band spectrum usually shows the emission feature of
SiC.
C.1.2 SiC dust
Around 40 years ago the production of SiC (Friedemann, 1969; Gilman, 1969) and
the presence of its emission feature near 11µm (Gilra, 1971) were predicted. This
feature was then discovered in the N band spectra of carbon stars (Hackwell, 1972),
including in IRC +10216 by Treffers and Cohen (1974, hereafter TC74). In this
paper we present observational evidence that either the spectroscopic SiC feature
in IRC +10216, or the underlying continuum, has undergone a significant change
in the last 15 to 20 years, so we will briefly discuss some of the previous work
attempting to connect the properties of this feature to the evolutionary state of
the underlying AGB stars. The Infrared Astronomical Satellite Low-Resolution
Spectrometer (IRAS/LRS) provided a wealth of data in the mid-IR spectral region,
including a catalog of AGB star spectra. These data have been used extensively
to study the ∼ 11µm SiC feature1 of carbon stars, generally finding a positive
1
We adopt the nomenclature “∼ 11µm” of Speck, Thompson, and Hofmeister (2005) to indicate
the varied peak wavelengths of this feature.
209
correlation between dust continuum temperature and the strength of the emission
peak (Baron et al., 1987; Chan and Kwok, 1990; Sloan et al., 1998).
A common feature of these efforts has been an attempt to relate the SiC feature
and other characteristics of the mid-IR dust spectra to the long term evolution
of the host AGB star. Thompson et al. (2006) provide a useful review of this
work, and use the more recent Infrared Space Observatory (ISO, Kessler et al.,
1996) Short Wavelength Spectrometer (SWS, ISO Handbook, Vol V) data set to
further investigate correlations between the SiC peak strength, peak wavelength,
and dust continuum temperature. They ultimately conclude that there are no useful
correlations, and blame poor continuum fitting for the previous results.
C.1.3 IRC +10216 in the spatial domain
IRC +10216 has also provided many fascinating results in the spatial domain. Given
its extreme brightness in the mid-IR, it was an early target for interferometry, and
has more recently been subject to intense study in the near-IR. At wider spatial
scales, visible wavelength imaging has shown an extended dusty envelope composed
of multiple shells. We will now briefly review some of these results, with particular
interest in their implications for the process and variability of mass loss from IRC
+10216.
Deep optical observations have shown that IRC +10216 is surrounded by multiple
dusty shells, which can be seen scattering ambient galactic light out to separations of
∼ 200”. Mauron and Huggins (1999) analyzed these shells in B and V band images
from the Canada France Hawaii Telescope (CFHT) on Mauna Kea and concluded
that some process modulates the mass loss on a timescale of 200-800 years, and later
found evidence for timescales as short as 40 years (Mauron and Huggins, 2000) using
Hubble Space Telescope (HST) imaging. Leão et al. (2006) used deep Very Large
Telescope (VLT) V band images to show that the shells can be resolved into even
smaller structures. These shells appear to be only approximately spherical and are
azimuthally incomplete, indicating that the mass loss is not isotropic. HST imaging
of the inner ∼ 10” shows a nearly bipolar structure, reminiscent of the typical but
210
poorly understood structure of planetary nebulae (Skinner et al., 1998).
High spatial resolution observations in the near-IR have produced a fascinating picture of the inner portions of the dusty envelope around IRC +10216 (which
are invisible in the optical). Using speckle-masking interferometry in the K’ band
Weigelt et al. (1998) found the inner 1/2” to be composed of at least 5 distinct
clumps, indicating an inhomogeneous recent mass loss history. Haniff and Buscher
(1998) then presented diffraction limited imaging data which showed that between
1989 and 1997 these clumps had undergone significant evolution, exhibiting relative motion and some either appearing or becoming brighter. Tuthill et al. (2000)
showed significant relative motion of various components of the dust, with possible
acceleration, based on 7 epochs of sparse aperture mask interferometric imaging in
K band using the Keck I telescope2 . Interestingly these authors found no evidence
for new dust production during these observations.
Relative motion within the inner regions of the dust shell were also found by Osterbart et al. (2000), who argued that this evolution was not related to the ∼ 2 year
luminosity cycle in any simple way. In a related effort, extensive radiative transfer
modeling was conducted by Men’shchikov et al. (2001) taking into account much of
the archival multi-wavelength data set (including spectral and spatial information).
Men’shchikov et al. (2002) used their model to explain the time evolution reported
by Osterbart et al. (2000). A key conclusion from this study is that since its discovery IRC +10216 has been undergoing an intense period of mass loss, probably
starting ∼ 50 years earlier. They also concluded that the mass loss rate had recently
increased.
IRC +10216 has been repeatedly studied by interferometers in the mid-IR. McCarthy et al. (1980, hereafter MHL80) measured visibilities at 2.2, 3.5, 5.0, 8.4, 10.2,
11.1, 12.5 and ∼ 20µm, at several epochs and position angles (PAs). They found
evidence for asymmetry at the short wavelengths, indicating an elongation along PA
∼ 25o , which matched the early optical images and has been confirmed repeatedly
by later observations (Skinner et al., 1998; Leão et al., 2006). No evidence of this
2
See the movie: http://www.physics.usyd.edu.au/~gekko/irc10216.html
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elongation was found at 11.1µm however. It was also noted that apparent size, but
not morphology, changes with photometric phase.
This object has also been observed at ∼ 11µm using the UC Berkeley Infrared
Spatial Interferometer (ISI). Danchi et al. (1990) generally confirmed the large
change in visibilities with photometric phase found by MHL80, and argued that
dust was being formed much closer to the star than previous studies had found.
Using data from the ISI taken ∼ 10 years later, Monnier et al. (2000) found that the
inner radius of the dust had moved away from the star. This result was based on
model fits to the visibilities, and led them to conclude that no new dust was being
formed for most of the 1990’s. This appears to contradict the radiative transfer
based mass loss predictions of Men’shchikov et al. (2002). Most recently the ISI
detected some asymmetry at 11.15µm using baselines of up to 12m (Chandler et al.,
2007).
C.1.4 New results from the MMT
Here we present new spatially resolved mid-IR photometry and spectroscopy of IRC
+10216 with high resolution, AO corrected, spatial information, obtained at the
MMT on Mt. Hopkins, AZ, in 2009 and 2010. We first describe our observations and
data reduction, paying particular attention to the correction needed when observing
an extended object with a spectroscopic slit and a diffraction limited beam. We also
review nearly four decades of measurements of the spectrum of IRC +10216. We
then discuss our new results in context with the previous work on IRC +10216.
C.2 Observations and data reduction
We observed IRC +10216 at two epochs separated by approximately 1 year, using the
4th generation Mid-Infrared Array Camera (MIRAC4), fed by the MMT Adaptive
Optics (MMTAO) thermally efficient adaptive secondary mirror (Wildi et al., 2003).
Infrared light first passes through the Bracewell Infrared Nulling Cryostat (BLINC,
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Hinz et al. (2000))3 , with visible light being reflected to the visible wavelength
wavefront sensor of the AO system. This system routinely achieves ∼ 98% Strehl
ratios at 10µm (Close et al., 2003), and can super-resolve structure smaller than its
diffraction limit (Biller et al., 2006; Skemer et al., 2008). In addition to imaging,
MIRAC4 has a grism spectroscopy mode described in Skemer et al. (2009).
C.2.1 2009 bandpass photometry
We observed IRC +10216 on 13 Jan 2009 UT with the imaging mode of
BLINC/MIRAC4 using its fine plate scale (0.055 arcsec/pixel). Conditions were
photometric, with excellent seeing, estimated to be better than FWHM=0.5” at V
from the AO acquisition camera. To avoid saturation from the extremely bright
source (∼40,000Jy) we read out MIRAC4’s array with a 0.008s frame time. IRC
+10216 is optically faint (R mag > 15), and we were unable to close the MMTAO
loop. As a result these observations were taken with the adaptive secondary in its
static position, which uses a pre-determined set of actuator commands to hold the
mirror shape. We took data in the typical fashion for MIRAC4: chopping using
the BLINC internal chopper and telescope nods in the perpendicular direction. In
the case of IRC +10216 we set the nod amplitude to be large enough that only one
pair of chops was on the detector since the object was expected to be significantly
extended. Observations of the standard star µ UMa were taken immediately after
IRC +10216 in identical fashion, but for µ UMa the nod amplitude was set so that
all four positions were on the detector to increase observing efficiency. Table C.1
lists the filters and airmasses for these observations.
The data were reduced by first applying a custom artifact removal script developed for the MIRAC4 detector (Skemer et al., 2008), which also performs the
background subtraction of the chop-nod sets. Each frame was then inspected to
look for bad chops (caused by the chopper sticking) and excessive pattern noise
from the detector. Frames with these problems were discarded. Photometry was
3
Further
information
on
MIRAC4
http://zero.as.arizona.edu/miracblinc
and
BLINC
can
be
found
at
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conducted on the individual images, rather than registering and combining, to allow an empirical estimation of the uncertainties from the artifact reduction and
background subtraction processes. We used the DAOPHOT package in IRAF, and
selected the best photometric aperture for the standard and object based on the
mean “curve of growth” for counts vs. aperture radius. Since IRC +10216 is extended, the aperture where the curve flattened was always much wider than for the
PSF.
Following Skemer et al. (2010) we applied a telluric correction to the photometry using transmission curves provided by Gemini Observatory4 calculated with the
ATRAN model atmosphere code (Lord, 1992), and an estimate of 3mm precipitable
water vapor (PWV) and the airmass of the observations. The PWV assumption
is supported by contemporaneous PWV measurements taken on Kitt Peak (74 km
west-northwest), and as noted in Skemer et al. (2010) the correction at these wavelengths is generally insensitive to PWV. In the 9.79µm filter the correction was
+2.5% (due to telluric ozone), and in all others it was < 1%. Finally, we normalized
the photometry by the Cohen et al. (1996) flux for µ UMa. The results are presented
in Table C.2.
The uncertainty in our photometry was calculated in similar fashion to that
used for grism spectroscopy in Skemer et al. (2010) and below (Section C.2.2),
with the exception that for bandpass photometry we did not assume a correlated
global uncertainty. As discussed above we performed photometry on individual
frames, which provides an empirical measurement uncertainty for both the object
and standard. Thus our measurement uncertainty includes the random effects of
detector artifacts and our removal procedure. We then add in quadrature the mean
uncertainty in the µ UMa standard flux across the filter bandpass from Cohen et al.
(1996), and use the telluric calibration uncertainties from Skemer et al. (2010),
which were measured the following night. The values used and the final total 1σ
uncertainty are included in Table C.2.
When compared to our (normalized) grism spectrum from a year later, the pho4
http://www.gemini.edu/sciops/telescopes-and-sites/observing-condition-constraints/
214
tometry from 9.8µm to 12.5µm matches very well. In the 8.7µm filter, however,
there is a ∼ 30% discrepancy between the bandpass photometry and the grism
data, as well as with archival data. We are suspicious of this data point since it
represents a high counts regime of the detector not well understood, but we do not
yet have any specific reason to discard it. We discuss this further in Appendix A.
C.2.2 2010 grism spectroscopy
We observed IRC +10216 nearly one year later on 1 Jan 2010, UT in the grism
spectroscopy mode of MIRAC4, using a 1” slit. With this configuration MIRAC4
has a spectral resolution of R ∼ 125 and a spatial resolution of λ/D ∼ 0.32” at
10µm. The detector wavelength scale was calibrated at the telescope using a well
characterized polystyrene sample and fitting a quadratic function to the measured
centroids of features in the spectrum. The coarse platescale used for grism work was
measured using the binary α Gem on 2 Jan 2010, UT and elements from the USNO
Sixth Catalog of Orbits of Visual Binary Stars5 (Hartkopf et al., 2001). We found
a value of 0.107”/pixel.
Conditions on 1 Jan 2010 UT were photometric. Through a combination of
excellent seeing conditions and IRC +10216 being near its brightness maximum, we
were able to lock the MMTAO system on IRC +10216 with a loop speed of 25Hz.
We set the frame time to 0.008s, and to ensure that we could take advantage of the
diffraction limited information being delivered by the MMTAO system we read out
each 0.008s frame. Due to its extreme brightness at 10µm only a few of these short
frames were needed to provide sufficient S/N, and this data taking mode allows us
to reject frames with bad slit alignment due to residual tip/tilt errors and frames
with excessive artifacts.
Observations of the standard µ UMa were challenging for nearly opposite reasons.
Ordinarily one tries to operate the AO system with identical parameters between
PSF and science object, but in the optical µ UMa saturated the wavefront sensor
(WFS) at speeds slower than 100Hz. At 10µm µ UMa is a factor of ∼ 500 fainter
5
http://ad.usno.navy.mil/wds/orb6.html
215
(even though it is one of the brightest 10µm standards), so longer integrations are
required to efficiently build S/N. Table C.1 lists the details of these observations.
Determining Strehl ratio for these observations is problematic. We did not take
data in the imaging mode (other than for slit alignment) because of the limited time
(∼ 1 hr) that conditions were good enough to lock the MMTAO system on this faint
star. Without two dimensional imaging data it is difficult to directly measure Strehl
ratio from our PSF observations. In addition, since we necessarily operated the AO
system with different parameters, any such measurement would not apply to IRC
+10216. At 10µm the dominant wavefront error term will be from loop delay (servo
error), even on an optically faint target such as IRC +10216. Based on the very
high Strehl ratios routinely achieved by MMTAO and MIRAC4 (98%), the WFS
integration times (40ms), and our use of short exposures, we estimate the Strehl
ratio of our IRC +10216 observations to be ∼ 80%.
The Moon moved closer to IRC +10216 on the following night (2 Jan) and seeing
was somewhat worse, so we were unable to lock MMTAO on IRC +10216. Though
we took seeing limited data, we find that the good spatial information provided
by AO is necessary to adequately correct for differential slit loss between the point
source standard and a resolved IRC +10216. We did, however, take AO-on spectra
of the standards µ UMa and β Gem, which we use to calibrate our slit loss correction
procedure. Details of these observations are also included in Table C.1.
Reduction of grism data is similar to the imaging procedure described above,
except that our data were taken with nods only, as the chopper is unnecessary for
very bright sources and can sometimes cause slit-misalignment. We used the same
artifact removal script, and the images at each position angle were registered and
median combined. Our fully reduced images of IRC+10216 and µ UMa are presented
in Figure C.1.
Our first step in analyzing the data was to fit the spatial profiles of the PSF and
IRC +10216 at each detector row. We found that a Lorentzian is a good fit for IRC
+10216 out to wide separations from the peak, generally achieving χ2ν < 2 across
the entire wavelength range. As expected a Gaussian was good for the core of the
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Airy pattern of our PSF standard. We used profile plots (an example of which is
shown in Figure C.2) to assess the quality of this analysis. The chosen functions
describe the core of the objects well, and we find that the Lorentzian full-width at
half-maximum (FWHM) is a meaningful proxy for the size of IRC +10216 relative
to the PSF. Based on this conclusion we show FWHM vs. wavelength in Figure C.3,
where we see that the PSF was essentially diffraction limited. The comparison is
not perfect due to the difference in AO system parameters between the two objects,
but it is clear that IRC +10216 is extended. It is also apparent that the dependence
of size on wavelength is much more complicated than mere λ/D scaling due to
diffraction.
Regarding data reduction, an important conclusion to draw from Figure C.3 is
that one cannot simply divide by a point source standard to calibrate this extended
object when using a slit, as a different amount of light is lost due to the slit, and
this effect depends on wavelength in a non-analytic way. To quantify the effect of
the slit we constructed a surface of revolution for IRC +10216 at each wavelength
using the 1-D spatial profile. We then calculated the fraction of flux enclosed by
the 1” slit, taking into account the width of the aperture used to extract flux at
each wavelength. The results of these calculations are shown in Figure C.4, for each
position angle.
For the PSF, in addition to the photometric standard taken on 1 Jan, we used
the AO-on standard observations from the following night in order to improve S/N.
Each standard was analyzed independently, then we took the median of the results
at each detector row (i.e. wavelength). We compare the outcome of this procedure
to that expected based on the theoretical Airy pattern for the MMT, which we
processed in similar fashion, in Figure C.4.
To correct for the differential slit-loss, we calculate the slit-loss correction factor
(SLCF) as the ratio of the enclosed flux of the PSF to that of IRC +10216. We
use the theoretically calculated curve for the actual aperture due to the relatively
noisier empirical results for the PSF. We use the average of the IRC +10216 results
to suppress noise, ignoring the small possible source asymmetry highlighted by our
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FWHM curves since it will cause only a small difference in the results. The resultant
SLCF curve is shown in Figure C.4.
We performed aperture photometry on IRC +10216 and the standard. As with
the bandpass photometry we corrected for airmass and used the Cohen et al. (1996)
standard spectrum of µ UMa to calibrate the results. In the PA=107.0 spectrum we
found a −1.7%/µm slope compared to the other three, likely due to a slight offset
in the slit or possibly a period of worse AO correction. This slope was removed. We
show the raw spectrum at each position angle prior to applying the SLCF in Figure
C.5. Most of the noise in the spectrum appears to be correlated noise, i.e. it is
identical in all four position angles, implying it comes from the standard. A simple
Poisson noise calculation indicates that we should have achieved slightly greater S/N
in the µ UMa observation. The higher noise in the standard is most likely due to its
lower flux relative to the background and the interaction of this with the MIRAC4
detector artifacts.
The SLCF was applied to each PA, and then we re-binned by 7 pixels using the
median as in Skemer et al. (2010). Though this sacrifices some spectral resolution,
it has the benefit of increasing the S/N in each bin and allowing a robust empirical
estimate of the uncertainties. We used the same prescription for calculating local
measurement error as Skemer et al. (2010), estimating the Gaussian 1σ error from
the 2nd and 6th ordered values in each bin. The global bias (correlated error)
reported by Cohen et al. (1996) for µ UMa is negligible, so we add their total
uncertainty in quadrature to the measurement error to calculate the total local
uncertainty.
Global telluric error was estimated from the four spectra, which were taken at
different airmasses. We find results similar to Skemer et al. (2010): 2.7% outside
the ozone feature and 10% inside. We do not include a separate local telluric error
as this will be included in our measurement error. Finally we adopt a 5% global
systematic error term from the SLCF procedure which is based on the scatter in the
IRC +10216 enclosed fraction results.
The fully calibrated and slit-loss corrected results are listed in Table C.3 and
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shown in Figure C.5, along with the local and total uncertainties. The effect of the
SLCF can be seen, in addition to the overall increase in flux the SLCF has effects
on the shape of the spectrum compared to the uncorrected curves. It highlights an
apparent “bump” at ∼ 9µm. The SLCF also reveals a steeper negative slope longer
than ∼ 11µm. This slope matches the bandpass photometry from 2009 very well,
giving us confidence in our slit loss correction procedure. We discuss these features
in more detail in section C.4.
C.3 Archival data
Since its discovery, IRC +10216 has been observed many times, at nearly every
wavelength available to astronomers. In this paper we concentrate mainly on the
region of N-band accessible through the Earth’s atmosphere. Some of the earliest
observations at these wavelengths were of IRC +10216, and it has been observed
regularly over the last four decades, though, ironically, increases in telescope size
and detector sensitivity may be curtailing this somewhat due to the dynamic range
required to avoid saturation. It would be impossible to account for all of the work
done on this object. Here we use a sample of N-band spectra, and several datasets
of bandpass photometry.
We present these data in the context of the light curve parameters of Le Bertre
(1992), where the period P = 649 days, and phase φ = 0 at JD 2447483 (where φ
varies from 0 to 1). Based on the spread reported in the various filters used, and
other determinations (e.g. 638 days in Dyck et al. (1991)), the period is uncertain
by ∼ 10 days. This should be kept in mind when comparing widely separated
measurements, i.e. nearly 21 cycles have occurred between the TC74 data and our
2010 measurement so the relative phase between them could be off by 30% or more.
This is less of a concern for more closely spaced data and we are not attempting a
light-curve analysis here, rather we claim that the ∼ 2 year Mira variability isn’t
the source of the changes we discuss. For our observations the star’s luminosity was
at φ = 0.27 on 13 Jan., 2009 and φ = 0.89 on 1 Jan., 2010, assuming Le Bertre
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(1992)’s parameters.
C.3.1 Introduction to the spectral datasets
Here we collect a sample of N-band spectra, choosing some of the earliest measurements, two space-based observations (IRAS/LRS and ISO/SWS), and a set of
observations taken on the same instrument (CGS3 at UKIRT) repeatedly over a
short period of time. We briefly describe these datasets here and any processing we
did. It is worth noting that none of these observations are affected by slit loss, as
they either used no slit or had large apertures.
The spectrum of Treffers and Cohen
The spectrum of TC74 was taken with a scanning Michelson interferometer (i.e.
a Fourier transform spectrometer (FTS)) on a 2.2m telescope on Mauna Kea on
15 and 16 Feb., 1973 (φ = 0.13). They used the Moon as a telluric standard,
and reported in arbitrary flux per unit wavenumber (Fν ) with a resolution of 2cm−1
(∼ 0.02µm). The gap in the spectral fragments was in the original data, and though
not commented on by TC74 is almost certainly due to the telluric ozone feature.
Below ∼ 8µm the spectrum appears to be unreliable due to telluric water vapor.
The Spectrophotometry of Merrill and Stein
Merrill and Stein (1976, hereafter MS76) used a circular variable filter (CVF) photometer to observe IRC +10216 from Mt. Lemmon, AZ. A date is not given for this
observation, but from the publication date and other dates given in the paper we
can infer that IRC +10216 was observed no later than 1975. Based on information
provided by the anonymous referee we believe the most likely date for this observation was early 1973. We extracted the data from their Figure 2, and converted from
λFλ units to arbitrary Fν .
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The IRAS LRS Spectrum
The IRAS LRS spectrum for IRC +10216 was extracted from a database maintained
by Kevin Volk6 . We spliced the blue and red fragments together and applied a
correction for the spectral shape of the IRAS standard α Tau using the procedure of
Cohen et al. (1992). It is not possible to assign a single epoch to IRAS observations,
so we adopt the range 1 Feb. to 1 Nov. 1983 (φ = 0.74 − 0.16).
The ISO/SWS Spectrum
We retrieved the reduced ISO/SWS observation of IRC +10216 from the ISO
archive7 , taken on 2 June 1996 (φ = 0.24). The ISO data presented in this paper
are from the Highly Processed Data Product (HPDP) set called ‘High resolution
processed and defringed SWS01s’, available for public use in the ISO Data Archive
(Frieswijk et al., 2007). The data we are interested in span detector bands 2C
(7.0-12.0µm) and 3A (12.0-16.5µm) (ISO Handbook, Vol V). Though the pipeline
attempts some defringing in band 3, we applied a 0.01µm binning (averaging) to
the data to reduce fringing, which is especially prominent in band 2C. This spectrum has been published previously by Cernicharo et al. (1999) who used an earlier
reduction pipeline and did not discuss the 8 to 13 µm region.
Spectra from UKIRT
Monnier, Geballe, and Danchi (1998) (hereafter MGD98) obtained spectra of IRC
+10216 at 4 epochs from 1994 to 1996 as part of a survey of variability in late type
stars, using the Cooled Grating Spectrometer 3 (CGS3) at UKIRT on Mauna Kea.
Several stars were used as photometric standards at each epoch. We considered
these measurements separately, and also averaged the 4 spectra for comparison with
our data, first normalizing each to 10.55µm and using 0.1µm bins to compensate for
the slight changes in wavelength scale between observations. The luminosity phases
6
7
http://www.iras.ucalgary.ca/~volk/getlrs_plot.html
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221
of these spectra were φ = 0.38, 0.47, 0.96, and 0.27. MGD98 noted some small
fluctuations in the spectral slope (across the 10µm window) with phase and though
they speculated that the changes were due to a rapidly changing dust condensation
zone, they could not rule out poor calibrations as the cause. We note that their
data from 22 June 1996 matches the 2 June 1996 ISO/SWS data fairly well.
C.3.2 Bandpass photometry archives
Bandpass photometry can provide a useful check on spectra, which can be plagued
by such things as uncertain slopes or slit effects. For these purposes we require
photometry taken in several filters at the same epoch (to within a few days) so that
any apparent changes with wavelength are not caused by the variation in overall
brightness. There are several datasets in the literature which contain measurements
of IRC +10216 across the 10 µm window. We use these primarily to confirm the
normalized shapes of the spectra discussed above, as the large error bars and uncertainties in normalization make epoch to epoch comparisons of the photometry
difficult. In all cases, we used the Vega spectrum of Cohen et al. (1995) to reduce
magnitudes reported in the literature. We describe our normalization method in
detail below.
Strecker and Ney
Strecker and Ney (1974, hereafter SN74) observed IRC +10216 at 5 epochs in 1973
at 8.6, 10.7, and 12.2 µm (as well as other points outside the N band) from the
O’Brien observatory in Minnesota, USA. Their measurements in Jan, Mar and Apr
1973 provide a nearly contemporaneous check on the spectral shape found by TC74,
and provide a useful comparison to the MS76 spectrum. Estimated errors were
reported as ±20%, which make individual points nearly useless for comparing to
spectra. To overcome this we average the three points from early 1973, and the two
points from late 1973, after applying the normalization procedure described below.
We could average all 5, however this method allows for the possibility of short term
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(< 9 months) variability in the spectral shape of IRC +10216.
McCarthy, Howell, and Low
MHL80 reported measurements of IRC +10216’s brightness at many epochs in the
late 1970s, taken on Kitt Peak, Arizona, using 4, 2.3, 1.5, and 1 m telescopes. These
data were taken in support of their interferometric size measurements. At only 2
of these epochs (17 Dec., 1977 and 18 Nov., 1978) were measurements made at
enough points across the 10 µm window to be useful for shape comparisons with
our spectra. We use the MHL80 photometry, with estimated errors of ±10%, for
comparison with the TC74 spectrum.
The Photometry of Le Bertre
Le Bertre (1997, hereafter LB97) obtained bandpass photometry using the European
Southern Observatory 1m telescope at La Silla Observatory, Chile, spanning 19851988. These are the same data used in part in the production or our adopted light
curve parameters in Le Bertre (1992). LB97 used filters with central wavelength of
8.38, 9.69, 10.36, and 12.89 µm and reported errors of 10%, 10%, 10%, and 15%
respectively. These data are used here to compare to the IRAS/LRS spectrum.
TIRCAM
IRC +10216 was observed in January 1993 by Busso et al. (1996) using TIRCAM,
a mid-IR camera equipped with a 10x64 array, on the 1.5m Telescopio Italiano
Infrarosso at Gornergat (TIRGO), Switzerland. The filters used had central wavelengths of 8.8, 9.8, 11.7, and 12.5 µm, with errors of 7%, 7%, 15%, and 15% reported
for IRC +10216. We compare the photometry of Busso et al. (1996) to the UKIRT
spectra of MGD98 and the ISO/SWS spectrum.
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C.3.3 Comparison of Archival Data
Our main reason for including this archival data is comparison with our new results.
First, though, we can compare the various measurements to each other. Have the
changes our measurements reveal been observed before? Are these changes part
of the regular variability of this object? The data sets we have extracted from
the literature were taken at various points in IRC +10216’s two year brightness
variations. To account for this we first normalize the spectra at λ = 10.55µm,
averaging across the MIRAC4 10.55µm filter bandpass. This area appears to have
had a very stable spectral slope throughout the nearly forty years of observations
we consider here.
Normalizing the photometry is a bit more challenging. Each instrument used had
a different photometric system, and authors did not always report results in all filters
at each epoch. Since we are most interested in analyzing the shape of the spectrum
for λ > 11µm, we proceed by first fitting a line to the spectra from 8 − 11µm after
they were normalized to the MIRAC4 10.55µm bandpass. The spectra all appear
to be roughly linear and similar in slope across this region, though with noticeable
variation at λ < 9µm. We then normalize the photometry to this line (which has
F ν(10.55µm) = 1), using the best-fit normalization factor for each epoch. We
also propagate errors from the fitting procedure to the new normalized photometric
points.
In Figure C.6 we show the bandpass photometry of SN74, the FTS spectrum of
TC74, the CVF spectrophotometry of MS76, and the photometry of MHL80. We
also show the spectrum of IRC +10216 in 2010 as measured by MIRAC4 in this work.
For λ . 11µm the photometry appears to agree nicely with the spectra, but from
12 − 13µm it is noticeably brighter in both SN74 and MHL80 - though consistent
with the spectra at the ∼ 2σ level. This could be explained by a slope offset in
the TC74 FTS spectrum, however the MS76 CVF spectrum would not likely have
such an artifact. Given the variability of IRC +10216, variations in spectral shape
hinted at by this plot might be associated with the 649 day cycle of IRC +10216’s
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luminosity. We note, however, that the SN74 and the first three TC74 points were
taken at nearly identical times, and our best guess at the epoch of MS76 indicates
it was taken very close to these data sets as well. This would require rapid short
term variability in the spectral shape over time scales much shorter than the 649
day brightness variation.
A comparison of data from the 1980s is provided in Figure C.7. The photometry
of LB97 and the IRAS/LRS spectrum agree well within the 1σ error, with the
exception of the June 1985 point which appears to have been strongly affected by
atmospheric O3 . As in Figure C.6 we see that the photometry is generally consistent
with the 2010 shape (and that measured by MS76) within the 2σ uncertainty.
We continue our decade by decade comparisons with Figure C.8, which shows
data from the 1990s. In this case the data agree quite well across the entire 10µm
window, and we note especially the agreement between the UKIRT and ISO/SWS
spectra taken twenty days apart in June 1996. These measurements span three and
a half years, and two full 649 day periods, so unlike the previous decades we can say
with some confidence that there is no variation in shape, large enough to explain our
2009/2010 results at λ & 11µm, occurring as part of the regular 649 day variability
of IRC +10216 during this time period.
C.4 Discussion
C.4.1 Changes in the 10 µm spectrum of IRC +10216
Figure C.9 shows a comparison of nearly four decades of N-band spectra of IRC
+10216 with the data normalized to Fν (10.55µm) = 1. We also include our 2009
photometry, which matches our 2010 grism spectrum very well. It is clear that a
significant change at wavelengths longer than ∼ 11µm was recorded in our 2009 and
2010 data when compared to the mid-1990s, and that a similar shape was observed
in the early 1970s. The negative slope of the spectrum has become steeper and the
continuum is lower at wavelengths redder than 13µm. The close match between our
bandpass photometry and grism spectrum gives confidence that this is not merely
225
a calibration error, and since they are taken 1 year apart at different luminosity
phases the shape appears to be stable at the time of our observations.
In Figure C.10 we plot the flux ratio Fν (12.5µm)/Fν (10.55µm) vs. time, where
flux at 12.5 µm was calculated as the mean between 12 and 13 µm for each of the
spectra. This figure illustrates the change in the shape of the spectrum over time.
The change from 1996 to 2009 does not occur as part of the 649 day Mira variability,
as evidenced by the mid 1990s data. We discuss two possible interpretations of this
plot further below.
Monnier et al. (1999) found long term changes in three carbon stars, including
IRC +10216 which had the smallest change. They used the MS76, IRAS/LRS, and
MGD98 data, and reported a change in spectral slope across the 10 µm window
(8 − 13µm) from the early 1970s to 1996. We now see a change in the opposite
direction from 1996 to 2009 in IRC +10216’s spectrum.
Perhaps the simplest interpretation of these results is that we have recorded
an episode of irregular variability (i.e. recurring but not periodic changes) in the
spectrum, rather than a trend. Due to the sparse sampling and relatively long time
periods between measurements (e.g. the gap from 1978 to 1983, or from 1996 to
2009) we can make no statements about how often this irregular variability occurs.
In the case of the 2009-2010 MIRAC4 data this new shape lasts for at least one year,
or half the period. Given the clumpy structure of the CSE (Weigelt et al., 1998),
the anisotropic nature of the mass loss history (Leão et al., 2006), and the rapid
variations seen in the inner regions of the CSE (Haniff and Buscher, 1998; Tuthill
et al., 2000), relatively rapid and irregular variability in IRC +10216’s spectrum
might be expected.
We also consider the possibility that these changes are occurring over a longer
term. Though sparsely sampled in time, figure C.10 has the appearance of a smooth
change over ∼ 40 years. Other circumstantial evidence for the longer term variability
is provided in the findings of previous studies we discussed in section C.1.3. Mauron and Huggins (2000) found evidence for ∼ 40 year modulation in the expanding
dust shells around IRC +10216 from deep V band observations. Men’shchikov et al.
226
(2002) claimed that the current episode of dust production began roughly in the
1950s, and that the mass loss rate had recently increased. Monnier et al. (2000)
claimed that dust production had stopped by the end of the 1990s in contradiction
to Men’shchikov et al. (2002). We won’t attempt to resolve these contradictory
modeling results, but rather take them as evidence that something had changed in
the mass loss rate at the end of the 1990s. This idea, coupled with the correspondence between the periods evident in the V band observations, the hypothesized
start date of the current mass loss episode, and the timing of the changes evident
in the spectrum by 2010, supports the possibility of a longer term change in IRC
+10216.
In any case, we can place the shape of IRC +10216’s N band spectrum in context with other carbon stars using the “Carbon-Rich Dust Sequence” of Sloan,
Little-Marenin, and Price (1998) (hereafter SLMP98). Their system is based on 96
carbon-rich variable stars observed by IRAS/LRS, from which they subtract a 2400K
blackbody to remove the stellar continuum. The blackbody is fit to the wavelength
range 7.67-8.05µm. After subtraction the spectra were normalized, and then were
grouped by inspection according to the shape of the ∼ 11µm SiC feature and the
presence and strength of the 9µm feature (which we acknowledge is likely not real).
In Figure C.11 we show their sequence, formed from averaging and smoothing each
spectrum in the class, as the solid black curves. As we discussed in Section C.1.2,
in light of the results of Thompson et al. (2006) we do not treat this sequence as
reflecting the evolutionary state of these carbon stars. Nevertheless, we have found
the system of SLMP98 to be a useful atlas of the SiC spectra in carbon stars and
as an aid to interpreting our results.
In Figure C.11, we show the IRAS/LRS spectrum of IRC +10216 in red, which
was classified by SLMP98 as “Red”, and cited as the prototype of that class. We also
show our 2010 spectrum in blue, continuum subtracted and normalized according
to the above prescription. In this framework, it appears that the center of the SiC
peak has shifted blue-ward, and the 9µm region is enhanced, which appears to be
true regardless of whether the minimum at ∼ 9.5µm is caused by ozone (it almost
227
certainly is). In 2010, IRC +10216 is a better match for the “Broad 2” (Br2) class
in the SLMP98 system. Even though SLMP98 does not represent an astrophysical
sequence for carbon stars, we see that the shape we observed does occur in other
carbon stars.
Regardless of whether this change occurs irregularly on timescales of a few years,
or represents multi-decade variability, such variability could easily be overlooked in
similar Carbon stars. The SLMP98 system is especially useful here, as it provides
a catalog of spectra and targets for follow-up observations to test this possibility.
We find that the IRAS/LRS spectra of sources RV Cen (Br1) and CR Gem (Br2)
are good qualitative matches for our 2010 MIRAC4 spectrum. We also checked
the SiC feature of LP And, the one other source in the Red classification that was
also observed by ISO/SWS, and found that it does not appear to have changed
between the two observations. All of the “Red” and “Broad” sources deserve future
observations in this wavelength range to check for any irregular variability or longterm changes.
In addition to follow up observations of IRC +10216 and similar carbon stars,
fully understanding the changes reported here will require detailed modeling of the
dusty CSE of IRC +10216. Given the wealth of data on this object and its complex
asymmetric structure, such modeling is beyond the scope of the current paper (see
Men’shchikov et al. (2001) for an example of such a comprehensive effort).
C.4.2 The spatial signature of SiC emission
In Figure C.12 we place our 2010 spectrum and corresponding FWHM measurement on a common wavelength axis. Here we have “deconvolved” IRC +10216 by
subtracting the FWHM of the PSF in quadrature, in order to estimate its intrinsic
size. IRC +10216 exhibits an apparent increase in size, quite separate from the effect of diffraction alone, in the wavelength range of the SiC emission feature. Fully
understanding the spatial signature of the spectral emission feature will require additional observations at different luminosity phases, including 2D imaging, as well
as detailed modeling.
228
A likely interpretation is that we have observed the effect of radiative transfer
through the CSE. SiC has higher opacity at the wavelengths of the feature, hence we
observe photons produced further from the star at those wavelengths, which causes
an apparent increase in size in the feature’s part of the spectrum. The change in
apparent size can be thought of as mapping the optical depth of the CSE as a
function of wavelength.
We can use these results to establish the plausibility of the changes in the spectrum being caused by the outflow of material from the star. If we treat the estimated
intrinsic size at 13µm, ∼ 70AU, as the diameter of the CSE, and take the time for
the changes in the CSE to occur as 12.5 years (1996.5 to 2009), we find an estimated
outflow velocity of 13 km sec−1 . Estimates in the literature for the expansion veloc-
ity of IRC +10216’s CSE range from 12 to 17 km sec−1 (Men’shchikov et al., 2001,
and references therein). Using their model, Men’shchikov et al. (2001) calculated
the deprojected radial velocities of the clumps observed by Osterbart et al. (2000) as
∼ 15km sec−1 . Hence, we find that the changes in the spectrum from 1996 to 2009
can plausibly be explained by evolution of the CSE, and the resultant estimated
outflow velocity is in good agreement with previous estimates.
A comment on the possible asymmetry evident in Figure C.3 should be made.
The FWHM is smaller in the East-West direction than in the North-South direction, roughly indicating an elongation towards the N-NE, exactly as expected from
imaging studies at shorter wavelengths. We are cautious with this result, however.
An important consequence of the profiles of IRC +10216 following a Lorentzian is
that small offsets in the slit will cause changes in the apparent shape of the object.
Whereas when a 2D Gaussian is sliced somewhere off the peak the same parameters
(i.e. FWHM) describe the resulting curve, the same is not true for a Lorentzian.
Since we were not able to repeat the observations at each position angle due to time
limitations, we have no way to estimate the uncertainties in the individual FWHM
curves at different position angles due to slit alignment.
229
C.5 Conclusion
We have presented new photometric and spectroscopic measurements of the wellstudied carbon star IRC +10216 in the N band atmospheric window. When compared to nearly 4 decades of prior observation we find that a significant change
(decrease in brightness) appears to have occurred in the 11 − 13.5µm region of
the spectrum, which includes the SiC emission feature, between 1996 and 2009.
Measurements taken in early 1970s appear to match the 2009/2010 shape, but data
from the 1980s and 1990s does not. We discussed two possible explanations for these
changes. We may have observed an episode of irregular variability distinct from IRC
+10216’s regular ∼ 2 year Mira variability. We also consider it a possibility that we
have observed a long term change occurring over several decades.
Critical to our reduction of the grism spectrum was the stable, high Strehl,
diffraction limited information provided by the MMTAO system, which was needed
to correct for the differential slit loss between the extended source IRC +10216 and
the point source standard. This spatial information, which allows us to analyze size
vs. wavelength, shows that the SiC emission feature has a clear spatial signature in
the dust surrounding IRC +10216. The CSE exhibits an increase in apparent size
of ∼ 30% between 10.2 and 11.6µm compared to the continuum on either side of
the SiC feature. This is likely tracing the higher optical depth due to SiC in the
∼ 70 AU CSE. We used this estimate of the object’s intrinsic size to establish that
the observed spectrum change over 12.5 years can plausibly be associated with the
evolution of the dusty CSE of IRC +10216 given 12-17 km s−1 outflow velocities.
We thank the anonymous referee for a thorough review and for providing insight
into 1970s spectrophotometry, which resulted in a much improved manuscript. We
thank John Monnier for providing data from UKIRT in tabular form. We thank
John Bieging for his comments on a draft of this manuscript. JRM is grateful for the
generous support of the Phoenix ARCS Foundation. AJS acknowledges the generous
support of the NASA GSRP program. This work and LMC were supported by the
NASA Origins program, and the NSF AAG and TSIP programs.
230
C.6 Appendix: The possibly erroneous 8.7µm photometry from 2009
Here we further discuss the MIRAC4 2009 8.7µm photometry data point, which
appears significantly over-luminous in Figure C.9. We see no evidence that a change
in weather or seeing affected the 8.7µm PSF measurement without affecting the
others, and there has so far been no evidence that this filter has a leak during
other BLINC/MIRAC4 observations. Nevertheless, since this data point was not
confirmed by our follow-up grism data and is in a high-flux regime of the detector
not well understood, nor tested by any of our other data, we remain suspicious of
the 8.7µm photometry.
The 8.7µm filter had ∼ 85% higher peak counts than the next brightest 10.55µm
filter (both are above the background), due in part to its width (∼ 40% wider than
10.55µm), as well as differences in detector quantum efficiency. This led us to suspect that the most likely culprit for the discrepancy would be non-linearity of the
MIRAC4 detector, which does exhibit an increase in slope at higher fluxes. As part
of the normal preparation for observing a linearity measurement was performed in
a laboratory at Steward Observatory one week prior to these observations. Unfortunately the bias level appears to have changed in the intervening period, which
prevents us from directly applying the curve to our data. Ordinarily this is of no
consequence when using chop and nod background subtraction, so it was not noticed until long after the observations were complete. We can still perform a worst
case analysis though, and decide what effect, if any, non-linearity has on the 8.7µm
measurement.
We start by assuming that the peak counts value in the 10.55µm image is the last
linear value and that all pixels in the 8.7µm data above this value have a different
slope. With this definition the fraction of flux in non-linear pixels in the 8.7µm
image is FN L = 32%. We can then estimate the change in slope ∆L required to
produce the change in total flux: ∆L =
∆F
.
FN L
Since we are trying to explain a
discrepancy of ∆F = 30% we need a slope change of nearly 100%. Figure C.13
shows the laboratory linearity measurement, along with a fit to the lower portion
231
of the curve. The data have been bias subtracted using the fit. We also show a
line with 12% higher slope, which represents the worst case prior to saturation. The
arrows on the plot indicate the peak counts per read in the 8.7 filter and in the 10.55
filter, where the 8.7 point is from raw counts prior to background subtraction (and
so includes the unknown bias level) and the 10.55 point is background subtracted.
Figure C.13 demonstrates that even in the worst case scenario where every nonlinear pixel has a 12% higher slope, non-linearity can explain at most ∼ 4% of the
excess flux in the 8.7µm filter. We see that the non-linearity in fact likely causes a
less than 1% error. Given this result, we have no reason to reject the 8.7µm data
point out of hand due to non-linearity.
Finally, we note that the archival photometry presented in Section C.3 has several
examples of apparent excesses at ∼ 8.7µm, but such a feature never appears in the
spectra. This points to unquantified systematics in broadband photometry in this
region, which is bounded closely by variable water vapor and ozone. We have tried
applying a correction for differences in spectral shape between object and standard,
and assuming large changes in PWV between object and standard using the ATRAN
model, and so far have not found an explanation for these excesses.
At this point in time, the evidence is inconclusive and we remain suspicious of
the 2009 MIRAC4 8.7µm filter photometry. The change from 2009 to 2010 would
require a significant decoupling at this wavelength from the rest of the spectrum with
regards to the regular 649 day variability. Though we have ruled out non-linearity
as a cause, the per-pixel flux achieved is the highest ever observed with MIRAC4
and we cannot yet rule out changes in the read-out artifacts (e.g. cross-talk) at
higher flux. Further observations, with both bandpass photometry and grism data
taken at the same epoch, are required to fully understand our 2009 data point.
232
Figure C.1 MIRAC4 grism observations of IRC +10216 and µ UMa with the MMTAO loop closed. Here we present ∼ 0.3” diffraction limited spatial information
in the vertical direction and R ∼ 125 spectral information in the horizontal. See
Table C.1 and the text for the details of the observations, especially AO system
parameters which were necessarily different due to the relative optical brightness of
the two sources. Compared to the PSF, IRC +10216 is clearly resolved. See Figures
C.2 and C.3 for the results of extracting profiles in the spatial direction and Figure
C.5 for the fully reduced spectrum of IRC +10216. Note the impact of telluric ozone
absorption between 9 and 10µm, and the decreasing sensitivity starting at 13µm.
233
Figure C.2 Normalized spatial profiles of IRC +10216 and the PSF standard µ UMa,
at three discrete wavelengths (i.e. single detector rows) for a single position angle
(129.4). The data are denoted by x’s for µ UMa and +’s for IRC +10216. The
PSF core is well fit by a Gaussian (dashed lines), as expected for a well corrected
Airy disk (we don’t fit past the first airy minimum, which can be seen along with
the first airy ring at ∼ 0.5”). IRC +10216 is well described by a Lorentzian profile
(solid lines), though there are apparent correlated discrepancies at wider separations.
This result, and similar results for the other position angles, gives us confidence that
IRC +10216 is resolved and the FWHM determined by fitting a Lorentzian gives a
meaningful proxy for object size vs. wavelength.
234
Figure C.3 The results of fitting profiles of the images presented in Figure C.1 as
a function of wavelength, plotted as FWHM. The PSF core was fit with a Gaussian, which is expected to match a well corrected Airy pattern inside the first Airy
minimum. For comparison we plot the predicted result for a circular pupil 6.35m
in diameter with an 11% central obscuration (i.e. the MMT with the adaptive secondary, dotted line). Though the slope of the line does not match perfectly (likely
due to a stop reducing the effective diameter or changing the central obscuration) it
shows that the MMTAO system reached the diffraction limit for these observations.
IRC +10216 was fit with a Lorentzian, which, though chosen for no astrophysical
reason, matches our data well. The fits show clear evidence of a size change with
wavelength, distinct from the effect of diffraction, between 10.2 and 12.6 µm, which
matches the SiC emission feature. To avoid confusion we have indicated the spectral
region typically impacted by telluric ozone. Also note the small feature at ∼ 8.8µm
which can be attributed to a sharp feature in the detector QE.
235
Figure C.4 Slit-loss correction calculations. We show the empirically calculated
flux enclosed by the slit and photometric aperture for IRC +10216 (colored dots,
using the same colors as Figure C.3 to denote PA), and the median of the 5 AOon PSF standards obtained (diamonds), four of which are from the night after the
IRC +10216 data were taken. Also plotted are the expected results for a centrally
obscured Airy pattern, which we use for our final correction factor calculation to
avoid introducing noise in our spectrum. Finally, we show the resultant slit-loss
correction factor (SLCF), which we multiply with the spectrum of IRC +10216.
236
Figure C.5 Calibrated flux before and after correction for differential slit loss. The
lower curves show the raw calibrated flux, before applying the SLCF, for each of
the four slit position angles. The top curve is our fully corrected median combined
spectrum, which takes into account the differential slit loss of the extended object
compared to the PSF standard. See Figure C.4 and the text for further discussion
of the SLCF. The error bars denote the local error, and the dashed lines denote our
total uncertainty, which in addition to the local error includes the global (correlated)
uncertainties. The average flux from 8 − 13µm is 47611 Jy, which is very similar
to the value of 47627 Jy obtained by Monnier et al. (1998) at similar phase (near
maximum brightness).
237
Figure C.6 IRC +10216 10µm spectra and photometry from 1973 to 1978 normalized
to F ν(10.55µm) = 1. Here we compare the bandpass photometry of Strecker and
Ney (1974, SN74), the FTS spectrum of Treffers and Cohen (1974, TC74), and the
CVF photometry of Merrill and Stein (1976, MS76), and the bandpass photometry
of McCarthy et al. (1980, MHL80). We also show the shape of the spectrum in
2010 as reported in this work for reference. The five SN74 photometry epochs have
been averaged (3 points from Jan-Apr, and 2 points in Sep-Oct) to reduce the
20% uncertainty in the individual points. Note that the Jan-Apr SN74 data and the
TC74 data are essentially contemporaneous. The photometry generally supports the
spectrum shape obtained by TC74, and is also consistent with the MS76 spectrum
within 2σ uncertainty.
238
Figure C.7 IRC +10216 10µm spectra from 1983 to 1988. Here we compare the
space-based IRAS/LRS spectrum, and the bandpass photometry of Le Bertre (1997,
LB97), normalized to Fν (10.55µm) = 1. The photometry appears to match the
IRAS/LRS spectrum well, though as in Fig C.6 it is consistent with our 2010 data
at the 2σ level. The LB97 points are taken far enough apart in time that we do not
average in case there is short term variation in the shape.
239
Figure C.8 IRC +10216 10µm spectra from 1993 to 1996. Here we compare the
bandpass photometry of Busso et al. (1996), the UKIRT spectra of Monnier et al.
(1998, MGD98), and the space-based spectrum obtained by ISO/SWS. We normalized the data to Fν (10.55µm) = 1. All three data sets are in good agreement during
this period, which spans three and a half years and well samples nearly two luminosity periods. The comparison with our 2010 data clearly shows that the change
in the spectrum at λ > 11µm is not simply associated with the regular 649 day
variation in brightness of IRC +10216.
Figure C.9 Our new N band spectrum and photometry compared to previous observations of IRC +10216 spanning
nearly 4 decades. As in Figures C.6-C.8 the data have been normalized at 10.55µm. At left we have added an arbitrary
constant to offset each epoch. The MIRAC4 photometry and grism spectrum, taken a year apart, match very well
from 9.8µm to 12.5µm. We present the same data at right without the offset. Of all the data from prior epochs, the
spectrophotometry of MS76 is most similar to the 2009/2010 MIRAC4 data red-ward of 11µm. The archival data rule
out these changes being simply related to the regular 649 day Mira variability exhibited by IRC +10216.
240
241
Figure C.10 The flux ratio Fν (12.5µm)/Fν (10.55µm) vs. time. Colors are the same
as in Figure C.9. Flux at 12.5 µm was calculated as the mean between 12 and
13 µm. MIRAC4 and IRAS/LRS errors are as given. We adopt local or relative
error of ±5% for the other data sets where such errors were not given. This plot
illustrates the change in the shape of the spectrum over time, highlighting variability
not associated with the regular 649 day Mira luminosity variations of IRC +10216.
Whether this is a recurring spectrum shape which occurs at irregular intervals, or a
longer term (& 40 year) periodicity cannot be determined from the available data.
242
Figure C.11 The current state of IRC +10216 plotted on the “Carbon-Rich Dust Sequence” classification system of SLMP98. This system was based on the IRAS/LRS
spectra of 96 carbon-rich AGB stars, and involves subtracting a 2400K blackbody
(an approximation for the stellar continuum), normalizing, and visually inspecting
the resulting curves. The heavy black curves are the summed and smooth spectra
used to illustrate the sequence, and we show the 1983 IRAS/LRS spectrum (dotted
red) and our 2010 MIRAC4 spectrum (blue). SLMP98 cited IRC +10216 as the
prototype of the Red class, but it now (2010) appears to be a better match to the
Broad 2 (Br2) spectra for λ > 11µm. Though the SLMP98 system does not represent an astrophysical sequence for C stars, it is useful in this case to show that our
measurement of IRC +10216’s spectrum matches other C stars.
243
Figure C.12 The spectral and spatial signatures of SiC dust around IRC +10216.
The well known SiC spectral feature can be seen in the MIRAC4 grism spectrum
from 2010 in the top panel. In the bottom panel we have deconvolved the FWHM
of IRC +10216 by subtracting the PSF FWHM in quadrature in order to estimate
its intrinsic size, after averaging the four PAs. To provide a physical scale, we follow
Men’shchikov et al. (2001) and adopt 130pc for the distance to IRC +10216 and
calculate the projected size corresponding to the FWHM. An increase in the size of
IRC +10216, clearly corresponding to the SiC feature, is evident (we have used the
typical bounds for this feature as found by Clément et al. (2003)).
244
Figure C.13 MIRAC4 detector linearity measurement. The data were taken prior
to the 2009 observations in a laboratory, and show that the detector becomes nonlinear at higher fluxes, exhibiting an increase in slope which could be an explanation
for the high flux detected at 8.7µm (see Figure C.9). We do not apply the curve
directly to the data due to an unnoticed change in the detector bias that occurred
between this measurement and the observations. The solid line is the fit to the first 8
data points. This fit was used to bias subtract the data. The dashed line has a 12%
higher slope, chosen to illustrate a worst case scenario where every pixel in the 8.7µm
that is brighter than the peak in the 10.55µm data has that slope. We also note the
actual peak counts per read in the 8.7µm filter prior to background subtraction, and
the peak counts per read in the 10.55µm after background subtraction (where the
arrows intersect the solid line). The peak pixel may have become slightly non-linear,
but the integrated non-linearity effect was likely < 1%, causing us to rule it out as
an explanation for the high flux at 8.7µm.
245
Table C.1 Observations of IRC +10216 and standards.
Object
Filter Airmass
(µm)1
2009 13 Jan UT
IRC +10216
8.7
1.35
IRC +10216
9.79
1.38
IRC +10216 10.55
1.32
IRC +10216 11.86
1.40
IRC +10216 12.52
1.31
µ UMa
8.7
1.23
µ UMa
9.79
1.22
µ UMa
10.55
1.18
µ UMa
11.86
1.20
µ UMa
12.52
1.19
2010 1 Jan UT
IRC +10216 Grism
1.06
IRC +10216 Grism
1.10
IRC +10216 Grism
1.12
IRC +10216 Grism
1.25
µ UMa
Grism
1.02
2010 2 Jan UT4
β Gem
Grism
1.01
β Gem
Grism
1.07
µ UMa
Grism
1.03
µ UMa
Grism
1.06
1
Pos. AO Speed
Angle2
(Hz)
No.
Frames
3
Total Exp.
Time (sec)3
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
8
16
12
4
12
24
20
20
24
16
1.76
3.52
2.64
0.88
2.64
5.28
4.40
4.40
5.28
3.52
107.0
129.4
2.6
32.6
73.1
25
25
25
25
100
5
2
8
6
6
0.040
0.016
0.064
0.032
10.000
144.3
164.0
133.7
92.1
150
550
550
550
20
8
8
8
200.0
80.0
80.0
80.0
Filter widths are given in Table C.2.
Position angle of the slit.
3
After rejecting bad chops, frames with excessive pattern noise, and bad slit alignment.
4
Data from this night were only used to check our slit loss correction procedure.
2
246
Table C.2 Bandpass photometry of IRC +10216 from 13 Jan 2009 UT.
Filter
(µm)
8.7
9.79
10.55
11.86
12.52
1
Width 1
(µm)
(8.08-9.32)
(9.33 - 10.25)
(10.06 - 11.04)
(11.29 - 12.43)
(11.94 - 13.11)
Fν
(Jy)
45099
31514
39408
37035
28790
Obj2σ
(%)
1.63
2.03
1.50
1.65
1.50
PSF3σ
(%)
0.78
1.50
1.52
1.37
2.10
Std.4σ
(%)
2.4
2.4
2.4
2.4
2.9
Atm.5σ
(%)
4
11
4
4
4
Total σ
(%)
5.0
11.5
5.1
5.1
5.6
Half power points of the manufacturer provided curves.
The measurement uncertainty in the IRC +10216 photometry, estimated empirically.
3
The measurement uncertainty in the µ UMa photometry, estimated empirically.
4
Mean value of the total uncertainty given by Cohen et al. (1996) between the half power points.
5
Based on the global and local telluric uncertainties of Skemer et al. (2010) from the following night.
2
247
Table C.3 Grism photometry from 1 Jan 2010 UT.
λ
(µm)
7.913
8.092
8.273
8.453
8.635
8.817
8.999
9.183
9.366
9.551
9.735
9.921
10.107
10.294
10.481
10.668
10.857
11.046
11.235
11.425
11.616
11.807
11.999
12.191
12.384
12.577
12.771
12.966
13.161
13.357
1
Fν
(Jy)
41810.8
40541.0
43087.7
44816.2
46551.8
48551.0
48513.1
48190.2
47983.4
43828.8
46788.7
50939.4
52751.5
52128.7
54768.2
55583.9
56168.0
55322.7
53247.8
52871.8
52857.9
50134.5
49050.2
44697.1
40722.9
38720.9
33237.0
33431.4
30643.0
31091.5
Meas.1σ
(%)
4.94
1.79
0.71
1.12
1.16
3.03
0.80
1.44
2.90
4.51
3.72
0.94
1.02
0.82
0.64
0.95
1.00
2.06
3.50
1.28
1.35
3.80
1.41
2.19
2.58
7.14
5.53
1.61
3.92
6.04
Local2σ
(%)
5.46
3.01
2.52
2.66
2.80
3.86
2.50
2.80
3.83
5.09
4.45
2.52
2.54
2.51
2.47
2.61
2.56
3.22
4.19
2.68
2.70
4.47
2.74
3.30
3.47
7.75
6.46
3.72
5.16
6.91
Global3σ
(%)
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
10.0
10.0
10.0
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
Total4σ
(%)
8.24
6.84
6.64
6.69
6.70
7.26
6.65
6.75
12.03
12.51
12.25
6.66
6.68
6.65
6.63
6.67
6.67
6.91
7.47
6.72
6.73
7.62
6.75
6.95
7.09
9.72
8.61
6.79
7.67
8.95
Measurement uncertainty, including IRC +10216 and the standard µ UMa.
Total local uncertainty, including 2.31-3.35% uncertainty from the µ UMa spectrum of Cohen et al.
(1996).
3
The estimated global telluric calibration uncertainty.
4
Includes 5% systematic uncertainty from the SLCF.
2
248
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