On the nature of early-type galaxies structure, kinematics and dynamics through

On the nature of early-type galaxies structure, kinematics and dynamics through
On the nature of early-type galaxies
structure, kinematics and dynamics through
ground and space-based observations
On the nature of early-type galaxies
structure, kinematics and dynamics through
ground and space-based observations
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van de Rector Magnificus Dr. D.D. Breimer,
hoogleraar in de faculteit der Wiskunde en
Natuurwetenschappen en die der Geneeskunde,
volgens besluit van het College voor Promoties
te verdedigen op dinsdag 12 oktober 2004
te klokke 15.15 uur
door
Davor Krajnović
geboren te Zagreb
in 1975
Promotiecommissie
Promotor:
Prof. dr. P.T. de Zeeuw
Co-promotor:
Dr. W. Jaffe
Referent:
Dr. E. Emsellem
Overige leden:
Prof. dr. R. Bacon
Prof. dr. R. Davies
Prof. dr. M. Franx
Prof. dr. K. Kuijken
Dr. R. F. Peletier
Pangur Bán
I and Pangur Bán my cat
’Tis a like task we are at:
Hunting mice is his delight,
Hunting words I sit all night.
Better far than praise of men
’Tis to sit with book and pen;
Pangur bears me no ill will
He too plies his simple skill.
Oftentimes a mouse will stray
In the hero Pangur’s way;
Oftentimes my keen thought set
Takes a meaning in its net.
’Gainst the wall he sets his eye
Full and fierce and sharp and sly;
’Gainst the wall of knowledge I
All my little wisdom try.
Practice every day has made
Pangur perfect in his trade;
I get wisdom day and night
Turning darkness into light.
Written by a ninth-century Irish monk in St Gallen, Switzerland
Front cover: a ceramic vessel from the Vučedol culture. Permission to reproduce the
picture of this vessel was kindly granted by Gradski Muzej Vinkovci (Vinkovci City
Museum). Help with the cover design was graciously given by Pedro Lacerda.
Back cover: A sequence of decorative symbols from the vessel shown on the front
page, representing stellar constellations characteristic for individual parts of the year
(see Chapter 1 for the reference with detailed explanations). Their meaning, from top to
bottom: summer Cassiopeia, the Pleides, Gemini, the Sun, Pegasus and Pisces, Orion,
and winter Cassiopeia.
Table of contents
vii
Table of contents
Chapter 1. Introduction
1 Understanding the world . . . . . . . . . . . . . . . . . . . . . .
2 Galaxies of the early type . . . . . . . . . . . . . . . . . . . . . .
3 A brief guide through the formation and evolution of galaxies
4 Activity in early-type galaxies . . . . . . . . . . . . . . . . . . .
5 Nuclear stellar discs in early-type galaxies . . . . . . . . . . . .
6 Integral-field spectroscopy . . . . . . . . . . . . . . . . . . . . .
7 Two-dimensional kinematic maps . . . . . . . . . . . . . . . . .
8 Dynamical models . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1 Stellar dynamical models . . . . . . . . . . . . . . . . . . .
8.2 Dynamical models of gas . . . . . . . . . . . . . . . . . . .
9 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . .
10 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Page
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Chapter 2. Relation between dust and radio luminosity in early type galaxies
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Data Acquisition and Reduction . . . . . . . . . . . . . . . . . . . . . .
3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Nature of Detected Radio Sources . . . . . . . . . . . . . . . . . . . . .
4.2 Radio Luminosity Function . . . . . . . . . . . . . . . . . . . . . . . .
5 Correlation of dust with radio emission . . . . . . . . . . . . . . . . . . . .
5.1 Crude Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Comparison of RLFs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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25
25
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28
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29
31
Chapter 3. HST observations of nuclear stellar disks
1 Introduction . . . . . . . . . . . . . . . . . . . . .
2 WFPC2 broad band imaging . . . . . . . . . . . .
2.1 Data reduction . . . . . . . . . . . . . . . . .
2.2 Isophotal analysis . . . . . . . . . . . . . . .
2.3 Broad-band color images . . . . . . . . . . .
2.3.1 B-V color images . . . . . . . . . . .
2.3.2 B,V-I color images . . . . . . . . . . .
3 STIS spectroscopy . . . . . . . . . . . . . . . . . .
3.1 Data reduction . . . . . . . . . . . . . . . . .
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Table of contents
viii
3.2 Stellar kinematics . . . . . . .
3.3 Line strengths . . . . . . . . .
4 Discussion . . . . . . . . . . . . . .
4.1 NGC 4128 . . . . . . . . . . .
4.2 NGC 4570 . . . . . . . . . . .
4.3 NGC 4621 . . . . . . . . . . .
4.4 NGC 5308 . . . . . . . . . . .
5 Conclusions . . . . . . . . . . . . .
A Extracted kinematics . . . . . . . .
B A transient in NGC 4128 . . . . . .
B.1 Extraction of light and results
B.2 Discussion and conclusions .
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48
52
55
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Chapter 4. Kinemetry: a method to quantify kinematic maps
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Theoretical background and motivation . . . . . . . . . . . . . . . . . . . .
3 The method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Expansion along elliptical annuli . . . . . . . . . . . . . . . . . . . . .
4 Kinematic parameters and their meaning . . . . . . . . . . . . . . . . . . . .
4.1 Model galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Odd kinematic moments . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Even kinematic moments . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Expansion of velocity maps using kinemetry along ellipses . . . . . .
5 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Prescription for axisymmetry . . . . . . . . . . . . . . . . . . . . . . .
5.2 A triaxial case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Comparison of velocity fields of early-type galaxies with velocity
fields of discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
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Chapter 5. Dynamical modelling of stars and gas in NGC 2974
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Observations and data reduction . . . . . . . . . . . . . . .
2.1 SAURON spectroscopy . . . . . . . . . . . . . . . . . . .
2.2 Absorption-line kinematics . . . . . . . . . . . . . . .
2.3 Distribution and kinematics of ionised gas . . . . . . .
2.4 Ground- and space-based imaging . . . . . . . . . . .
3 Quantitative analysis of velocity maps . . . . . . . . . . . .
3.1 Harmonic Expansion . . . . . . . . . . . . . . . . . . .
3.2 Kinemetric analysis of velocity maps . . . . . . . . . .
3.3 Signature of bars in NGC 2974 . . . . . . . . . . . . . .
3.4 Case for axisymmetry in NGC 2974 . . . . . . . . . . .
4 Stellar Dynamical Modelling . . . . . . . . . . . . . . . . . .
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92
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109
Table of contents
5
6
7
4.1 The Multi-Gaussian Expansion mass model . . . . .
4.2 Construction of three-integral models . . . . . . . .
4.3 Stellar dynamics - modelling results and discussion
Tests of Schwarzschild’s orbit-superposition models . . .
5.1 The input two-integral test model . . . . . . . . . . .
5.2 Recovery of input parameters . . . . . . . . . . . . .
5.3 Effect of the field coverage on orbital distribution . .
5.4 Recovery of the internal moments . . . . . . . . . . .
5.5 Recovery of the distribution function . . . . . . . . .
Modelling of emission-line gas . . . . . . . . . . . . . . . .
6.1 Inclination of the gas disc . . . . . . . . . . . . . . .
6.2 A simple dynamical model for the disc . . . . . . . .
Concluding remarks . . . . . . . . . . . . . . . . . . . . . .
ix
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110
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Nederlandse samenvatting (Dutch summary)
135
Hrvatski sažetak (Croatian summary)
145
Curriculum vitae
153
Nawoord / Acknowledgments
154
Chapter 1
Introduction
1 Understanding the world
T
HE urge to comprehend and describe the world is a defining characteristic of mankind. One remarkable illustration of this urge is shown on the cover of this thesis.
This ceramic vessel, with an ordered sequence of different symbols, is approximately
4500 years old. It was created by a craftsman of the Vučedol culture and excavated in
1978 in the town of Vinkovci in eastern Croatia. The classical Vučedol culture belongs
to the European Neolithic period and was created by newly arrived Indo-European
people. This widespread European culture was named after its central site on the river
Danube in eastern Croatia. The meaning of the symbols on the vessel was a mystery until recently when Durman (2000) suggested they represent the different stellar
constellations which dominated the Vučedol sky five millennia ago. The half-broken
pot from Vinkovci is very likely the oldest European calendar, used by the people of
Vučedol for the organisation of their every-day life 1 .
Five thousand years ago, stock-raising people of the Panonic plane were looking at
the night sky. They noticed regularities and formed an elaborate system to measure the
passing of time. In this way, they were able to describe a crucial aspect of the world using primitive but straightforward astronomical observations. Nowadays, astronomy
is a science, having undergone the process of transformation from predicting the future
by early astrologers to explaining the facts by modern astronomers observed with telescopes and instruments using the laws of physics. Still, at the centre of the science of
astronomy lies the same wish that led the Vučedol people: to comprehend, describe
and tame the world around us.
Our methods are much more sophisticated, but the astronomical themes have changed as well. Astronomy had a profound influence on the Vučedol people giving them
the calendar. It produced valuable information relevant for life. Unlike some other sciences in the present times, astronomy does not directly influence our everyday life
anymore. Modern astronomical research is focused on processes that shape the Universe, starting from our Sun, its neighbours, the Milky Way, and other galaxies, to
distant quasars and relics of the Big Bang. In a broader sense, the astronomy of today
is an idealised pursuit of knowledge of the Universe. Complementary to this, astronomy also records mankind’s perception of the world. The advances in astronomy are
reflected in changes in philosophy and culture. In the 1960s the size of the Universe
1
An in-depth description of the Vučedol culture and particularly the oldest European calendar is
given in the exhibition catalogue The Vučedol Orion (Durman 2000).
1
Chapter 1. Introduction
2
was changing almost on a daily basis with discoveries of ever more distant quasars
(e.g. Schmidt 1963). It seems a matter of time only before the first Earth-like planet
outside the Solar system2 will be discovered. The next step will be to search for life
on such a planet. Our lives do not directly depend on astronomy anymore, but it does
have a long term influence on the human society. Astronomy is our window into the
complexity of the Universe. This thesis focuses on a particular aspect of astronomy:
the formation and evolution of galaxies.
2 Galaxies of the early type
Galaxies were perhaps most elegantly described by Immanuel Kant in the 18th century
as “island universes”. Neither he nor anybody else until the astronomers of the early
20th century knew what these island universes, that appeared like nebulae on the sky,
actually were; what they were made of, or even how far they were from Earth. Observations with the Mount Wilson 100 inch telescope provided the first clues about the
nature of galaxies. They are made of stars and they are at a great distance from our
own “island universe”, the Milky Way. Galaxies come in different flavours and they
are usually classified in four distinctive groups according to their apparent shape (see
Fig. 1 of Nederlandse Samenvatting or Hrvatski sažetak). This classification scheme
was introduced by Hubble (1936) and it is known as the Hubble sequence of galaxies
(Hubble diagram or Hubble tuning fork are also frequently used terms). The sequence
starts with elliptical galaxies that seemingly have little or no structure. At the other end
are disc galaxies, very different with prominent spiral arms. They are usually called
spirals emphasising their eye-catching structure. Lenticular galaxies (also simply called
S0s) look like transition objects between ellipticals and spirals: they have a prominent
disc without a significant spiral structure embedded in a nearly spherical distribution
of stars. The fourth group of galaxies consists of all galaxies without a regular shape,
appropriately called irregulars. When constructing the diagram, Hubble was led by
the idea of galaxy evolution. Spiral galaxies with their complicated and easily visible
structure were natural candidates for complex and evolved systems, while elliptical
galaxies were obvious examples of simpler systems. Lenticulars were seen as a stage
between the two classes. Although such reasoning is not valid anymore and galaxy
evolution should be viewed the other way around (e.g. Kormendy & Bender 1996), the
ellipticals and lenticulars are still called early-type galaxies and the spirals are, hence,
known as late-type galaxies.
Galaxies are not made only of stars. They also contain gas and dust in different
amounts that change with Hubble type: late-type galaxies are observed to have more
gas and dust than early-types. A big discovery of the 1970s is that spiral galaxies are
embedded in dark matter halos (Rubin & Ford 1970; Rogstad & Shostak 1972; Ostriker
et al. 1974). It is believed that all galaxies have dark halos, but the observational evidence for dark halos around elliptical galaxies is not as decisive (Romanowsky et al.
2003). The nature of the dark matter is, however, still unknown, but the observations
clearly show that most of the matter in the Universe (> 90%) is non-baryonic, dark matter. Any theory of the formation and evolution of galaxies has to take this into account
2
More then a hundred Jupiter-like gas giants orbiting other stars have already been found.
Section 3. A brief guide through the formation and evolution of galaxies
3
and explain the variety of morphologies and specific characteristics observed. Unfortunately, the timescales over which galaxies evolve is not comparable to the life span
of an astronomer, who must act as a detective looking for evidence of the processes
that shaped the observed galaxies. These processes are easily masked by frequent and
intensive starformation which is common in late-type galaxies. By contrast, early-type
galaxies are particularly well suited for investigation because they do not contain much
gas and dust, and, having no recent star formation, retain fossil records of their formation history. Specifically, nearby (< 50 Mpc) early-type galaxies are very interesting,
since we are able to obtain accurate, spatially-resolved information (unfortunately not
the individual stars, which is currently possible only for the nearest3 galaxies).
Although generally fairly simple and uniform in appearance, early-type galaxies
show a rich structure on a closer look. High-resolution observations are necessary to
provide data that can be used to construct theoretical models of early-type galaxies.
The observations can be from ground- or space-based telescopes, each contributing in
a particular way. The goal is to construct theoretical models and test their description of the processes that shape galaxies with state-of-the-art observations. Indeed, the
connection between theory and observations is very important because only by combining their different approaches it is possible to ascertain the nature of the early-type
galaxies.
3 A brief guide through the formation and evolution of galaxies
Galaxies originate from fluctuations in the dark matter density of the early Universe.
An area of higher density accretes material through gravitational interaction until the
system becomes unstable and collapses dissipating energy into a small-scale object
(∼ 106 M ). According to the hierarchical scenario of galaxy formation (e.g. Press &
Schechter 1974; Kauffmann & van den Bosch 2002) small systems merge to form larger
and larger objects. These objects are made of gas, but are gravitationally dominated by
the dark matter distributed in halos. The temperature of the gas (infalling or already
present) is crucial. Stars can form only from cold gas, but gas is easily heated by several
processes: motion in the gravitational potential of a galaxy, heating by the new-born
stars and supernovae, and interaction with already heated (virialised) gas (e.g. Binney
2004). Heated systems are pressure supported and have a spheroidal structure, but in
certain cases cold gas can fall into the equatorial plane forming stars and creating what
can be observed today as disc galaxies (e.g. White & Rees 1978).
Early-type galaxies are thought to be formed in mergers of disc galaxies (Barnes
& Hernquist 1996). The gas content of the resulting galaxy can be replenished by accretion from larger gaseous structures. This may result in formation of a new disc,
renewed star formation and restoration of the galaxy into a late-type. However, each
merger will heat the stellar component and form spheroidal structures. These pro3
Nearby is a relative term in astronomy. About 40 galaxies (Courteau & van den Bergh 1999), of
which only one (the Andromeda galaxy) is comparable in size to Milky Way, make up the Local Group of
galaxies and are our nearest neighbours, within approximately 1 Mpc. Galaxies discussed in this thesis,
which we consider “nearby”, are at distances of 5 to 40 Mpc, but astronomers use the term “nearby” for
object which are up to a few times further. Beyond that begins the far Universe.
Chapter 1. Introduction
4
PROTOGALACTIC
COLLAPSE
Fast
versus
Slow
INTERNAL SECULAR
EVOLUTION
Driven by bar instabilities
by dark matter halos
by bars and oval distortions
by spiral structure
by nuclear black holes
etc.
Internal versus External
Star formation,
Gas recycling,
Metal enrichment,
Energy feedback via supernovae,
etc.
Internal versus External
GALAXY MERGERS
RAM-PRESSURE STRIPPING
OF GAS
Fast
versus
Slow
ENVIRONMENTAL SECULAR
EVOLUTION
Driven by prolonged gas infall
by minor mergers
by galaxy harassment
etc.
Figure 1 — Morphological box of processes of galactic evolution (from Kormendy & Kennicutt 2004).
Processes are divided horizontally into internal (left) and external (right); and vertically into fast (top)
and slow (bottom). Fast processes happen on a dynamical time scale, while slow processes last several
rotation periods. The processes at the centre happen in all types of galaxy formation scenarios.
cesses can repeat several times depending on the environment thus changing the shape
of galaxies. Confirmation of this scenario comes from ever-improving N-body simulations (e.g. van Albada 1982; Navarro et al. 1996; Naab & Burkert 2003) and observations
that in the dense cluster systems there are more early-type than late-type galaxies. Similarly, at higher redshifts (z ∼ 0.5), the relative contribution of disc galaxies in clusters
is larger (e.g. Combes 2004). In this way the Hubble sequence of galaxies should be
interpreted from right to left, starting from spiral and finishing with elliptical galaxies.
Galaxy evolution, however, is not restricted to the relatively fast processes of galaxy
mergers and interactions. They also evolve on longer time scales. This secular evolution of galaxies is driven by a number of internal and external conditions and by slow
processes including: bar instabilities (see Section 8.2 for more details), the shape of
the dark matter halos, the presence of supermassive nuclear black holes, supernova
winds, spiral structures, gas infall, minor mergers, etc. An instructive classification of
the different processes that operate in galaxy formation and evolution is presented in
Fig. 1, taken from Kormendy & Kennicutt (2004). As stressed by these authors, in the
present-day Universe, both short and long timescale processes are important, although
the secular evolution will dominate in the future (expanding) Universe.
A theory of the formation and evolution of galaxies has to be able to explain all
observational facts. Early-type galaxies are our probes into the distant past of the Universe and their observed properties can be used to constrain and validate the theoretical models of the processes that shaped the galaxies. For example, N-body simulations
of hierarchical galaxy formation produce galaxies that have triaxial dark halos (Frenk
et al. 1999). By contrast, observations of the luminous parts of elliptical galaxies show
Section 4. Activity in early-type galaxies
5
that, although there are true triaxial galaxies, the majority are only mildly triaxial, almost consistent with axisymmetry (Franx et al. 1991; see also Fig. 2 for preliminary
results from SAURON observations). This dark versus luminous matter discrepancy is
a stimulus to both theoretical models and observations in search for the true answer.
Galaxy formation and evolution is complex and consists of many pieces that have to
be well understood individually and assembled together into a coherent picture. Each
chapter of this thesis is devoted to a somewhat distinct issue of galaxy evolution. Details on each aspect are given in the following section.
4 Activity in early-type galaxies
The centres of many early-type galaxies emit non-stellar radiation. This so-called ‘activity’ is confined to a region within a few parsecs from the centre, and such centres
are usually called active galactic nuclei (AGN). The same acronym is often used to also
specify the whole host galaxy. AGN are sometimes even called monsters (Gunn 1979),
because they radiate enormous amounts of energy into the surrounding space (e.g. E
∼ 1061 erg in total). Generally, AGN appear to be very diverse, and a classification according to their properties is very broad. The bestiary of AGN includes radio-loud and
radio-quite quasars, optically violent quasars, broad and narrow line galaxies, Seyferts
(of type 1 and 2) and low-ionisation narrow-line regions (LINERs)4 , each with different
defining characteristics (e.g., Krolik 1999). However, there are also many similarities
and properties that lead to a unification scheme and a paradigm that the activity of
all AGNs is produced by matter falling onto a supermassive black hole that resides
at the bottom of the galaxy’s potential well (Hoyle & Fowler 1963; Lynden-Bell 1969).
Different species of AGN are then the manifestation of the same process viewed from
different angles and under different conditions.
Distant AGN are on average several orders of magnitude stronger than the AGN
residing in the nearby galaxies. Quasars and most of the radio-loud AGN are found
at higher redshifts (the population peaks at redshifts of 2-3) while the local population
of AGN consists mostly of Seyferts and LINERs. Most quasars reside in early-type
galaxies which look similar to normal nearby elliptical galaxies (Ho et al. 1997; McLure
et al. 1999, 2000). Still, some amount of activity is present among many of the nearby
galaxies, although often of barely detectable intensity: about 40% of all nearby galaxies
show some AGN activity and ∼ 60% of nearby early-type galaxies show AGN characteristics (Ho et al. 1997). In a somewhat limited sample of nearby galaxies we found
that 47% of early-type galaxies are active at the level of 0.1 mJy (Chapter 2, Krajnović
& Jaffe 2002).
If some nearby galaxies are direct descendants of high-redshift quasars and other
AGN, the supermassive black holes should still be present in the nuclei of many galaxies (Soltan 1982). This is now largely accepted and confirmed by the search for black
holes in nearby galaxies over the last two decades. The success of the hunt for supermassive black holes was largely the result of the unprecedented spatial resolution
offered by the HST. Masses of about thirty supermassive black holes ranging between
106 − 109 M have been measured to date (e.g. Tremaine et al. 2002). A tight correla4
LINERs are, however, not necessarily connected to AGN.
6
Chapter 1. Introduction
tion between black hole mass and velocity dispersion (of the central spheroidal part
of the galaxy) suggests that the formation and evolution of supermassive black holes
and their host spheroids are connected (Haehnelt et al. 1998; Richstone et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Monaco et al. 2000). Perhaps most galaxies
go through a violent quasar period that starts with intensive accretion of (cold) gas
which falls towards the black hole in the centre of the galaxy. The violent process that
creates the quasar’s light also increases the mass of the black hole, which can reach
the observed values in a few times 109 years (for details see Yu & Tremaine 2002).
However, as mentioned before, in nearby galaxies, the supermassive black holes are
dormant or barely emitting radiation. The activity then, clearly, has to be connected to
the existence of fuel material that can be accreted by the supermassive black hole.
Large-scale dust and gas are not often seen in early-type galaxies (but more often in
lenticulars than in ellipticals), and the amount of available fuel is less compared to the
high-redshift objects. However, higher-resolution imaging by means of the HST shows
that dust is common on smaller scales in nearby early-type galaxies (van Dokkum &
Franx 1995; Verdoes Kleijn et al. 1999; Rest et al. 2001; Tran et al. 2001). Dust indicates
the presence of gas: the fuel for the AGN engine. An immediate question arises: how
is the presence of dust and gas connected to the activity in nearby early-type galaxies? Observations presented in this thesis (Chapter 2) suggest that although galaxies
without dust have a somewhat lower probability of AGN activity, the existence of dust
in HST images is certainly not a necessary condition for the existence of an AGN. On
the other hand, a recent study (Kauffmann et al. 2003) showed that, although the AGN
host galaxies morphologically look very similar to present-day ellipticals, they often
have a young stellar population component and in this way differ dramatically from
nearby ellipticals. There might be more subtle differences between the nearby normal
and AGN host galaxies.
There are many processes at play that determine the activity in galactic nuclei. Major mergers and interaction between galaxies (more common at higher redshifts) act as
reservoirs of fuel for starving central engines. Minor mergers and motion of gas in the
gravitational potential of a galaxy perturbed by bar instabilities can have a crucial role
in transporting gas to the bottom of the potential well and the black hole. The amount
of gas and the specific physics of accretion will define the resulting AGN (quasar, radio
galaxy with jets, LINER, etc), as well as the influence of the AGN on the evolution of
the whole galaxy. Detailed observational and theoretical studies of the accretion processes in galactic nuclei as well as secular evolution are still needed to understand the
nature of the activity in galaxies.
5 Nuclear stellar discs in early-type galaxies
The central regions of galaxies are not easily observed from the ground because of the
limiting influence of atmospheric seeing on the observations. Early-type galaxies often
look simple and featureless on ground-based images. High-resolution observations
with HST have revolutionised our knowledge of the nuclear regions (approximately
inner 1 kpc) of early-type galaxies (Jaffe et al. 1994; van den Bosch et al. 1994; Lauer
et al. 1995; Carollo et al. 1997a; Carollo et al. 1997b; Rest et al. 2001). Among several
Section 5. Nuclear stellar discs in early-type galaxies
7
discoveries, these observations revealed the existence of small nuclear stellar discs,
with sizes of the order of 100 . These discs can be remarkably thin (30 pc compared with
300 pc of disc in our galaxy) and are often related in some way to the large scale discs,
but are not necessarily connected to them since outer discs often have an inner cutoff radius (Scorza & Bender 1995; Scorza & van den Bosch 1998; van den Bosch 1998;
Chapter 3 of this thesis). These features clearly point to a complex formation scenario,
possibly involving secular evolution. Studies of larger samples of galaxies showed that
they occur in about 50% of early-type galaxies, and since discs are easily found only if
seen near to edge-on (Rix & White 1990), they might be very common features.
Discs are generally dynamically simpler than spheroids. They are very flattened
axisymmetric structures dominated by rotation which can be used to determine the
galaxy’s potential (assuming circular motion of stars in the disc). It is easy to determine
the inclination of a disc and correct for its effects. As a result, nuclear stellar discs can
be used to measure the mass of the black hole in the centre of the galaxy. Perhaps the
most interesting consequence of the existence of nuclear discs is the fact that they can
be used as probes of galaxy evolution scenarios.
There are two likely scenarios for nuclear disc formation. Discs could be the end
result of a minor merger of galaxies. In this scenario a satellite galaxy interacts with
the bigger host galaxy and the captured gas is transported to the centre where it settles in (one of) the principal planes of the host galaxy. Frequently the infalling gas
has enough angular momentum to form a disc. Interaction with the black hole can
result in an AGN, but also stabilises the disc leading to the formation of stars (Loeb &
Rasio 1994). An alternative scenario, that, unfortunately, can result in similar observational properties, invokes the secular evolution of galaxies, where bar instabilities play
a critical role in transporting gas towards the centre of the galaxy, creating a nuclear
disc (e.g. van den Bosch & Emsellem 1998). Discriminating between these two very
different scenarios (positioned in opposite corners of Fig. 1 - upper right and lower
left) is difficult. However, it is probably a combination of both scenarios that occurs in
galaxies leaving signatures in the observed structures. Generally, the different formation paths of a nuclear stellar disc and the rest of the galaxy, are expected to result in
differences in the age and metallicity of their stellar component.
In edge-on galaxies, where nuclear stellar discs are most easily detected, the effects
of bar instabilities are hard to observe. A range of different observations, including
imaging and spectroscopy are necessary to investigate the effects of the above mentioned processes. Chapter 3 presents such a comprehensive observational study of
galaxies with four previously-known nuclear stellar discs. Assembling all observational evidence from Chapter 3, there are no clear proofs of bar-driven evolution in
any of the observed galaxies, although some are strong candidates. Our long-slit spectroscopic data are of high resolution, but they cover only a small fraction of the nuclei
and discs. Additional observations of the two-dimensional kinematic properties and
their connection to the distribution of line-strengths (metal content and age of stellar populations) would probably offer decisive insight in the formation of the nuclear
stellar discs.
Chapter 1. Introduction
8
6 Integral-field spectroscopy
Recent developments in instrument design have introduced a new acronym in the astronomical jargon, IFU (integral-field unit), specifying an instrument capable of producing simultaneous spectroscopic measurements over an area (field) rather than along
a slit. There are several possible ways to construct an IFU. All IFUs have a mechanism
for separating the light coming from the sky, whilst retaining the information of the
sky coordinates from which each separated light beam has originated. In this way, it is
possible to observe an extended astronomical object, as with traditional imaging, but at
the same time to extract spectral information from different parts of the object. An alternative is to stack a number of long-slit measurements together, but since the spectra
are not taken simultaneously it is generally not considered to be an IFU measurement,
nor it is anywhere near being efficient in time. Due to the time limitations, the multipleslit approach has been used for only a few galaxies (e.g. Statler & Smecker-Hane 1999).
The final observational product of an IFU is a three-dimensional data-cube with spatial and spectral information (x, y, λ). These data can be presented as two-dimensional
kinematic and line-strength maps5 , bringing a wealth of spatially-resolved information
of observed objects (e.g. Bacon et al. 1995, 2001).
The true power of IFUs is revealed when observing objects with complicated morphologies whose properties cannot be accurately measured with just one or two longslits. Galaxies of all types, and merging objects, are typical examples. Astronomical
objects, in general, are three-dimensional structures, but we see them only as twodimensional projections onto the sky. With an IFU we can efficiently observe the projected distribution of light and obtain spectra integrated along the line-of-sight. This
gives valuable additional information for understanding and constraining the internal
structure of the observed objects. Chapters 4 and 5 of this thesis analyse the integralfield observations of early-type galaxies showing their advantages and usefulness for
the study of internal structure of galaxies.
IFU observations are currently mostly used to observe nearby galaxies (e.g. the
SAURON project de Zeeuw et al. 2002), with the purpose to construct dynamical models
of galaxies, and constrain the distribution of their stellar content. The diversity of the
science done with IFUs is, however, continuously growing: solar system bodies, planetary nebulae, young stellar objects, supernova remnants, extragalactic supernovae,
merging galaxies, gravitationally-lensed galaxies and deep-field studies to name a few
(e.g. Swinbank et al. 2003; Bower et al. 2004). The next generation of IFUs mounted
on 8-10m telescopes with a wide field coverage and assisted with adaptive-optics systems, will be capable of observing objects at higher redshifts, probing earlier stages of
galaxy formation and evolution.
7 Two-dimensional kinematic maps
Assuming there are no objects in front and behind an observed stellar system, spectroscopic observations can be used to constrain the system’s kinematic properties. Each
5
It is important to note that radio astronomers have observed two-dimensional velocity fields for
more then thirty years. The IFU technology is, however, a relative novelty in optical astronomy.
Section 7. Two-dimensional kinematic maps
9
(unresolved) star will contribute to the observed spectrum. Its absorption lines will
be Doppler shifted according to the star’s line-of-sight (LOS) velocity. Generally, stars
have different velocities and directions of motion which are reflected in the integrated
spectrum as a broadening of the (combined) absorption lines. The distribution of stellar velocities along the line-of-sight can be described by a broadening function, usually
called the line-of-sight velocity distribution (LOSVD)6 . Commonly, the LOSVD is decomposed into orthogonal functions, e.g., as a Gauss-Hermite series. This expansion
exploits the fact that LOSVDs are to first order well-approximated by a Gaussian, so
that the deviations can be described by a small number of Gauss-Hermite terms. The
spectra of bright nearby galaxies can be used to extract the first four terms of the GaussHermite series measuring: the mean velocity V, the velocity dispersion σ , and two
Gauss-Hermite coefficients, h3 and h4 . These coefficients measure the asymmetric (h3 )
and symmetric (h4 ) departures of the LOSVD from a Gaussian (van der Marel & Franx
1993; Gerhard 1993).
Observing nearby galaxies with an IFU provides two-dimensional kinematic maps,
i.e., maps of their kinematic moments V, σ , h3 , h4 . The maps offer a wealth of information important for understanding the shape and properties of a galaxy, as well as
for constructing dynamical models that describe its internal structure. However, the
important information has to be extracted efficiently from the maps. A simple and
straightforward approach is to use a harmonic expansion along concentric annuli to
describe each two-dimensional map. The result is a set of coefficients describing the
amplitude and orientation of the kinematic moments. These parameters are related to
the intrinsic properties of the observed galaxy. A similar approach is used in photometric analysis of optical surface brightness images (e.g. Lauer 1985; Jedrzejewski 1987).
Chapter 4 presents a general method for analysing and describing two-dimensional
kinematic maps of early-type galaxies. Due to the similarities with the surface photometry of early-type galaxies, we called our technique kinemetry7 .
The internal kinematic moments of stationary triaxial systems show a high degree
of symmetry. Following these symmetries we distinguish between even and odd moments. This is reflected in the symmetries of the observed kinematic maps. Generally,
maps of even moments are point-symmetric [µ e (r, θ + π ) = µe (r, θ )], while maps of odd
moments are point-anti-symmetric [µo (r, θ + π ) = −µo (r, θ )], where µo and µe are arbitrary odd and even moments of the LOSVD, respectively, with dependence on radius
r and angle θ . As a consequence, the terms of the harmonic expansion will behave
accordingly: the even terms will be nearly zero for maps of odd moments and the
odd terms will be nearly zero for maps of even moments. Alternatively, the observed
symmetry of kinematic maps makes it possible to ascertain the symmetry of the density distributions and kinematics of the observed galaxy. If all kinematic maps of a
galaxy show an additional signature of mirror-(anti)-symmetry [µ e (r, π − θ ) = µe (r, θ )
for even and µo (r, π − θ ) = −µo (r, θ ) for odd moments] the galaxy will be consistent
with being intrinsically axisymmetric. An example of the application of kinemetry on
velocity maps is shown in Fig. 2. Using kinemetry we analysed velocity maps of 48
6
Sometimes, the broadening function is simply called the velocity profile (VP)
Again, radio astronomers pioneered a similar although less general technique (Begeman 1987;
Schoenmakers et al. 1997)
7
10
Chapter 1. Introduction
Figure 2 — Histogram of the kinematic misalignment angle ψ measured for a sample of 48 E/S0 galaxies
from the SAURON survey (de Zeeuw et al. 2002). The angle ψ is the angle between the photometric and
kinematic axes (Franx et al. 1991). The kinematic major axes were measured using kinemetry (Chapter 4)
at radii of 500 , 1000 and 1500 . The photometric major axis was determined using the inner 15 00 of the galaxy.
About 35% of galaxies have small misalignment angle (< 5◦ ) and are consistent with axisymmetry at
the given radii. The measured number of galaxies consistent with axisymmetry increases with radius,
showing that the central regions are often very different from the rest of the galaxy.
galaxies from the SAURON survey, extracting the position angle of the maps, the socalled kinematic angle. Comparing this angle with the photometric position angle, the
position angle of the light distribution, we can measure the apparent (projected on the
sky) misalignment between the two angles, which constrains the intrinsic shape of the
galaxy (Franx et al. 1991).
Kinemetry is a powerful tool for describing and analysing kinematic maps, but it
can be also used as a noise filter. Its most obvious usage is on the mean velocity maps
which were already studied theoretically (e.g. Franx et al. 1991; Statler 1991, 1994a;
Statler & Fry 1994; Statler 1994b; Arnold et al. 1994), but, as presented in Chapter 4,
kinemetry can also be applied to higher moment maps. Kinemetry can hence be used
to extract useful information from the observed objects, and so to serve as a bridge
between observations and theoretical modelling.
8 Dynamical models
A full understanding of the intrinsic shape and structure of galaxies can only be obtained through detailed dynamical modelling. Construction of such models is a theoretical undertaking which is based on the general laws of physics and incorporates
ideas and assumptions about the investigated objects (or processes). However, only
models which can reproduce the observations (experiments) can be considered as physically meaningful. Theoretical constructions are limited only by the inventiveness of
the human mind, but the natural world around us is unique. In order to explain it,
theory must agree with the observations.
Section 8. Dynamical models
11
8.1 Stellar dynamical models
The structure and dynamical properties of a collisionless stellar system are fully specified by its phase space density or distribution function, f = f (~
x, ~
v, t), where ~
x and
~v label the position and velocity of stars at a time t. The distribution function must
be non-negative, must satisfy the continuity equation and if it describes a system in
a steady state (no changes with time), it does not depend on the time variable t. The
distribution function, however, cannot be measured directly because individual stars
are resolved only in the nearest stellar systems and observations cannot be expected
to be complete. The distribution function can be partially constrained by observations
of the object’s surface brightness, which is the line-of-sight projection of the density of
the system. Unfortunately, the deprojection of the surface photometry is non-unique
(Williams 1981; Rybicki 1987) and the density itself does not fully constrain the possible
orbits of stars. On the other hand, the projected kinematics (two-dimensional observation with large coverage of the object) provide a significant additional constraints on
the stellar distribution function.
The six-dimensional phase-space (~
x, ~
v) dependence of the distribution function can
be substituted by, in the most general case, a dependence on only three conserved
quantities. The Jeans theorem (Jeans 1915; Lynden-Bell 1962) states that f is a function
of the isolating integrals of motion, functions of ~
x and ~
v that are constant along every orbit in a given gravitational potential. The reduction from six to at most three variables
is a significant simplification. The actual number of integrals of motion depends on
the symmetry of the potential. Spherical potentials, with an isotropic velocity distribution, correspond to a one-integral distribution function: f = f (E) having energy E
as the integral of motion8 . Axisymmetric potentials conserve the energy and the one
component of the angular momentum, L z , but most of the orbits in a realistic potential are regular and also conserve an effective third integral of motion, I3 (Contopoulos
1960, Ollengren 1962). This quantity is non-classical in the sense that it cannot be analytically known, except in the rather special, but instructive case of Stäckel potentials
(Kuzmin 1956; de Zeeuw 1985a), so we expect f = f (E, L z , I3 ) . The most complicated
is the case of the triaxial potential. Non rotating triaxial potentials9 conserve energy
and two non-classical integrals, I2 and I3 (Schwarzschild 1979; de Zeeuw 1985b).
In Chapter 5 we construct axisymmetric models that conserve two- and three-integrals of motion, (E, L z ) and (E, Lz , I3 ) respectively. Two-integral models can be constructed following the Hunter & Qian (1993) method. Since both integrals are analytically known, it is possible to derive a distribution function, f = f (E, L z ). On the
other hand, the distribution function of the three-integral models, cannot be computed
directly due to the nature of the unknown third integral, I3 . An elegant numerical
method for the construction of three-integral dynamical models, however, was introduced by Schwarzschild (1979, 1982). In this method, the galaxy is built as an ensemble of stellar orbits, that are assumed to be independent. Each orbit contributes with
8
In spherical potentials it is also possible to construct models of the form f = f (E, ~L) and f = f (E, L2 ).
The former have a preferred axis and are usually not considered, while the latter conserve the amplitude
of angular momentum, but not its direction.
9
Bars provide examples of rotating triaxial systems. Although there is lack of observational evidence,
elliptical galaxies are generally considered to have nearly stationary figures.
12
Chapter 1. Introduction
certain mass and kinematic properties. Determining a superposition of orbits that best
reproduces the observed galaxy (surface brightness and kinematics), one obtains an orbital representation of the galaxy. Since the method results in a superposition of orbits,
specified by the integrals of motion (E, L z , I3 ), it is possible to construct an equivalent
form of the distribution function, f = f (E, L z , I3 ), describing the galaxy. The threeintegral method is more general than the two-integral method and produces more realistic models of the observed galaxies. The finite number of orbits, however, is much
smaller than the number of stars and even sometimes than the number of observables
used to constrain the model (10000 orbits vs 1011 stars vs ∼ 5000 kinematic observables
in the case of integral-field data), and the effects of the discreteness of the method have
to be properly understood. Schwarzschild’s method has been successfully applied in
a number of cases to recover the mass of central black holes, the mass-to-light ratios,
and to describe the internal (kinematic) structure of the modelled galaxies (e.g van der
Marel et al. 1998; Cretton et al. 1999; Cretton & van den Bosch 1999; Cappellari et al.
2002; Verolme et al. 2002; Gebhardt et al. 2003).
Properties of the observed galaxies are not known a priori, and we do not know
whether the models recover the true galaxy parameters and its correct orbital structure.
One way of testing the modelling results is to construct artificial models of galaxies for
which one knows all details to arbitrary accuracy. Two-integral models are useful for
this purpose and one can use them as inputs to the three-integral models. Comparing
the results with known inputs, one can attach confidence levels to the three-integral
models. The physics of stellar motion belongs to classical Newtonian dynamics, but
the observed galaxies are complex systems with innumerable stars. A proper understanding of the dynamical structure of galaxies continues to pose a challenge.
8.2 Dynamical models of gas
In the interstellar medium of galaxies some of the gas, if present, is ionised by the radiation of stars or an AGN and gaseous emission-lines are often easily observed. In an
axisymmetric potential, gas eventually settles in a disc in the equatorial plane of the
galaxy. Gas is said to be dynamically cold if it is observed in a disc configuration where
non-selfintersecting clouds of gas move in circular orbits in the equatorial plane. This
situation is observed in galaxies such as M87 (van der Marel 1994) and NGC 7052 (van
den Bosch & van der Marel 1995), but gas is often observed with irregular morphologies and disturbed kinematics. In these cases the treatment of gas needs to go beyond
gravitational forces, by including hydrodynamical effects. There are also intermediate
cases10 when gas is observed in a regular disc but its velocity dispersion is high (gas is
not cold) and is comparable with the measured rotation velocity.
The velocity dispersion of a settled (cold) gas disc is expected to be ∼ 10 km s−1
(Osterbrock 1989) due to its temperature (∼ 104 K in galaxies without any or with low
ionisation activity). However, the measured velocity dispersion is often larger for reasons that are presently not well understood. In some cases it is possible to assume
10
The gas disc can also display spiral structure, which happens when the mass of gas is large and
self-gravity becomes important, or, generally, as a result of a perturbation in the potential, like a barinstability or interaction with a neighbour galaxy.
Section 8. Dynamical models
13
that the velocity dispersion is the result of local turbulence which does not disturb the
bulk flow of gas rotating at nearly the circular velocity (e.g. van der Marel & van den
Bosch 1998; Verdoes Kleijn et al. 2000) and the gas bulk motion is explained with cold
gas disc models. Alternatively, the non-thermal component of the velocity dispersion
comes from collisionless gravitational motion of the gas: gas clouds act as stars moving on self-intersecting orbits. In this case one can use the epicyclic approximation11
to the motions of gas clouds and evoke the so-called asymmetric drift correction to
the circular motion of collisionless gas clouds (Cinzano & van der Marel 1994; Cretton
et al. 2000; Barth et al. 2001; Aguerri et al. 2003; Debattista & Williams 2004; Chapter 5
of this thesis). Neither of these approaches are entirely physically justified, although
these approximations often do reproduce observations.
Flattened potentials are prone to perturbations which disrupt their shape. An example of such a perturbation is the bar instability, which is typical for disc systems
(roughly two thirds of disc galaxies have bars). Bars are triaxial structures that rotate
with a pattern speed, Ω p . Stars, having their own rotation speed, Ω, feel the gravitationally pull of the bar potential which perturbs their orbits. This effect is seen in the
existence of several resonances in the galaxy, one of which happens when the rotational
speed of the bar (pattern speed, Ω p ) matches the speed of the stars and it is called corotation (CR, Ω p = Ω). Other strong resonances are: Inner Lindblad (ILR, Ω p = Ω − κ/2),
Outer Lindblad (OLR, Ω p = Ω + κ/2) and Ultra-Harmonic (UHR, Ω p = Ω + κ/4), where
κ is its radial epicyclic frequency. The allowed orbits are aligned with the bar between
the ILR and CR, and perpendicular to the bar between the CR and OLR. Each time a
resonance is crossed stellar orbits change direction perpendicularly(Binney & Tremaine
1987; Athanassoula 1992).
The existence of resonances will also shape the gas disc pushing gas away from
corotation towards the Inner and Outer Lindblad resonances. Unlike stars, gas can collide and the orbits of cold gas change smoothly between resonances. In strong bars this
will result in the formation of gas rings, followed by starformation. On the other hand
weak bars do not betray their existence so easily and are hard to detect. Often they are
not visible on images of galaxies. Twists of velocity contours on two-dimensional maps
are, however, likely signatures of bars. For an in-depth review of bars see Sellwood &
Wilkinson (1993) and Kormendy & Kennicutt (2004).
Observations of gas kinematics in many galaxies is simpler than measuring the
stellar kinematics, because the gas emission-lines are bright and easier to detect than
stellar absorption lines. Dynamical models of gas discs can be used to determine the
properties of the gravitational potential, its symmetry, inclination as well as mass of
the central black hole. Gas particles move in the same potential as the stars and so
dynamical models of gas and stars should give the same results, or at least can be used
to verify each other and their underlying assumptions. Observation and models of gas
shed light on the evolutionary stage of the observed host galaxy.
11
The epicyclic approximation is valid in the limit of small radial oscillations.
14
Chapter 1. Introduction
9 Outline of this thesis
The research presented in this thesis deals with different aspects of galaxy formation
and evolution. It is based on observations with ground- and space-based telescopes,
in the radio and optical wavelength range. The work focuses on nearby early-type
galaxies and their properties, ranging from nuclear structures and activity to global
kinematic and dynamical properties. A short outline of each chapter is given here.
Chapter two presents a survey of an optical/IR selected sample of nearby E/S0
galaxies with and without nuclear dust structures on the HST images. The observations were obtained with the Very Large Array radio interferometer at 3.6 cm to a
sensitivity of 100 µJy. The Radio Luminosity Function (RLF) of the observed galaxies down to ∼ 1019 W Hz−1 shows that ∼ 50% of these galaxies have AGNs at the
surveyed level. The space density of these AGN equals that of starburst galaxies (at
the same luminosity). The main result of the survey is that several dust-free galaxies
have low-luminosity radio cores, and their RLF is not significantly less than that of the
dusty galaxies. This implies that the existence of dust visible with the HST is not a
necessary requirement for the existence of an AGN in nearby early-type galaxies.
Chapter three discusses observations of four nearby early-type galaxies with previously known nuclear stellar discs. The galaxies were observed using two instruments
on-board the Hubble Space Telescope. The Wide Field Planetary Camera 2 observed
NGC 4128, NGC 4621 and NGC 5308. The Space Telescope Imaging Spectrograph observations also included NGC 4570. Numerous nuclear colour features were detected,
such as: a red nucleus in NGC 4128, a blue nucleus in NGC 4621, and a blue disc in
NGC 5308 only 30 pc thick. Additionally, a blue disc-like feature with position angle
∼ 15◦ from the major axis in NGC 4621, possibly related to the kinematically decoupled core discovered by Wernli et al. (2002), was found. In NGC 5308 there is evidence
for a blue region along the minor axis. A blue transient on the images of NGC 4128 at
a position of 0.00 14 west and 0.00 32 north from the nucleus was discovered. The nature of
the transient is not certain, although it could have been a supernova.
The extracted kinematic profiles belong to two distinct groups: fast (NGC 4570 and
NGC 5308) and kinematically disturbed rotators (NGC 4128 and NGC 4621). The discovery of a kinematically decoupled core in NGC 4128 is also reported. Galaxies have
mostly old (10-14 Gyr) stellar populations with a large spread in metallicities (sub- to
super-solar). In this chapter possible formation scenarios are discussed, including bardriven secular evolution and the influence of mergers, which can explain the observed
colour and kinematic features. The available evidence unfortunately cannot entirely
distinguish between the two cases, and it is likely that a combination of processes may
have shaped the galaxies.
Chapter four describes a general method for analysing and describing two-dimensional kinematic maps of galaxies observed with integral-field spectrographs. The
method is based on the harmonic expansion of kinematic maps along concentric annuli in the plane of the sky similar to those used in observations of cold gas (e.g. Begeman 1987; Franx et al. 1994; Schoenmakers et al. 1997) and in the surface photometry
approach to broad-band imaging, but without assuming any a priori knowledge of the
galaxies (Lauer 1985; Jedrzejewski 1987; Franx et al. 1989). We call it kinemetry. Using
Section 9. Outline of this thesis
15
symmetries of the kinematic moments (even moments are point-symmetric and odd
moments are point-anti-symmetric) it can be used to parametrise trends and detect
properties of the host galaxies and as a diagnostic tool of underlying symmetries of the
gravitational potential. Kinemetry is also a powerful filter. The method is presented,
tested and applied to model maps of kinematic moments as well as actual SAURON
observations of a few galaxies. An interesting, preliminary, finding is that the velocity
maps of nearby early-type galaxies are very similar to the velocity maps of discs. This
is somewhat unexpected since early-type galaxies are (flattened) spheroidal systems,
and warrants a detailed study of a larger sample of two-dimensional velocity maps of
early-type galaxies.
Chapter five contains a detailed dynamical study of the E4 galaxy NGC 2974. The
observations include ground- and space-based imaging and integral-field spectroscopy
with SAURON , which were used to extract stellar and gaseous kinematics. The kinematic maps are quantified with kinemetry and the large-scale kinematics show only
small deviations from axisymmetry (which are, however, visible in the central 3 00 of
the gas kinematic maps). General axisymmetric dynamical models for the stellar motions are compared to the observations of the galaxy. The three-integral models ( f =
f (E, Lz , I3 )) presented here are based on Schwarzschild’s orbit superposition method.
The models are constructed to determine the mass-to-light ratio, ϒ, and inclination, i,
of the galaxy, as well as its internal orbital structure. The best fitting parameters are
ϒ = 4.5 ± 0.1 M / L and i = 65 ± 2.5◦ .
The results of the stellar dynamical modelling are tested on the gas kinematics. The
inclination of the gas disc can be obtained from its velocity field. The measured value,
i = 58 ± 5◦ , is close to the stellar dynamical value. The observed gas disc was modelled
with the asymmetric drift approximation in the potential derived from the stellar models. The gas models are able to accurately reproduce the large-scale kinematic structure, but fail to do so in the inner 300 , which are influenced by the non-axisymmetric
perturbations.
A large section of Chapter 5 is devoted to tests of the three-integral method, as well
as the importance of the two-dimensional maps for constraining models of observed
galaxies. The robustness of the method is tested against two-integral models with
analytic DF ( f = f (E, L z )). We used these models to test: (i) the influence of the radial
coverage of the kinematic data on the internal structure, (ii) the recovery of the test
model parameters (ϒ,i), and (iii) the recovery of the test model DF.
Results show that increasing the radial coverage of the kinematic data from 1r e to
2re does not change the internal structure within 1r e . The results of the dynamical models of the SAURON observations of NGC 2974 would not change if the radial coverage
would be increased by a factor of 2. Also, three-integral models can accurately recover
the mass-to-light ratio. Although the models are also able to constrain the inclination of
the test model formally, the apparent differences between the models are very small (as
in the case of real observations). Under a careful examination, it is possible to choose
the best model by eye, but the decisive kinematic features are below (or at) the level
of the systematics in the data (e.g. template mismatch) and might be influenced by
uncertainties in the models (e.g. regularisation or variations in the sampling of observables with orbits). This suggests a degeneracy of models with respect to the recovery
16
Chapter 1. Introduction
of inclination. More general tests on other galaxies and theoretical work is needed for
a better understanding of this issue. Finally, three-integral models are able to recover
the true input DF, to the level of the discreteness effects in the models.
10 Future prospects
Basic concepts of galaxy formation and evolution, as well as the cosmological background, are generally agreed upon and can be used as a working paradigm of modern
astronomy. We believe we understand the processes that shape and control the nature
and nurture of galaxies. N-body simulations and three-integral Schwarzschild models
are able to simulate interactions and create representative models of observed galaxies,
respectively. We may even boast that we understand the global picture and certainly it
is true that observations and theory are starting to agree. However, there are a number
of loose ends to be tied and questions to be answered.
The advent of integral-field units opens a detailed view into the structure of galaxies. Two-dimensional spectroscopic observations are clearly very important in constraining the models (kinematic maps), but also complementary to the photometric observations for distinguishing the stellar populations of galaxies (maps of line-strength
indices). This is shown by the results of the SAURON survey of nearby galaxies (Verolme
et al. 2002; Emsellem et al. 2004; Chapter 5 of this thesis; McDermid et al. 2005;
Kuntschner et al. 2005; Cappellari et al. 2005, Sarzi et al. 2005). The next natural step is
to look back in time, using new two-dimensional spectroscopic glasses that are being
commissioned on the 8-10 meter class telescopes, towards higher redshifts and earlier
epochs when interactions between galaxies were more frequent and galaxies look different from today. Comparing the properties of galaxies at redshifts between 0.5 and
1, when the Universe was between three-quarters and half its current age respectively,
with the properties of nearby galaxies will show the actual evolution of galaxies.
Another approach is to observe (with the same new instruments on the largest telescopes) nearby objects that were not often studied up to now due to technical limitations. One such class of objects are small galaxies with low-surface brightness. These
galaxies are interesting because they have not yet participated in merger events (in
a way they are real fossils of Universe), they have experienced only limited starformation, and clearly reside in different potential wells than large luminous galaxies.
Dynamical models of dwarf galaxies will also give low-redshift constraints to cosmological models.
There are possible advances on the modelling front. Firstly, models of triaxial galaxies which also fit the observed kinematics will soon be ready (van den Ven et al. in
prep). They are more complex than axisymmetric models, due to the large parameter
space that describes a triaxial body. On the other hand, models of real galaxies must
include both kinematic and line-strength information, because, after all, galaxies are
not made of one population of stars and a true distribution function is dependent on
the age and metallicity of stars. The modelling approach here differs from the conventional approach: instead of fitting LOSVDs, new models will directly fit observed
spectra giving simultaneous information about the kinematics and distribution of stellar populations (Cappellari et al. in prep.).
Section 10. Future prospects
17
The impact of the Hubble Space Telescope on modern astronomy cannot be properly acknowledged in a single paragraph (nor in a much thicker book!), however, at
this moment of its uncertain future and perhaps even a premature demise, and, here,
thinking of the next steps, it is important to remember its profound role in the increase
of our understanding of the Universe. Discoveries related to the nearby early-type
galaxies are numerous, some of which are presented and discussed in the following
chapters. Modern ground-based telescopes are almost an order of magnitude larger
than HST and have a huge advantage in the collecting power: very important in astronomy where every photon counts. The new technology of adaptive optics with
natural or laser guide stars is almost completely able to correct for atmospheric seeing
(although currently at longer wavelengths only) and scientific observations from the
ground are entering a promising new era. From this point of view we can be satisfied
and encouraged because new observations will surely bring new excitements. Still,
HST will remain a unique human eye into the vastness of the Universe.
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Chapter 2
Relation between dust and radio
luminosity in optically selected early
type galaxies
Davor Krajnović, Walter Jaffe, 2002, Astronomy and Astrophysics, Vol. 390, p. 423
We have surveyed an optical/IR selected sample of nearby E/S0 galaxies with and
without nuclear dust structures with the VLA at 3.6 cm to a sensitivity of 100 µJy.
We can construct a Radio Luminosity Function (RLF) of these galaxies to ∼ 1019
W Hz−1 and find that ∼ 50% of these galaxies have AGNs at this level. The space
density of these AGNs equals that of starburst galaxies at this luminosity. Several
dust-free galaxies have low luminosity radio cores, and their RLF is not significantly less than that of the dusty galaxies.
1 Introduction
R
conducted during the last decade gave a new view of nearby elliptical
galaxies previously considered as old, uniform systems with little gas or dust. Images from the Hubble Space Telescope (HST) have shown that many early-type galaxies have a large amount of dust (103 − 107 M ), either in the form of a nuclear disk or in
the more diverse form of filaments. Among different studies there is a large variation
in the detection rates which may be due to the different methods, resolutions, and sensitivities of the observations (Sadler & Gerhard 1985 40%; Goudfrooij et al. 1994 41%;
van Dokkum & Franx 1995 48%; Ferrari et al. 1999 75%; Tomita et al. 2000 56%; Rest et
al. 2001 43%; Tran et al. 2001 (IRAS bright sample) 78%), but the general conclusion is
that dust is common in nearby ellipticals.
Establishing the presence of dust in nearby early-type galaxies is only the first step
towards determining the role of dust in these systems. It is already a well-known fact
that radio-loud ellipticals often have large amounts of dust but there are some open
questions, especially for the radio-weak sources. Verdoes Kleijn et al. (1999) found that
the incidence of dust in radio-loud early type galaxies is 89% while Tran et al. (2001)
has a value of 43% for the occurrence of dust in their snapshot sample of relatively
radio-quiet nearby early-type galaxies (for a description of the sample see Sec. 2). In
the same sample, 66% of dusty galaxies have NRAO VLA Sky Survey (NVSS) 1.4 GHz
flux detections (Condon et al. 1998), while only 8% of galaxies without dust are listed
as radio sources.
ESEARCH
21
22
Chapter 2. Relation between dust and radio luminosity in early type galaxies
These results raise a question: how important is the presence of dust for radio emission in the nuclei of ellipticals? Plausibly, dust indicates the presence of gas, and gas is
necessary to fuel the activity of a central massive black hole (BH). However, this line of
reasoning is highly incomplete. Gas may be present without dust. Dust may be present
but not visually detectable (Goudfrooij & de Jong 1995). Dust and gas that have fed a
BH in the past may not be observable at the time when the nuclear activity is observed.
These arguments justify a careful study of the relation between dust and nuclear radio
emission to determine the relevance of radio luminosity, dust morphology and other
effects.
There are two approaches to the study of extragalactic radio sources. The first one
is based on catalogs of discrete radio sources followed by an analysis of the optical
counterparts. The second involves searching for radio emission from optically chosen
objects. The first approach (e.g. de Koff et al. 2000) is relatively efficient in finding radio
galaxies, but emphasizes powerful radio sources and may not provide a good countersample of radio-quiet galaxies. The second approach conversely emphasizes weak
radio sources (e.g. Sadler, Jenkins & Kotanyi 1989; Wrobel 1991; Wrobel & Heeschen
1991; Sadler et al. 2002).
Both types of radio surveys are important. Here we have chosen the second method
primarily so that the optical selection of the sample, including Hubble type and especially dust content, is not biased by a priori selection for radio emission or other “interesting”properties of the galaxies. The survey objects are selected on their optical/IR
properties only and then observed with the VLA with the purpose of establishing the
presence of nuclear AGNs. We compare our dusty and non-dusty parts of the sample
to investigate the importance of dust (as a fuel reservoir) for the existence of nuclear
activity.
In Section 2 we present the sample and discuss the observations and the data reduction. In Section 3 we present the results of our study. They are followed with a
discussion in Section 4. Section 5 brings a discussion on correlation of dust with radio
emission. The conclusions are given in Section 6.
2 Observations
2.1 Sample
Our sample is compiled from two different samples described by Rest et al. (2001) and
Tran et al. (2001). The first sample was created by selecting E/S0 galaxies on their
optical properties only from the Lyon/Meudon Extragalactic Database (LEDA). A randomly selected subset of 68 galaxies from this sample was observed with HST using
WFPC2 in snapshot mode and thus this sample is referred to as the “snapshot” sample. An additional sample of galaxies was assembled from archival HST images of
nearby E/S0 galaxies selected for their 100 µm IRAS emission as these were likely to
contain large amount of dust (Tran et al. 2001). This sample is referred to as the “IRAS
sample”. From these two samples, we have selected 36 objects (18 from each) according to their optical/IR properties, with no regard to radio properties. The reason for
this selection was to avoid biasing in picking a priori ”interesting”objects and objects
with strong radio fluxes. Galaxies in our sample are nearby ellipticals and lenticulars
Section 3. Results
23
(E/S0), cz < 3200 km s−1 , at galactic latitude exceeding 20◦ to minimize Galactic extinction, and with absolute V-band magnitude less then -17. Because of their optical/IR
selection they tend to have low radio powers.
The global properties of galaxies in our sample are listed in Table 1 of Rest et
al. (2001) and in Table 7 of Tran et al. (2001). In the list of 36 galaxies, 18 of them
were chosen because they have dust in the form of disks or filaments. The other 18
non-dusty galaxies were selected to match dusty galaxies in optical properties, redshift, magnitude, and IRAS flux. However, after the initial selection, more detailed
studies (Rest et al. 2001, Tran et al. 2001) showed that 6 of the “non-dusty” galaxies
showed faint dust structures and have here been included in the “dust” class. We used
H=80 km s−1 Mpc−1 to be consistent with the papers defining the samples.
2.2 Data Acquisition and Reduction
The observations were undertaken with the VLA in C configuration at 3.6 cm wavelength. All sources were observed at two frequencies in the 8 GHz X-band (8.4351 and
8.4851 GHz) with a bandwidth of 50 MHz for each frequency. We observed 68 sources
in total, 36 galaxies and 32 calibrators. Each galaxy was observed for 15 minutes while
calibrators were observed for 130 seconds. Most of the calibrators had position code
A (positional accuracy < 0.00 002), but four calibrators had B (0.00 002 - 0.00 01) and three
had C (0.00 01 - 0.00 15) as is indicated on the calibrator web page of the VLA. The radio
positions of the detected sources are limited by this positional accuracy of the calibrators, as well as by the accuracy of the Gaussian fit to the source brightness distribution,
which is dependent on the signal-to-noise ratios. Taking this in account the overall
accuracy is about 50 mas for mJy sources and about 100 mas for 100 µJy sources. The
observations were taken on March 13, 2000.
We used the Astronomical Image Processing System (AIPS) to reduce the data using the standard procedures from the AIPS cookbook. After initial calibration, the
data were imaged using the task IMGR. The data were self-calibrated in phases to improve the image dynamic range, using a model derived from the same data. In some
cases amplitude self-calibration was performed on the data to improve the final images. For our astrometric purpose, the positions of the sources were extracted before
self-calibration so that phase information was preserved. All the images were examined using the tasks JMFIT and IMSTAT.
3 Results
Twenty galaxies in our sample of 36 were detected as radio sources. Three detected
sources (associated with NGC 2986, NGC 3610, NGC 4125) cannot be matched with
the central regions of the galaxies and there are no visible counterparts on the available
HST pictures, hence they are most likely background sources. The radio sources lay far
from the nuclei (about 2.0 67 for NGC 2986, 3.0 84 for NGC 3160, and 1.0 44 for NGC 4125).
Although the fluxes and positions of these sources are listed in Table 1 (with asterisks)
we treat them as non-detections of central AGNs in the surveyed galaxies. This leaves
17 AGN detections in 36 galaxies (47 % detection rate). The smallest signal to noise
ratio (SNR) is about 10σ with a survey average rms σ = 2.8 × 10−5 Jy/beam. For non-
Chapter 2. Relation between dust and radio luminosity in early type galaxies
24
name
(1)
dust
(2)
ngc1400
ngc1439
ngc2549
ngc2592
ngc2699
ngc2768
ngc2778
ngc2974
ngc2986*
ngc3078
ESO437-15
ngc3156
ngc3226
ngc3348
ngc3377
ESO378-20
ngc3595
ngc3610*
ngc4125*
ngc4233
ngc4365
ngc4406
ngc4476
ngc4494
ngc4552
ngc4697
ngc4742
ngc5198
ngc5322
ngc5557
ngc5576
ngc5812
ngc5813
ngc5845
ngc5982
ngc6278
2
4
0
4
4
4
0
3
0
4
3
2
3
0
1
0
0
3
4
4
0
4
3
4
4
4
3
0
4
0
0
4
4
4
0
0
D
(3)
peak flux
(4)
RA
(5)
DEC
(6)
L
(7)
δ
(8)
NVSS flux
(9)
25.4 P 2.092 ± 0.02 03 39 30.815 -18 41 17.42
1.61 ± 0.02
1.80 2.5 ± 0.5
20.9T
<0.1
15.7 R
<0.1
0.32 ± 0.01
0.65
25.5 R
0.41 ± 0.02 08 27 08.040 25 58 13.00
21.8 R
<0.1
3.59 ± 0.01
0.54 14.5 ± 0.6
16.7T 10.71 ± 0.02 09 11 37.418 60 02 14.84
25.4T
<0.1
25.9T
5.22 ± 0.02 09 42 33.310 -03 41 57.09
4.19 ± 0.02
0.93 10.4 ± 0.5
22.3T
8.40 ± 0.03 09 44 27.256 -21 16 11.23
160.14
1.45 279 ± 8
29.0 R 124.95 ± 0.04 09 58 24.630 -26 55 36.09 125.73 ± 0.04
32.3 R
1.76 ± 0.04 10 36 58.100 -28 10 34.70
2.20 ± 0.05
0.80 3.2 ± 0.6
<0.1
14.0T
17.3 R
7.29 ± 0.05 10 23 27.005 19 53 54.75
2.61 ± 0.02
0.97
38.5 R
1.66 ± 0.02 10 47 10.000 72 50 22.71
2.94 ± 0.04
1.36 7.8 ± 0.5
9.1T
<0.1
35.6 R
<0.1
30.4 R
0.22 ± 0.01 11 15 25.180 47 26 50.60
0.24 ± 0.01
3.87
26.8 R
1.17 ± 0.03 11 18 20.700 58 49 38.11
230.78
20.1 R
1.23 ± 0.02 12 08 04.180 65 09 41.32
86.29
29.6 R
2.52 ± 0.01 12 17 07.679 07 37 27.33
2.64 ± 0.01
1.02 2.9 ± 0.5
15.7 R
<0.1
17.0V
0.59 ± 0.02 12 26 11.770 12 56 46.40
0.204 ± 0.07
1.37
24.7T
<0.1
17.8 R
0.27 ± 0.01 12 31 24.030 25 46 30.01
0.10 ± 0.01
2.00
17.0V 93.40 ± 0.02 12 35 39.805 12 33 22.78
32.30 ± 0.01
0.35 100 ± 3
15.5T
<0.1
15.9T
<0.1
34.1 R
0.83 ± 0.02 13 30 11.390 46 40 14.80
1.15 ± 0.03
1.16 3.6 ± 0.4
23.9T 13.60 ± 0.02 13 49 15.269 60 11 25.92
9.33 ± 0.01
1.08
64 ± 2
42.5 R
<0.1
19.1 R
<0.1
24.6 R
<0.1
24.6 R
2.95 ± 0.02 15 01 11.234 01 42 07.10
2.14 ±0.01
0.72 12.3 ± 0.7
18.1T
<0.1
39.3 R
<0.1
37.1 R
1.06 ± 0.01 17 00 50.325 23 00 39.73
1.75 ± 0.02
0.62
Table 1 — Radio properties of the galaxies. Col.(1): name of the galaxy, sources with a star are far from
the nuclear region of the corresponding galaxies and were treated as non detections; Col.(2): level of
dust: 0 = no dust, 1 = filamentary low, 2 = filamentary medium, 3 = filamentary high, 4 = dusty disk
(Tran et al. 2001); Col.(3): distance in Mpc from (P) - Perrett et al. 1997, (T) - Tran et al. 2001, (R) - Rest
et al. 2001, (V) - Virgo galaxies, assumed to be at distance of 17 Mpc; Col.(4): flux at 3.6cm in mJy, or 4σ
upper limits for non-detections; Cols.(5) and (6): radio position (h, m, s) and (deg, arcmin, arcsec) from
our maps (J2000); Col.(7): luminosity in 1020 WHz−1 ; Col.(8): offset in arcseconds, between the 3.6 cm
radio position and the position of the galaxy optical nucleus on HST images (Tran et al. 2001, Rest et
al. 2001); Col.(9): peak flux from NVSS survey (Condon et al. 1998).
Section 4. Discussion
25
detected sources we calculated the 4σ upper limits on detection, thus, the detection
limit of our survey is about 0.1 mJy. Radio properties of the sample are given in Table
1. By comparison, the detection limit of the NVSS (Condon et al. 1998) used by Tran et
al. (2001) to discuss radio properties of our sample is ∼ 3 mJy, a factor of 30 higher.
Most of the detections are point-like, unresolved structures. NGC 5322 is the only
galaxy with noticeable jet-like structure. Typical detected sources are on the level of a
few mJy; the weakest detections were ∼ 200µJy. Of the 36 galaxies in the sample, 24
galaxies show disk or filamentary dust structure and 13 (54%) of them are detected as
radio sources. Twelve show no dust of which four (33%) are detected.
4 Discussion
4.1 Nature of Detected Radio Sources
Most of the detections are unresolved radio sources easily associated with the central
1.00 5 on the HST image. At 25 Mpc, the mean distance of the galaxies in the sample,
100 is about 120 pc. Thus the emission is clearly (near) nuclear, but not necessarily of
AGN origin. Since the sources are weak (radio power ranges from 1019 W Hz−1 to 1021
W Hz−1 with a few higher exceptions) there is a possibility that they arise from a nonAGN mechanism, e.g. nuclear starbursts. Since we are interested in the AGN/dust
connection we wish to exclude this possibility. We argue here that the dominant source
of radio emission in our detections is a non-thermal mechanism similar to that which
operates in more powerful radio sources.
There are several radio and infrared criteria that can be used to distinguish between
emission from starburst and AGN galaxies: (i) radio morphology, (ii) far-infrared to
radio flux-density parameter u ≡ log(S60µm / S1.4GHz ), (iii) infrared spectral index α IR ≡
log(S60µm / S25µm )/ log(60/25) (Condon & Broderick 1988 and 1991; Condon et al. 1991;
Condon, Huang & Thuan, 1991), and (iv) the steepness of the radio spectra. Radio
morphology implies coherent radio jets and radio lobes that may lie well outside the
optical galaxy. Starburst galaxies usually have u ≥ 1.6, and α IR ≥ +1.25. Steepness of
the radio spectrum is also used as a criterion since optically thick AGN cores usually
have flat spectra, while the dominant emission from star-forming regions (supernova
remnants, and cosmic rays diffusing from them) have steep spectra. Nearly all spirals
and unclassifiable objects (e.g mergers) have steep spectra, while flat spectra and other
AGN characteristics (radio morphology, u ≤ 1.6, and α IR ≤ +1.25) are associated with
ellipticals (Sadler, Jenkins, & Kotanyi 1989, Condon 1991).
All detected galaxies in our sample have low-luminosity unresolved sources in the
innermost central regions. Although the sources are certainly nuclear in origin (suggesting AGN activity) any radio classification according to radio morphology is not
possible (except in the clear case of a jet in NGC 5233). Half of the galaxies were picked
based on their large-scale dust and infrared properties from the IRAS survey. This
means that those galaxies are going to have larger α IR indices, which would mark
them as starburst, although they still might have nuclear AGN which are the subject
under discussion. Using the large scale IR emission to determine the nature of the
nuclear radio emission does not seem to be a very good discriminator between SBs
and AGNs. However, most of our objects have measured nuclear Hα fluxes or upper
26
Chapter 2. Relation between dust and radio luminosity in early type galaxies
Figure 1 — The integral luminosity function
derived from 17 detected sources out of a total of 36. The dots represent a crude LF calculated from the detections as the integral of
a series of delta functions. A detection at Li
contributes 1/Nd (Li ) where the denominator
is the number surveyed galaxies detectable at
Li . The steep rise flattens off below of 1020 W
Hz−1 . The error bars are not plotted since the
bins in the integral RLF are not independent.
limits (Tran, private communication), and standard calculations (Osterbrock 1989) indicate that the free-free fluxes from these regions would be below 3 µJy, which is about
two to three orders of magnitude smaller than our observed fluxes. Other evidence
that we are dealing with non-thermal radiation comes from the flatness of the spectra
in our sample. Eleven of the galaxies were detected before in the NVSS (Condon et
al. 1998) and comparing the fluxes at our frequency (8.45 GHz) and the frequency of
the NVSS (1.4 GHz) it is clear that most of the detected galaxies have flat spectra (Table
1).
Previous studies (Phillips et al. 1986; Sadler, Jenkins & Kotanyi 1989) have shown
that HII regions in early type galaxies are not likely to contribute to the radio galaxy
population above 1019 W Hz−1 . Keeping in mind that all galaxies in our sample are Es
and S0s, that emission is confined to nuclei of the host galaxies, and that the sources
have flat spectra, we can assume that the dominant radio component in our case is
synchrotron emission from an active nucleus producing low-luminosity counterpart
of more distant, luminous AGNs.
4.2 Radio Luminosity Function
The size of our sample is too small and too limited in radio luminosity range to construct a complete local radio luminosity function (RLF) of early-type galaxies. In any
case, the sample was not constructed for that purpose. Still, we can make a useful estimate of the low luminosity end of the local RLF in order to see how it corresponds
with previously found local RLFs and offer an estimate of the behavior of RLF at low
luminosities. For this purpose we define the fractional luminosity function (Auriemma
et al. 1977):
Fi (L, z) = ρi (L, z)/ϕi (z),
(1)
where ϕi (z) is the volume density of objects of type i at the redshift z, and ρ i (L, z) is
the density of sources associated with optical objects of type i with the given radio
Section 4. Discussion
27
Figure 2 — Comparison of AGN and starburst (SB) local radio luminosity function.
Filled symbols (circles: AGN, triangles: SB)
are data from Sadler et al. (2002) and Condon
(1991), while open circles are our data. The local density of AGN rises continuously at low
luminosities, reaching the value of SB, suggesting that AGNs are as common as SB in
local universe. It is possible that at this low
luminosity level both processes are present in
galaxies, but in some galaxies one of the engines is stronger.
luminosity L and at the given redshift z. The fraction of all elliptical galaxies with
luminosity at a given frequency between L and L + dL at the redshift z, of optical magnitude M is given then by FE, M (L, z)dL. In order to estimate the “bivariate” RLF defined
in this way we can calculate the fractional detection f i j = ni j / Ni j , where n(Li , M j ) is the
number of actually detected galaxies within the optical magnitude range M j ± 0.5 and
radio luminosity interval logLi ± 0.2, while N(Li , M j ) is the number of galaxies in the
sample which could have been detected if their optical magnitude and radio luminosity were in the given interval. In our case we did not bin in optical magnitude but only
in radio power since the sample is limited. Our first estimate of the RLF is then given
by f L = n L / NL and it is shown in Fig. 1 in integral form, F(>L). As it can be seen from
the Fig. 1, the integral RLF of nearby ellipticals rises steeply with decreasing of the
radio luminosity and only at the lowest intensities (1019 W Hz−1 ) levels off at a point
where ∼ 50% of all E/S0 galaxies show activity.
Previous RLFs (Auriemma et al. 1977; Sadler, Jenkins, & Kotanyi 1989; Condon
1991; Sadler et al. 2002) of nearby ellipticals with an AGN signature were made for
galaxies with radio luminosities higher than 1021 − 1022 W Hz−1 . The more recent studies considered also starburst galaxies. While AGN were found in ellipticals, starbursts
inhabited spirals. These different distributions had different RLFs and often starburst
RLFs extended to the level of 1020 W Hz−1 . With our low luminosity data, we are able to
extend the existing RLFs of AGN down to 1019 W Hz−1 and can construct an exclusively
AGN RLF.
We compare our data with two studies (Sadler, Jenkins, & Kotanyi 1989 and Condon 1991) in Fig. 2 (AGNs and starbursts plotted). We have converted our differential
data from F(L) to a spatial density φ (number of sources per Mpc3 per 0.4 in log L) using the value for spatial density of early type galaxies, from Sadler, Jenkins, & Kotanyi
(1989), which is 10−2.33 mag−1 Mpc−3 . Gratifyingly our data agrees quite well with the
previous data in the region of overlap. Together these data confirm the flattening of
the RLF for AGNs below ∼ 1020 W Hz−1 . It is also interesting that the space density
28
Chapter 2. Relation between dust and radio luminosity in early type galaxies
Figure 3 — Plot of log radio luminosity in W Hz−1 versus absolute optical magnitude. Filled symbols are radio-detected nuclei of
galaxies, while open symbols indicate upper limits for the rest of
the galaxies. Triangles are sources
in galaxies without dust and circles are sources in dusty galaxies. Sources in dusty galaxies have
a slight tendency for being more
powerful than the sources in nondusty galaxies. Luminosity error
bars are smaller than the symbols.
of low luminosity AGN is very similar to starbursts galaxies of the same luminosities.
The RLFs of the two distributions are basically overlapping in this luminosity range.
5 Correlation of dust with radio emission
5.1 Crude Statistics
The HST pictures of the galaxies in the original sample (Tran et al. 2001) confirm that
dust is very common in ellipticals. There are two different morphologies in which
dust appears in the galaxies from our sample: disky and filamentary. We have 15
galaxies with disks and 9 with large amount of dust in filaments. Thirteen of the 24
dusty galaxies have a radio detection (54%), while 4 out of 12 non-dusty galaxies show
a detection (33%). There is no significant difference in radio luminosity between the
galaxies with disky and filamentary dust: 60% detections in galaxies with disks and
44% in galaxies with filaments. This finding is in general agreement with the findings
by Tran et al. (2001).
The relationship between optical absolute magnitude and radio luminosity for our
weak radio sources is shown in Fig. 3. There is little difference in the distributions of
the dusty and non-dusty galaxies, except perhaps that the three most powerful galaxies
are all dusty. As expected, the more powerful radio sources are found in the brighter
galaxies.
Most nearby high luminosity radio sources are found in dusty early type galaxies
(de Koff et al.(2000)), which suggests a link between dust and the existence of a radio
source. Our wish now is to see if at the lower levels of radio luminosity dust also
plays an important role. We divide the detections in two sets of sources: dusty and
Section 5. Correlation of dust with radio emission
29
Figure 4 — The separated integral luminosity function. Open circles present the RLF for
sources from galaxies lacking dust. Filled circles present the RLF of sources from dusty
galaxies. Statistical tests show that the two
distributions are not distinguishable, suggesting that dust is not important for the existence
of low-luminosity AGN in nearby early-type
galaxies.
non-dusty according to the descriptions in Tran et al. (2001). As we see above, the
dusty galaxies show a somewhat higher detection rate, but, given the steepness of the
RLF, this could be influenced by slight differences in the distances to the two samples,
or slight differences in the achieved sensitivities. Therefore it is more meaningful to
compare the RLFs of the two samples than the detection percentages.
5.2 Comparison of RLFs
The integral RLFs for the two samples, computed by the same algorithm as that in
Fig. 1 for the whole sample, are shown in Fig. 4. In this representation also, the dusty
galaxies seem more active, but the difference is relatively small (a factor of ∼ 1.6) and
we wish to test the significance of this difference.
The integral RLFs for the two samples, computed by the same algorithm as that in
Fig. 1 for the whole sample, are shown in Fig. 4. In this representation also, the dusty
galaxies seem more active, but the difference is relatively small (a factor of ∼ 1.6) and
we wish to test the significance of this difference.
We have tried two statistical tests: Kolmogorov-Smirnoff (K-S) and a test using
maximum likelihood method (ML). The K-S test has the advantage of being parameter
and form free, but the disadvantage of not being very conclusive for small samples.
We have two data sets, one with 13 sources in dusty galaxies and one with 4 sources
in non-dusty galaxies. We used routines from Numerical Recipes (Press et al. 1992).
The probability that these two observation sets could be obtained from the same RLF
is 64%, hence the RLFs are statistically indistinguishable. However, the K-S test is sensitive to the effective number of data points, Ne , which in our case of two distributions
is Ne = N1 N2 /(N1 + N2 ) = 3.1. Press et al. (1992) give Ne ≥ 4 as a limit for a decent
accuracy. Thus, the above probability is not very accurate, but it still implies that the
two data sets (two luminosity functions) are not significantly different.
Another approach that is more sensitive, but requires more a priori assumptions,
is to fit a specific, parameterized, function to the RLF data using the maximum likeli-
30
Chapter 2. Relation between dust and radio luminosity in early type galaxies
Figure 5 — Estimated integral luminosity
functions compared to the data. The drawn
lines show the ML model fits (equations 2
and 3) to the data, while the points are computed from individual detections. Field circles present dusty galaxies while open circles
present non-dusty galaxies. The thick line
shows the ML model fit for dusty galaxies and
the thin line for non-dusty galaxies.
hood method, and compare the fitted functions. Since there are a limited number of
degrees of freedom in the function, more powerful statistical statements can be made.
To estimate the integral luminosity function we used a set of two power-law functions
allowing for a break in the RLF. Our choice is similar to some previously used functions
(Auriemma et al. 1977):
F = A0 · 10−β (x−xc )
for x > xc
(2)
β
for x < xc
(3)
F = A0 · (1 + (10−α(x−xc ) − 1))
α
where x = log10 L, and L is radio luminosity in W Hz−1 . The normalization constant
A0 is chosen so that at x = xc , F = A0 . Originally we assumed that at low luminosities
the value of F(x) had to approach F = 1 as x → −∞, thus providing an additional constraint on the model. These solutions provided poor fits to the data and were dropped.
This implies, however, that there is another break (or continuous change of slope) in
the RLFs below the limits of our survey.
The system of coefficients α, β (slopes of the curve), xc (the position of the break)
and A0 (normalization) that maximize the probability in the method, provide also the
best fit to the data. Table 2 contains the calculated values for α, β , x c and A0 .
The best-fit integral luminosity functions are compared to the observed values in
Fig. 5. The symbols are filled circles for dusty and open circles for non-dusty sources.
The thick represents the model fit to dusty sources, while the thin line shows the fit to
the non-dusty. The model curves fit the individual points reasonably well. The three
radio brightest galaxies lie somewhat above the best two power-law fit in the region of
the break, but the best fit value of the slope above the break, β ' 0.75, agrees with the
slope measured by Sadler et al. (2002) (Fig. 2) based on much more data in the higher
luminosity ranges.
The ML parameters α, β , and xc are essentially identical for dusty and non-dusty
galaxies, indicating that the forms of the RLF are similar. Not surprisingly the normal-
Section 6. Conclusions
31
Table 2 — Estimated integral luminosity coefficients. Values of coefficients of estimated integral luminosity function F obtained by maximum likelihood method. Errors are 1σ estimates.
data sample
all data
dust data
non-dust data
α
−0.6 ± 0.3
−0.6 ± 0.4
−0.5 ± 0.3
β
0.80 ± 0.10
0.74 ± 0.09
1.20 ± 0.60
xc
20.41 ± 0.04
20.40 ± 0.10
20.24 ± 0.04
A0
0.21 ± 0.04
0.25 ± 0.07
0.14 ± 0.02
ization A0 is higher for the dusty galaxies by a factor of about 1.8, but this is only 1.6
times the uncertainty.
Another way to globally judge the significance of the difference between these RLFs
it to ask if the “true”RLF were given by the dusty model, how unlikely is it that we
would only detect four (or less) of the twelve non-dusty galaxies. If this probability is
small, then the samples are significantly different. From Poisson statistics the probability of 4 or less non-dusty detections given the dusty RLF (thick line on Fig. 5 or the
second line values in the Table 2) is 27%, indicating a low statistical significance. If,
hypothetically, the true non-dusty RLF is a factor of 1.6 lower than the dusty RLF we
can ask how many non-dusty galaxies must be surveyed in order to demonstrate the
RLF difference at a reliability of, say, 5%. Repeating the Poisson analysis indicates that
a sample about four times the current size is needed, or about 50 non-dusty galaxies.
Perhaps the most important result of this investigation is that in any case, a sizable
fraction of the non-dusty galaxies, ∼ 30%, are radio emitters, so that the presence of
visible dust is not necessary for radio emission from an AGN.
6 Conclusions
We report 3.6 cm VLA observations of a sample of 36 near-by ellipticals selected on
their optical/IR properties. We detected 17 unresolved (except the jet in NGC5322),
compact, flat-spectrum radio cores associated with the central 1 00 of the nuclei, suggesting that all detected sources are low luminosity AGNs. The lowest detected luminosities are ∼ 1019 W Hz−1 .
We determine the Radio Luminosity Function (RLF) from these galaxies down to a
luminosity almost two orders of magnitude lower in luminosity than previously published studies. It shows the continuation in the rise of space density of sources with
AGN signature, which was expected from other, unpublished, studies (Condon, private communication). At the luminosities considered (i.e L ∼ 1019 - 1022 WHz−1 ), the
space densities of the AGNs and starburst galaxies approach each other, becoming
hardly distinguishable. At the lower luminosity end of our sample ∼ 50% of E/S0
galaxies have detectable radio-AGNs.
Although the non-dusty galaxies show an indication of a lower probability of radio
emission, the difference is not statistically significant in a sample of this size. Dust detectable in HST images is certainly not necessary for nuclear radio emission. This situation may be different for the more powerful radio galaxies observed in earlier surveys.
32
Chapter 2. Relation between dust and radio luminosity in early type galaxies
This takes us back to the question of fuel for the central engine of our low luminosity AGNs. If fuel is necessary for nuclear activity why do we find weak AGNs without
visible dust? It should be noted that our non-dusty galaxies with radio detections lay
further away (D > 30 Mpc) and it might be possible that small amounts of dust were
not detected. Also, extremely diffuse gas and dust would not be visible (Goudfrooij
& de Jong, 1995) but current theories of accretion require bars and disks and other
distinct structures, so fueling from diffuse gas seems unlikely. Similarly, these galaxies could be fueled by hot, dust-free gas, but it seems unlikely that any mechanism
in these low-luminosity sources would destroy dust more than in the high luminosity
sources were dust is common. A more likely explanation is that the amount of dust
and gas present near the nucleus is in some sense positively correlated with the AGN
luminosity. The sources in our study are two to three orders of magnitude less luminous than the 3C sources in de Koff et al. (2000), where typical dust optical depths
were of order unity. In the HST images, optical depths of less than 1% would probably be missed. Alternatively, AGN fueling may be cyclic, and AGN radio emission is
now fueled from material at a few Schwarzschild radii, after the material in a larger
circumnuclear accretion disk has been temporarily consumed.
The luminosity of an AGN is determined by the fueling rate and the mass-toradiation conversion efficiency. The latter is influenced by the degree of advection
which is in turn influenced by the Eddington luminosity and the mass of the BH. As
recent evidence suggests (Ho, 2002 and references therein) many of the characteristics
of low luminosity AGN could be explained by an advection-dominated accretion flow
(Narayan & Yi 1995; Narayan, Mahadevan, & Quataert 1998). The explanation of the
dust/radio emission/luminosity relations may perhaps be found when we know the
BH masses of the galaxies, or when we understand the characteristics of non-steady
accretion flows.
Acknowledgements
DK was supported by Institute Ruder Bošković in Zagreb and NOVA, the Netherlands
Research School for Astronomy. The VLA is operated by the National Radio Astronomy Observatory for the U.S. National Science Foundation.
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Chapter 3
HST observations of nuclear stellar disks
Davor Krajnović, Walter Jaffe, Astronomy and Astrophysics, in press, [astro-ph/0409061]
We present observations of four nearby early-type galaxies with previously known
nuclear stellar disks using two instruments on-board the Hubble Space Telescope.
We observed NGC 4128, NGC 4612, and NGC 5308 with the Wide Field Planetary
Camera 2, and the same three galaxies, plus NGC 4570, with the Space Telescope
Imaging Spectrograph. We have detected a red nucleus in NGC 4128, a blue nucleus in NGC 4621, and a blue disk in NGC 5308. Additionally, we have discovered
a blue disk-like feature with position angle ∼ 15◦ from the major axis in NGC 4621.
In NGC 5308 there is evidence for a blue region along the minor axis. We discovered a blue transient on the images of NGC 4128 at position 0.00 14 west and 0.00 32
north from the nucleus. The extracted kinematic profiles belong to two groups:
fast (NGC 4570 and NGC 5308) and kinematically disturbed rotators (NGC 4128
and NGC 4621). We report the discovery of a kinematically decoupled core in
NGC 4128. Galaxies have mostly old (10-14 Gyr) stellar populations with large
spread in metallicities (sub- to super-solar). We discuss the possible formation scenarios, including bar-driven secular evolution and the influence of mergers, which
can explain the observed color and kinematic features.
1 Introduction
T
decade of Hubble Space Telescope (HST) observations have revealed the existence of small scale nuclear stellar disks in early-type galaxies. This discovery
was an important step in the long process of recognizing the complexity of early-type
galaxies. Ground-based studies preceding the HST era, having lower resolution and
polluted by typically > 100 seeing, already recognized two distinct classes of elliptical
galaxies (Davies et al. 1983) that differed in photometric appearance – disky vs. boxy –
and kinematic properties – rotationally vs. pressure supported – (Bender 1988; Bender
et al. 1989). Follow-up studies discovered the existence of embedded stellar disks in
elliptical and lenticular galaxies (Scorza & Bender 1995; Seifert & Scorza 1996). These
disks, although similar to their counterparts in spiral and S0 galaxies, have smaller
scale length and higher central surface brightness. They often do not follow the same
exponential profiles, and are closer to r1/4 profiles, reflecting formation in a different
potential: dark halo potentials for disks in late-types, and bulge potentials for disks
in early-type galaxies (Scorza & Bender 1995). The existence of the embedded disks
also supports the idea of the morphological connection between spiral, lenticular and
elliptical galaxies (Kormendy & Bender 1996).
HE
35
36
Chapter 3. HST observations of nuclear stellar disks
The properties of the nuclear regions (inner few 100 pc) of early-type galaxies are,
however, not easily accessible from the ground. High resolution imaging surveys with
HST discovered small scale nuclear stellar disks in early type galaxies (Jaffe et al. 1994;
van den Bosch et al. 1994; Lauer et al. 1995; Rest et al. 2001,hereafter R01). They were
followed by detailed photometric and kinematic studies on a few individual objects,
principally NGC 4342 (Scorza & van den Bosch 1998; van den Bosch et al. 1998,hereafter BJM98), NGC 4570 (BJM98; Scorza & van den Bosch 1998; van den Bosch &
Emsellem 1998), NGC 4594 (Burkhead 1986; Kormendy 1988; Emsellem et al. 1996),
NGC 7332 (Fisher et al. 1994; Falcón-Barroso et al. 2004). A detailed study of early-type
galaxies with kinematicaly distinct components (Carollo et al. 1997a,b) found photometric evidences for faint nuclear stellar disks in a number of dust free galaxies.
The next step was a search for embedded nuclear stellar disks in bulges of spiral
galaxies. The high resolution studies of spiral galaxies with HST showed that a significant fraction of galaxies classified as early-type spirals have a rich variety of central
properties, and show little evidence for r1/4 law expected for smooth bulges (Carollo
et al. 1998). Similarly, Balcells et al. (2003) found moderately large fraction (34%) of
nuclear bars or disks in their HST near-infrared survey of S0 – Sbc galaxies. Using
archival HST imaging, Pizzella et al. (2002) reported evidence for nuclear disks in three
early-type spirals and concluded that the disks are restricted to S0 and unbarred spiral galaxies. Having in mind that nuclear stellar disks are detectable only when seen
nearly edge on (Rix & White 1990), they appear to be very common, perhaps universal,
in flattened ellipticals and S0s.
The large fraction of detected nuclear disks in early-type galaxies (51% in the R01
sample) presents the questions: how and when did the nuclear stellar disks form?
Nuclear stellar disks are found in S0 and disky ellipticals, but they are not simple extensions of large scale disks to the center of the galaxy. Often there is clear photometric
and kinematic evidences for double disk structures (van den Bosch et al. 1994; Scorza
& Bender 1995; Scorza & van den Bosch 1998), where the double disk structures are
represented by two morphologically separated disks, having different scale lengths,
lying in nearly same plane, but possibly with different inclinations, and having an inner/outer separation radius between the disks. On the other hand, Erwin & Sparke
(2002) show evidences that some inner disks seen in edge-on galaxies could be bars
mistaken for disks. In any case, the two dynamically different structures are not easily
distinguished in all cases.
Inner disks are also found inside bars or rings (van den Bosch & Emsellem 1998;
Erwin & Sparke 1999; Erwin et al. 2003). This is important for understanding their
formation. Nuclear stellar disks could be the result of mergers in hierarchical galaxy
formation scenario: accretion of gas during the merger which settles in the principal
plane of the galaxy and then makes stars. On the other hand, disks could be formed
from the galaxy material transported to the nucleus by a bar, or perhaps from a mixture
of these processes, in which a bar fuels the center effectively with gas captured at some
previous epoch. Whatever scenario we choose, it has to be consistent with the high
metallicities seen in the disks (BJM98; Emsellem et al. 1996) as well as their blue colors
(BJM98; Kormendy et al. 2002) implying younger stellar populations.
Nuclear stellar disks with their cold dynamical properties and high surface bright-
Section 2. WFPC2 broad band imaging
galaxy
(1)
type
(2)
NGC 4128 S0
NGC 4570 S0
NGC 4621 E
NGC 5308 E-S0
37
MB
(3)
-19.89
-20.39
-20.49
-20.38
B − V vrad
(4)
(5)
1.02
0.97
0.97
0.93
2610
1811
524
2299
PA
(6)
D scale
(7) (8)
58
159
165
60
36.3
25.2
7.3
31.9
175.7
121.9
35.3
154.8
Table 1 — The properties of sample galaxies. Col. (1): galaxy name; Col. (2): morphological type;
Col. (3): absolute B-magnitude; Col. (4): apparent B-V color within the effective aperture in which half
of the B-flux is emitted; Col. (5): radial velocity (cz) in km s−1 corrected for LG infall onto Virgo; Col. (6):
major axis position angle in degrees; Col. (7): distance in Mpc, as derived from radial velocity (column
5) using Hubble constant H0 =72 km s−1 Mpc−1 (Freedman et al. 2001); Col. (8): distance scale in pc
arcsec−1 . Values listed in columns 2 – 6 are taken from Lyon/Meudon Extragalactic Database (LEDA).
ness provide an excellent measure of the central mass-to-light ratio, as well as of the
mass of the central black hole (van den Bosch & de Zeeuw 1996). A few studies used
this to determine the mass of the back holes in galaxies with nuclear stellar disks (Kormendy et al. 1996a; Kormendy et al. 1996b; Cretton & van den Bosch 1999; Emsellem
et al. 1999).
Early-type galaxies are also interesting for studying stellar populations. The absence of strong and continuous star-formation as well as emission line gas makes it
easier to investigate the formation history and the connection between the photometric morphology, dynamical structures and corresponding stellar populations.
In order to increase the available dataset and to investigate the dependencies between the kinematics and line-strengths, as well as to determine the mass of black
holes, we obtained high resolution spectra of four galaxies known to have nuclear
stellar disks from the R01 sample: NGC 4128, NGC 4570, NGC 4621 and NGC 5308.
In addition, we also imaged three of the galaxies, except NGC 4570 which was thoroughly investigated in the previous studies (BJM98, Scorza & van den Bosch 1998; van
den Bosch & Emsellem 1998). In this paper we present data observed with two instruments on-board HST during Cycle 9 (Program ID 8667) and concentrate on the
photometric and spectroscopic properties and dependencies. Dynamical modeling of
the galaxies with the purpose of determining the masses of the central black holes will
follow in a separate paper.
Section 2 presents broad band photometry, data reduction, isophotal analysis and
color images. Section 3 deals with spectroscopic observations, data reduction, extraction of kinematics and measurements of line-strengths. Section 4 presents a discussion
of the results for individual galaxies. The conclusions and summary of the work are
presented in Section 6.
2 WFPC2 broad band imaging
The Wide Field Planetary Camera 2 (WFPC2) observations (Biretta et al. 1996) included
imaging in V (F555W) and B band (F450W). The general properties of the sample galaxies are presented in Table 1, the observations are summarized in Table 2 and the details
of the filter properties are listed in Table 3. The centers of the galaxies were positioned
Chapter 3. HST observations of nuclear stellar disks
38
galaxy
filter
NGC 4128 F450W
F555W
NGC 4621 F450W
F555W
NGC 5308 F450W
F555W
date
14.05.2001
14.05.2001
14.05.2001
14.05.2001
07.05.2001
07.05.2001
time # exp
1400
800
1200
800
1400
800
Table 2 — Summary of HST/WFPC2 observations.
2
2
2
2
2
2
on the PC CCD. The size of the PC CCD is 800 × 800 pixels of 0.00 0455 × 0.00 0455. All exposures were taken with the telescope in fine lock. In addition to newly acquired data,
we used existing archival I (F814W) band images for NGC 4621 (Program ID 8212, PI
Ajhar) and NGC 5308 (Program ID 5512, PI Faber). There were no I band observations
for NGC 4128 in the archive.
2.1 Data reduction
The images were reduced through the standard HST/WFPC2 pipeline. Upon request
of the data, the On-The-Fly reprocessing system re-reduced the data using the best calibration files. The standard reduction steps include correction for analog to digital conversion error, bias and dark current subtraction and flat-fielding (for more description
see Holtzman et al.( (1995)). Our observations were divided (CR-SPLIT) in two (per
filter). To combine them and to remove the cosmic rays we used a set of IDL routines
from The IDL Astronomy User’s Library (Landsman 1993)1 . The WFPC2 images (PC,
WF2, WF3, and WF4 for both CR-SPLIT sections) are cross-correlated to determine a
possible shift between the exposures, aligned and combined removing the cosmic rays
using an IDL equivalent of the IRAF task CRREJ.
We then constructed color images: B-I, V-I and B-V. To construct the color images
we had to align the individual images very precisely. This was achieved by rotating
the original images for the difference in the telescope orientation angle, sub-sampling
pixels by a factor of six and cross-correlating images to find the shift. After all shifts
were applied, the images were rebinned to the original pixel size. Both images used
for the construction of a color image were initially convolved with the PSF of the other
image. The PSFs were constructed using Tiny Tim software (Krist & Hook 2001). The
raw counts of the images were converted into Johnson-Cousins B,V and I magnitudes
following the guidelines given by Holtzman et al. (1995), using the zero points as
given by Dolphin (2000)2 and iterating the calibration until convergence. Note that the
iteration was not performed for the B-I color images, because there were no published
transformation for the F450W filter using B and I. We estimate our relative photometric
accuracy to be ≈ 0.02 mag, while the absolute uncertainty is ≈ 0.05 mag (and ≈ 0.1
for B-I color). In Figs. 1 and 2 we present WFPC2 observations, isophotal analysis,
broadband and color images of three observed galaxies.
1
2
http://idlastro.gsfc.nasa.gov
http://www.noao.edu/staff/dolphin/wfpc2 calib/
Section 2. WFPC2 broad band imaging
Table 3 — Properties of the WFPC2 broad band filters used (from
WFPC2 Instrument Handbook).
39
filter
λ
∆λ
F450W 4410 925
F555W 5202 1223
band
B
V
2.2 Isophotal analysis
In order to investigate the disky structure of the galaxies we used the IRAF task ‘ellipse’ to perform isophotal fits to the light distributions. We measured the ellipticity
and position angle of the isophotes, as a function of radius. The method (for a full
description see Jedrzejewski (1987)) first fits elliptical isophotes to a Fourier expansion
of first and second order terms. The next step in the method is to measure the higher
order terms of the Fourier expansion. The pure ellipse is given by the first two order
terms in the expansion. Any non zero values of the higher order (> 2) terms means
a deviation from the perfect ellipse. Peletier et al. (1990) and Goudfrooij et al. (1994)
found that cos3θ terms (b3 ) are sensitive to the presence of dust (as well as the difference
between the higher order terms in different bands), while the cos4θ terms (b 4 ) describe
the shape by distinguishing boxy (b4 < 0) from disky (b4 > 0) galaxies (e.g. Lauer 1985;
Bender 1988). The isophotal parameters for three galaxies are shown in Fig 1. Different
studies (van den Bosch et al. 1994,R01) showed that although the isophote parameters
can be fitted down to 0.00 03, they are not reliable and only values > 0.00 2 should be used
for analysis.
The galaxies were selected on the basis of having a nuclear stellar disk and our
isopohotal analysis agrees well with the R01 results. For all three galaxies the b 3 terms
are consistent with being zero in the reliable range (> 0.00 2). The b4 terms have clear
disky deviations, but there are differences between the galaxies. NGC 4128 shows the
smallest positive values of b4 coefficient, and is the only galaxy where b4 becomes negative. It drops below zero at a radius of ∼ 300 from the center. The isophotes remain boxy
in the rest of the investigated range (3 – 10 00 ). The fourth order term in NGC 4621 is
positive in the investigated range, although it starts to decrease beyond 3 00 . NGC 5308
shows the sharpest rise of the b4 coefficient, but it drops to zero around 700 before it
rises again. The analysis of photometric higher order terms suggests the nuclear stellar
disks are separated from the large scale disks.
The coefficients of this isophotal analysis are one-dimensional representations of
2D structures in the galaxies. In order to see more clearly the nuclear disks we constructed residual B and V images by subtracting a model galaxy from the original. The
model galaxy was constructed using the IRAF task ‘bmodel’. It had the same luminosity profile as the original galaxy, but it was constructed from perfect ellipses (first two
terms in the Fourier expansion). The contour maps, shown in the middle row in Fig. 2,
reveal the disky structure that is responsible for the existence of the higher order terms.
These disky structures do not necessarily show the full disks, because some information on the disks is also contained in the ellipticity, which was subtracted by the model.
However, to the first approximation, these structures are a good representation of the
relatively faint nuclear stellar disks in the observed galaxies. The disks have various
sizes between 2 – 500 , corresponding to 150 – 600 pc, and are in a good agreement with
40
Chapter 3. HST observations of nuclear stellar disks
Figure 1 — Isophotal analysis results for NGC 4128, NGC 4621 and NGC 5308 in two observed filters:
B (F450W) and V (F555W). First row: surface brightness profiles. Filled symbols correspond to B and
open symbols to V filter. Errors are smaller then the symbols. Second row: position angles measured
east of north; in the case of NGC 4621 we added 90◦ to the measured position angle (east of north) for
presentation purposes. Third row: ellipticity. Fourth row: higher order parameters b 4 (the coefficient of
cos(4θ )), showing deviations from perfect ellipses.
the spatial extent of positive values of b4 terms. The noise structure in Fig. 2 perpendicular to the disks (along the minor axis) is not real and is an artifact of subtracting a
Section 2. WFPC2 broad band imaging
41
perfect elliptical structure from a very disky one.
2.3 Broad-band color images
We constructed several broad band images using our data and archival images as described in Section 2.1. In the bottom two rows of Fig. 2 we show B-V and B-I images
for all three galaxies except for NGC 4128 which does not have archival I band images.
These color images are color coded such that lighter shades indicate redder colors.
2.3.1 B-V color images
The nuclei of the galaxies show different structures in the B-V color. The nucleus of
NGC 4128 is redder then the surrounding bulge, NGC 4621 has a convincingly blue
nucleus, while NGC 5308 is rather uniform with a slightly bluer central pixel. The
magnitudes measured on the constructed color images are presented in Table 4. We
measured the color within a small circular aperture (6 pixels in diameter) to point out
the subtle differences in colors between different regions and features. The blue feature
on the color image of NGC 4128 corresponds to a transient object detected in the galaxy.
The nature of the transient is not known (see Appendix B for a detailed discussion).
In NGC 4128 isochromes trace the nuclear disk, while in the case of NGC 5308 there
is weak evidence of a blue disk outside 0.00 3 of the nucleus. The difference is ≈ 0.02
magnitudes. NGC 4621 is a special case different from both previous galaxies. Here
we have a prominent blue nucleus on top of the red bulge. The other particularity of
this galaxy is in the blue component that stretches southwards from the nucleus. The
average difference between this component and the rest of the bulge is again ≈ 0.02.
2.3.2 B,V-I color images
A bigger color difference is seen in the B-I and V-I images which we constructed for
NGC 4621 and NGC 5308. The archival I-band images of NGC 4621 were of good
quality, while images of NGC 5308 were saturated, and the very central parts of the
images are not reliable.
The interesting blue feature southwards from the nucleus on the B-I image of NGC
4621 is more prominent and we can quantify its extent. The color difference between
the red bulge-like background and the blue patch is here ≈ 0.12 mag in its extreme. The
extent of the feature is ≈ 1.00 35 on each side of the nucleus, being somewhat bluer on
the south side. The feature lies generally in the north-south direction making an angle
of 15◦ to the major axis. It is in no obvious plane of symmetry of the galaxy. The rest of
the bulge is red, but a region of enhanced red color lies in the east-west direction. The
angle between this reddest region and the major axis of about 103◦ , making the angle
between the bluest and the reddest regions about 118◦ . The V-I color image confirms
this finding, also noticed by Wernli et al. (2002), hereafter WEC02, on their V-I images.
We postpone the discussion and interpretation of these features to Section 4.3.
NGC 5308 is an equally interesting case. The center of the I band image was saturated and the blue nucleus is an artifact. Generally, one has to be very careful in
interpreting the saturated images. Aware of problems in dealing with saturated images, we used them to verify the faint suggestion from the B-V images of the blue disk.
42
Chapter 3. HST observations of nuclear stellar disks
Figure 2 — WFPC2 observation of NGC 4128, NGC 4621, NGC 5308. First row: images in the V (F555W)
filter. The arrows and their associated dashes mark the North and East orientation of the images. Second
row: residual stellar disks after subtraction of perfect elliptical model galaxy (in V band). Contours were
slightly smoothed and logarithmically scaled with steps of 0.5 magnitudes. Third row: B-V images, with
grayscale such that brighter means redder. The blue feature next to the center of NGC 4128 is due to the
transient and is discussed in Appendix B. The plotted range is (in magnitudes) 0.6 (black) to 1.0 (white)
for NGC 4128, 0.5 (black) to 1.05 (white) for NGC 4621, and 0.5 (black) to 0.98 (white) NGC 5308. Fourth
row: B-I images. The central blue feature on the NGC 5308 color map is an artifact of saturation and was
not considered in the analysis. Range is from 1.93 (black) to 2.16 (white) for NGC 4621, and 1.1 (black)
to 2.07 (white) for NGC 5308.
Section 2. WFPC2 broad band imaging
galaxy
(1)
NGC 4128
NGC 4621
NGC 5308
43
B−V
V−I
B−I
center average center BF bulge BF
(2)
(3)
(4)
(5)
(6)
(7)
1.00
0.87
0.97
0.95
0.99
0.94
–
1.22
–
–
1.16
–
–
2.14
–
–
2.05
–
Table 4 — Color in magnitudes measured with aperture of 6 pixel (0.00 273) diameter. Col. (1): galaxy
name; Col. (2): B–V color measured at the center of the galaxies; Col. (3): B–V color averaged over 8
apertures placed around center on a square grid centered on the nucleus with size 2 × 14 pixels (∼ 1.00 27),
except for NGC 4128 where the blue feature next to the center was excluded; Col. (4): V–I color measured
at the center of galaxy; Col. (5): V–I color measured at the blue feature (BF) 0.00 90 from the center; Col. (6):
B–I color measured at bulge of the galaxy; Col. (7): B–I color measured at the BF 0.00 90 from the center.
We do not consider the central 0.00 5 of the B-I and V-I color images (the area somewhat
larger than the blue dip in the images), but concentrate on the larger-scale features.
Along the minor axis of the galaxy, the B-I color image also reveals blue regions
on each side of the nucleus, as well as a red feature in the east-west direction. These
features were not anticipated and we checked whether they are real or artifacts of saturation since they are close to the nucleus (r < 1 00 ). We first constructed color image
from unconvolved F4550W and F814W images. On the resulting color image, there
was a hint of the east-west red feature. The other approach included deconvolution of
the B and V images using Richardson-Lucy algorithm with 20 iterations. The resulting
images were convolved with the PSF of the I image, and used to make color images
(B-I and V-I). On both color images, next to the red east-west feature, we also detected
the blue region on the minor axis. These tests suggest the color features on the last
panel of the Fig. 2 are real, although could be augmented by the convolution process
due to its proximity to the saturated nucleus.
The remaining and real (clearly visible on all test images), thin blue feature follows
the major axis of the galaxy, along which there is clear evidence for a very thin disk on
all scales, from the nucleus outwards. The position angle of the thin blue component
is the same as of the nuclear stellar disk.
The marginal difference in color (≈ 0.01 − 0.02 mag) is almost razor sharp and it
looks like the signature of the thin disk visible also in the residual image (second row
of Fig. 2). We compared the sizes of the disk in the residual image and the blue feature
in the B-I color image. The comparison is made by extracting and averaging together
several profiles of intensity and color perpendicular to the disk, on both sides of the
nucleus (avoiding the central 200 ). The final profiles were fitted with Gaussians. The
size (FWHM) of the disk feature on the residual disk image is ∼ 5.6 pixels and the
size of the color feature is ∼ 4.4 pixels. These numbers correspond to 0.00 25 and 0.00 20
respectively, and they are in good agreement, enforcing the connection between the
components. At the distance of NGC 5308, the blue component in the color image is
approximately 30 pc thick.
A way to quantify the relative difference in color between the disk and the bulge is
shown on Fig. 3. We measured the color along slit-like apertures (1 pixel wide) along
44
Chapter 3. HST observations of nuclear stellar disks
Figure 3 — Comparison of B-I color
profiles extracted (and smoothed) along
the disk (thin line) and parallel to disk
(thick line) in NGC 5308. The slit-like
apertures were 200x1 pixels in size.
One slit (thin line) was placed along
the major axis (and the disk), while
two other slits (averaged together and
presented by the thick line) were placed
parallel to the major axis, 10 pixels
(0.00 45) above and below it. Vertical
dashed lines show the nuclear region
excluded from the measurement due to
the saturation effects.
the disk and parallel to it, on both sides of the nucleus. The central 1 00 of all slits were
omitted, and the two slits, positioned on each side of the central slit, were averaged
and presented as one color profile. The disk is clearly bluer then the bulge in the inner
800 . Beyond 3.00 5 on each side of the center colors of the disk and bulge become similar.
Briefly summarizing, we list below the important observed color features to which
we refer later in the text:
NGC 4128 has (i) a red nucleus and (ii) a blue feature 0.00 14 west and 0.00 32 north of the
galaxy center;
NGC 4621 has (i) a blue nucleus, (ii) an extended blue component with PA ≈ 150◦ (east
of north), and (iii) an extended red component with PA ≈ 268◦ (east of north);
NGC 5308 has (i) an extended blue component along the major axis and (ii) a wide
blue component along the minor axis, (iii) an extended red component with an eastwest orientation.
3 STIS spectroscopy
Spectra of all four galaxies were obtained using the Space Telescope Imaging Spectrograph (STIS) with aperture 5200 x0.00 2 and grating G430M (for details see Kimble et al.
(1998)). The observations are summarized in Table 5. The configuration of STIS and
the properties of the grating are listed in Table 6. With this setup we chose to observe
Mg lines at 5180 Å rather then Ca lines at 8700 Å which are commonly used for extracting stellar kinematics. The reasons were: (i) the Mg lines provide simultaneous
kinematic data and a commonly used index of stellar metallicity, (ii) STIS shows problems with scattered light inside the CCD chip in the near infra-red which generates
artificial “wings” on spectral features, and (iii) the spatial resolution along the slit in
V-band is better by almost a factor of two due to the decreased Airy disk size.
Section 3. STIS spectroscopy
Table 5
— Summary
of
HST/STIS
observations.
Col. (1): galaxy name; Col. (2):
the position of slit, cen – center,
pos – positive offset, neg – negative offset (see text for details);
Col. (3): date of observations;
Col. (4): total exposure time
(exposure time of central slits
is the average time of all added
observations); Col. (5): number
of observations used in data
reduction; Col. (6): distance
of the center of the slit from
the galaxy nucleus in arcsec;
Col (7): position angle of the slit
in degrees east from north.
Table 6 — The configuration of STIS
and the properties of the grating.
45
galaxy
(1)
slit
(2)
NGC 4128 cen
pos
neg
NGC 4570 cen
pos
neg
NGC 4621 cen
pos
neg
NGC 5308 cen
pos
neg
Quantity
date
(3)
time
(4)
# exp
(5)
∆cen
(6)
PA
(7)
02.12.2001
02.12.2001
02.12.2001
01.04.2001
01.04.2001
01.04.2001
01.04.2001
01.04.2001
01.04.2001
12.07.2000
12.07.2000
12.07.2000
2568.5
2700
2697
2249.5
2369
2520
2260.5
2380
2520
2525.0
2667
2670
3+3
3
3
3+3
2
2
3+3
3
3
3+3
3
3
0.00
0.16
-0.40
-0.20
0.68
-0.56
-0.12
0.40
-0.44
0.00
0.36
-0.36
-112.9
-112.9
-112.9
152.1
152.1
152.1
161.1
161.1
161.1
60.4
60.4
60.4
Value
Aperture
52x0.2
Grating
G430M
λ-range (Å)
5050.4-5381.6
λcen (Å)
5216
−
1
Scale ∆λ (Å pixel )
0.28
Spatial scale (arcsec pixel−1 )
0.05
Comparison line FWHM (pixel)
2.9
R = λ/∆λ
6461
Instrumental dispersion (km s−1 )
19.76
3.1 Data reduction
The galaxies were observed in a similar manner with a total of four orbits per galaxy.
Spectra were taken at three parallel positions per galaxy during the four orbits. Each
orbit was divided (CR-SPLIT) into 3 shorter exposures. Two orbits were used for the
slit placed on the center of the galaxies (cen), along the major axis. Between orbits, the
galaxy was shifted along the slit for about 0.00 2, or 4 pixels, to get a better estimate of detector sensitivity variations and to identify hot pixels. This strategy was not successful
for the case of NGC 4128, where the measured shift was ∼ 1 pixel. The remaining two
orbits were split between two slit positions on either side of the central slit, covering
the bulge parallel to the nuclear stellar disk. One slit was targeted at the position +0.00 3
away from the central slit (positive offset – pos), and the other at the position -0.00 3 away
from the central slit (negative offset – neg).
Most of the data reduction was performed by the HST/STIS calibration pipeline
CALSTIS (Hodge et al. 1998), including subtraction of overscan, bias and dark, then
flat-fielding, hot pixel and cosmic-ray removal, absolute sensitivity calibration and
wavelength calibration. CR-SPLIT data sets were combined automatically in the pipeline.
The additional combination of the two central slit exposures was performed manually
outside the pipeline in IRAF, using the STSDAS task MSCOMBINE. This task aver-
46
Chapter 3. HST observations of nuclear stellar disks
Figure 4 — Galaxy light profile
along the STIS slit. The full spectral range was used. Thin dark
line is the profile along the cen slit,
thick gray lines are profiles along
the side slits: dashed line along the
pos slit and full line along the neg
slit. The profiles were normalized
to the maximum of the cen slit in order to emphasize the difference of
intensities.
ages the exposures scaled by their exposure times, and combines the separate exposures using a robust sigma clipping rejection method. This was done on the files that
have crj extension, i.e., after pipeline co-addition of CR-SPLIT images and before the
calibrations. The combined files were then returned to CALSTIS for the calibrations.
The same procedure, however, was not possible on the side slits which were taken
during only one orbit. As there were still some cosmic rays left after the pipeline reduction, we used Laplacian Cosmic Ray Identification (LAcosmic) developed by van
Dokkum(2001) () to remove them. LAcosmic was also applied on the crj files. The
detection limit for the outliers was 3.5σ . To improve the quality of the images and
remove additional negative pixels we tried a few techniques. For spectra with very
low signal-to-noise it was possible to compare different exposures (e.g. the two side
slits) and to recognize the same negative pixels and create a mask of them. For spectra
with higher signal to noise this was not effective and a different approach was used.
Using a boxcar filter we smoothed each LAcosmic-filtered image. These images were
subtracted from the corresponding original LAcosmic-filtered images to emphasizes
the outlying pixels. They were flagged creating a mask image. Masked pixels were
interpolated using IRAF task FIXPIX. The resulting images were returned to CALSTIS
and processed to the end of the pipeline.
The final STIS light profiles are shown in Fig. 4. A noticeable feature is the difference
in the intensity of the side slits. If the centering and shifting process worked properly,
as the light profiles of the galaxies are quite symmetric, it is expected that the side slits
should have very similar profiles. This is true for the case of NGC 5308 and NGC 4621,
suggesting those slits were on similar but opposite positions. However, the other two
galaxies show significant deviations. It is therefore necessary to find the exact positions
of all slits.
We checked the actual positions of the slits by comparing the light profiles from
Section 3. STIS spectroscopy
47
Figure 5 — Plots of χ2 versus the
positions of the slits for each galaxy.
The line connecting the diamonds
is the relative χ2 of the central slit.
The line connecting asterisks is the
total relative χ2 obtained by including the side slits in calculations.
the STIS spectra with the WFPC2 images. The width of the slit (dispersion direction)
is 0.00 2, which corresponds to 4 pixels on the STIS CCD. We sub-sampled the image
such that the slit width projects to 5 pixels, in order to center the slits more correctly.
Summing up along the dispersion axis (x-axis on the CCD) we created a STIS light
profile. This was repeated for all slits. The F555W images, which were used in the
comparison, were accordingly re-sampled. In each case we scanned the WFPC2 image
by a combination of the three slits, independently varying the distances between the
slits. The comparison of the STIS and WFPC2 profile was expressed by the relative χ 2
(profile(WFPC2)/profile(STIS) - 1). In this process we assumed that the position angle
of the telescope did not change between different slit positions. The resulting χ 2 estimates are shown in Fig. 5. If the central slit is not on the nucleus, the χ 2 is expected to
have double minima and it is hard to distinguish which one is correct (NGC 4621 and
NGC 4570 are clear examples). However, using the additional light profiles of the side
slits tightens the constraints producing one clear minimum, which corresponds to the
position of the central slit. The uncertainty of our estimate is 0.00 04. The positions of the
central and the side slits with respect to the nucleus are given in last two columns of
Table 5. The slits in NGC 5308 and NGC 4128 are centered on the galaxy nucleus, while
for NGC 4621 and NGC 4570 the slits were offset. The side slits were roughly on the
requested positions for NGC 4621 and NGC 5308. In the case of NGC 4128, the side
slits are the least symmetrically positioned and the pos slit is almost coincident with
the central slit; while in the case of the NGC 4570 the positions of the side slits are the
farthest apart, as suggested from the profiles (Fig. 4).
The general characteristic of the spectroscopic data is their low signal-to-noise ratio (S/ N). Only the major axis spectra have an S/ N sufficient for the extraction of
kinematics and line-strengths as a function of radius. The side slits are much noisier and no kinematic measurements were possible. It was possible however to extract
48
Chapter 3. HST observations of nuclear stellar disks
line-strength information from a few central rows, summed together to increase S/ N
creating one spectrum per side slit per galaxy.
3.2 Stellar kinematics
All available information about the stellar kinematic properties of galaxies are given by
the line-of-sight velocity distribution (LOSVD). The process of extracting kinematics is
based on the deconvolution of the observed galaxy spectra in order to recover the full
LOSVD. The idea behind this is that the galaxy spectrum can be reproduced using a
combination of several representative stellar spectra convolved with the true LOSVD.
Unfortunately, the LOSVD is not a priori known and the deconvolution process is illdetermined, being heavily dependent on the quality of the data. Over the last thirty
years a number of methods were invented to tackle the problem and deliver the best
possible estimates of the LOSVD (see de Bruyne et al. (2003) for an overview of methods). Here we choose to use a parametric method operating in the pixel space because
of the low S/ N of our data and very short wavelength range. We use the penalized
pixel fitting (pPXF) method (Cappellari & Emsellem 2004). We derive the LOSVD parameterized by a Gauss-Hermite series (van der Marel & Franx 1993; Gerhard 1993).
The method finds the best fit to a galaxy spectrum by convolving an optimal template
spectrum with the corresponding LOSVD given by the mean velocity V and velocity
dispersion σ , as well as higher order Gauss-Hermite moments h 3 and h4 . The higher
order moments measure asymmetric and symmetric deviation of the LOSVD from a
Gaussian respectively.
An element which can heavily influence the extracted kinematics is the stellar template used to convolve the LOSVD to reproduce the galaxy spectra. There are methods,
such as Fourier correlation quotient (Bender 1990) or Cross-correlation method (Statler
1995), which are less sensitive to template mismatch. Pixel fitting techniques are much
more sensitive to template mismatch and it is crucial to have a good stellar template
before starting the extraction. The usual way is to observe a number of representative
stars (matching the spread in metallicity and age of stars in the observed galaxy) with
the same instrumental set-up and to build an optimal template as a weighted linear
combination of the observed stellar spectra.
After searching through the HST archive we decided to use a set of stellar population models instead of the one star from the archive that matched our set-up (the same
grism being the most important, while size of the slit can be accounted for). Using
single-metallicity stellar population models of Vazdekis (1999) we constructed a large
stellar library from which to build the optimal stellar template. Each galaxy long-slit
spectrum was summed up along the slit to make a higher S/ N spectrum, which was
used to obtain the optimal template. We also used additive Legendre polynomials to
adapt the continuum shape of the templates. This optimal template was then used in
the fit of the individual spectra along the slit.
A disadvantage of the Vazdekis models is that they are of lower resolution than the
STIS data. The FWHM of the Vazdekis library is 1.8 Å compared to 0.8 Å from STIS.
This requires a degradation of our data by ∼1.6 Å. Although certain information is in
this way lost and the STIS spectral resolution is degraded, the smoothing of the data
helps in removing noise and the library ensures the extracted kinematics do not suf-
Section 3. STIS spectroscopy
49
Figure 6 — Example of spectra for the four studied galaxies. From bottom up: NGC 4128, NGC 4570,
NGC 4621 and NGC 5308. The spectra are shifted vertically to avoid overlap. The thin black lines
indicate spectra of galaxies. The dashed thick lines are broadened optimal templates. The dots below
the spectra are residuals of the fit (difference between galaxy spectra and optimal templates). Vertical
and horizontal lines shows the region used in the fit. Two solid vertical lines crossing the spectra show
the spectral regions excluded from the fit which tested the influence of Mgb region to the extracted
kinematics.
50
Chapter 3. HST observations of nuclear stellar disks
fer from an important systematic template mismatch effect. Examples of constructed
optimal templates are shown in Fig. 6. The presented spectra are the sum of the central 10 rows, having a high S/ N which is needed for properly estimating the optimal
template. The overplotted dashed lines are our resulting optimal templates for the
galaxies, convolved with the determined LOSVD of the galaxy. Typically a few (2-3)
old-type stars from the Vazdekis library were selected by the fitting routine for the optimal template. The residuals between the galaxy and the optimal template spectra are
shown below each spectrum. The presented optimal templates were used to extract
the kinematics from the spatially binned spectra. An alternative way would be to construct the optimal template for each spatial bin and then use this to extract kinematics
in the same bin. This method is important for galaxies with stellar populations changing between bins (∼ 0.00 05), but in this case the low S/ N of the individual spectra do
not justify this approach.
Table 7 summarizes the details about the spatial bins used for the extraction of
kinematics. They were chosen after some experimenting as a compromise between the
S/ N and the spatial resolution. The galaxies have different surface brightnesses and,
since the exposure times were similar, a unique scheme for all galaxies was not useful.
For each galaxy we assumed a target S/ N and we binned accordingly. Generally, the
spectra become too noisy to measure the kinematics beyond 1 00 . In some cases, the
central few rows of spectra have S/ N high enough for extraction of the higher order
terms of LOSVD, but in general the S/ N is too low. Hence, we decide to confine the
extraction to only the first two moments (assuming a Gaussian shape for LOSVD):
mean stellar velocity (V) and velocity dispersion (σ ).
Another element which can heavily influence the results of the extraction is specific
to the spectral region of the observations. Barth et al. (2002) compared the kinematics
of a number of galaxies extracted in two spectral regions: one around Mgb lines and the
other around Ca triplet. They found that if the metallicities of the galaxies and template
stars are not well matched then direct template-fitting results are improved if the Mgb
lines themselves are excluded from the fit and the velocity dispersion is determined
from the surrounding weaker lines. For galaxies with high velocity dispersion this
will be more important because of the correlation between the velocity dispersion and
the [Mg/Fe] ratio (Worthey et al. 1992; Trager et al. 1998; Kuntschner et al. 2001), which
increases the strength of the Mgb lines relative to the surrounding Fe lines. Following
the suggestion of Barth et al. (2002) we also extracted kinematics excluding from the
fit the Mgb lines (the excluded regions are shown on Fig. 6 as vertical lines crossing
the spectra). When there are significant differences between the two sets of extracted
kinematics we used the set obtained by excluding the Mgb lines from the fit for the
further analysis and interpretations.
The errors were estimated using Monte-Carlo simulations. The LOSVD parameters
were derived from 100 realizations of the input spectrum, where the value at each
pixel is taken from a Gaussian distribution with the mean of the initial spectrum and
standard deviation given by a robust sigma estimate of the residual of the fit to the
initial spectrum. Fig. 6 shows an example of the residuals used to estimate the standard
deviation used in Monte-Carlo simulations (dots under the spectra). All realizations
provide a distribution of values from which we estimate the 1σ confidence limits. The
Section 3. STIS spectroscopy
galaxy
51
bin
r (arcsec) range width (pix) S/ N
NGC 4128 center
r1
r2
r3
r4
r5
l1
l2
l3
l4
l5
l6
0.00
0.05
0.15
0.25
0.50
1.25
-0.05
-0.10
-0.15
-0.30
-0.50
-0.95
1
1
2
3
6
24
1
1
2
3
5
13
599-599
600-600
601-603
604-607
608-612
613-637
598-598
596-597
593-595
589-592
583-588
569-582
15
14
15
13
12
12
14
12
14
13
12
12
NGC 4570 center
r1
r2
r3
r4
r5
r6
l1
l2
l3
l4
l5
0.00
0.05
0.10
0.15
0.30
0.50
0.80
-0.05
-0.15
-0.25
-0.45
-0.70
1
1
1
2
3
5
8
1
2
3
4
6
599-599
600-600
601-601
602-604
605-608
609-614
615-623
598-598
595-597
591-594
586-590
579-585
22
21
18
20
20
19
19
19
21
21
19
18
NGC 4621 center
r1
r2
r3
r4
r5
l1
l2
l3
l4
l5
l6
0.00
0.05
0.10
0.20
0.35
0.65
-0.05
-0.10
-0.15
-0.30
-0.50
-0.95
1
1
1
2
4
8
1
1
2
3
6
11
599-599
600-600
601-601
602-604
605-609
610-618
598-598
597-597
594-596
590-593
583-589
571-582
40
34
25
26
27
26
36
28
29
26
27
25
NGC 5308 center
r1
r2
r3
r4
r5
l1
l2
l3
l4
l5
l6
0.00
0.05
0.10
0.20
0.30
0.55
-0.05
-0.10
-0.15
-0.30
-0.50
-0.90
1
1
1
2
3
6
1
1
2
3
5
11
599-599
600-600
601-601
602-604
605-608
609-615
598-598
597-597
594-596
590-593
584-589
572-583
27
23
17
17
15
15
23
17
18
17
16
15
Table 7 — Bins for kinematic extraction
Chapter 3. HST observations of nuclear stellar disks
52
index
slit
cen
NGC 4128
neg
pos
cen
NGC 4570
neg
pos
cen
NGC 4621
neg
pos
cen
NGC 5308
neg
pos
Mgb 5.0 ± 0.2
Fe5720 2.9 ± 0.1
–
–
5.0 ± 0.4 4.5 ± 0.2 2.9 ± 0.3 3.7 ± 0.4 5.9 ± 0.1 6.6 ± 0.3 4.7 ± 0.3 4.8 ± 0.1 5.5 ± 0.5 5.8 ± 0.6
2.6 ± 0.4 3.1 ± 0.1 1.7 ± 0.3 1.5 ± 0.4 3.7 ± 0.1 3.4 ± 0.3 3.4 ± 0.3 3.1 ± 0.1 4.1 ± 0.4 3.5 ± 0.5
Mgb 4.8 ± 0.2
Fe5720 2.8 ± 0.1
B−V
0.97
–
–
–
5.0 ± 0.4 4.4 ± 0.2 2.9 ± 0.3 3.5 ± 0.4 5.6 ± 0.1 6.4 ± 0.3 4.6 ± 0.3 4.7 ± 0.1 5.3 ± 0.5 5.7 ± 0.5
2.6 ± 0.4 3.1 ± 0.1 1.7 ± 0.3 1.4 ± 0.4 3.6 ± 0.1 3.4 ± 0.3 3.3 ± 0.3 3.0 ± 0.1 4.0 ± 0.5 3.5 ± 0.4
0.96
–
–
–
0.99
1.00
1.00
0.96
0.94
0.96
Table 8 — Line-strength indices measured in 0.00 55 x 0.00 2 aperture. First two rows in the table present
line-strengths corrected by the velocity dispersion measured using the whole spectral region. The second two rows present line-strengths corrected by the velocity dispersion measured excluding the Mgb
region from the fit during extraction of kinematics. The last row presents B-V color measured at the
actual positions of slits within the same slit-like aperture used for measuring line-strengths. The errors
on the color values estimated to be 0.05 mag.
values of the extracted kinematics are presented in Tables A.1-2 of Appendix A and
shown in Figs. 8 – 11.
All galaxies except NGC 4621 show rather fast major axis rotation. NGC 4621 is
a special case with a previously discovered counter-rotation in the center (WEC02).
There are some differences between the kinematics extracted fitting the full spectral
range and excluding the Mgb lines. They are the strongest for NGC 4621 and NGC 4570.
The somewhat larger error bars of the kinematic measurements obtained not fitting the
Mgb region are the consequence of lowering the S/ N by excluding the dominant spectral feature. We postpone detailed description of all kinematic curves to Section 4.
3.3 Line strengths
The spectral range of our observations is very limited covering only the Mgb and
Fe5270 Lick/IDS indices (for definition of Lick/IDS system and indices see Burstein
et al. (1984); Worthey et al. (1994); Trager et al. (1998)). The red continuum pass band
of the Fe5270 index is truncated by the edge of our spectral range and this index cannot be used in its defined form. A similar case is found in Kuntschner et al. 2004 (in
preparation) and Falcón-Barroso et al. (2004) where Fe5270 cannot be mapped over
the whole field-of-view of the integral-field spectrograph SAURON (Bacon et al. 2001)
due to the varying bandpass of the SAURON instrument. In their case, Kuntschner et
al. (2004) redefine the index to maximize the coverage of the field-of-view and retain
the sensitivity of the index towards changes in age, metallicity and abundance ratios.
The new index name is Fe5270s. It measures the same spectral feature, but has a reduced spectral coverage in the red pseudo-continuum band. The new index can be
converted to the original Lick/IDS system via the empirical formula (Kuntschner et al.
2004, Falcón-Barroso et al. 2004):
Fe5270 = 1.26 × Fe5270s + 0.12
The 1σ standard deviation of the above empirical calibration is ±0.05 Å for the Fe5270
index. More details on the derivation of the new index and its relation to the standard
Lick/IDS index are given in Kuntschner et al. (2004).
Having this in mind we measured Fe5270s and Mgb indices. The Mgb index was
measured using the Lick/IDS index definition, and all spectra were first broadened
Section 3. STIS spectroscopy
53
to the resolution of the Lick/IDS system. The Fe5270s index was later converted to
index Fe5270 using above relation. Unfortunately, we were not able to determine the
relevant offset to the Lick/IDS system, and correct for the systematics, which come
from differences in the continuum shape, because there are no reference stars in the
HST archive observed by our and by the Lick/IDS instrumental setup. The size of the
corrections are probably similar to (or less than) our measurement errors. To first order,
as well as for determining the relative trends in a galaxy, this is not very important, but
has to be noted when comparing with other studies.
Broadening of the lines by the velocity dispersion weakens most of the lines and the
index we measure must be corrected for this effect. This can be achieved by determining an empirical correction factor C(σ )=index(0)/index(σ ) for a star observed with the
same instrumental setup. Index(0) is the index measured from the stellar spectrum, σ
is the velocity dispersion of the LOSVD with which the stellar spectrum is convolved
and from which the index(σ ) is measured. We used our unbroadened optimal template
spectra to calculate the index at σ = 0 and at the corresponding velocity dispersion, σ ,
of the galaxy spectrum. The proper correction factor C(σ ) was then applied to both
measured indices. We used two approaches to extract kinematics and measure the velocity dispersions (fitting the whole spectral region and excluding Mgb region from the
fit). If the measured velocity dispersions differ, the velocity dispersion correction in the
two cases will also be different. We noted the difference applying both corrections on
the measured line-strengths.
We measured the Mgb and Fe5270 indices from each spectral bin used for kinematics. The corrected values and corresponding errors of the index are presented in the
Tables A.1-2 and shown in the Figs. 8 – 11. The measured line-strengths for galaxies
with higher S/ N are relatively uniform with radius, rising towards the center, with
dips in the case of the nuclei of NGC 4621 (Mgb) and NGC 5308 (Fe5720). NGC 4128
does not show any trend, but rather a scatter of values, presumably due to the low
S/ N, while in case of NGC 5308 Mgb line-strengths are slightly higher on one side of
the galaxy. Generally, galaxies have high values of Mgb and Fe5270 indices. Detailed
descriptions of spatially resolved line-strengths for all galaxies are given in Section 4.
The slits that were offset to the sides of the central slit do not have the required S/ N
to extract kinematics, but their summed spectra can be used to determine the indices
on the positions of the galaxy outside the stellar disk. The binning of spectra is only
useful up to the point at which summing more spatial elements does not simply add
noise. We decided to use an aperture of 0.00 55 × 0.00 2 (summing up 5 rows on each side of
the central row in the spectral direction). With this approach the final side spectra used
for the measurements of line-strengths had at least S/ N ≈ 10. In the case of NGC 4128,
however, from one side spectra we were not able to extract any trustworthy measurement. Table 8 presents line-strengths corrected for velocity dispersions measured by
fitting to the whole spectral range and excluding the Mgb lines from the fit. As it can
be seen, the differences between the lines are negligible and generally fall within the
1σ error bars. Only in the case of the central slit of NGC 4621 which has the highest
velocity dispersion as well as S/ N, there is a significant difference. Adopting a conservative approach, we compared line-strengths from the second two rows in Table 8
with the stellar population synthesis models in Fig. 7.
54
Chapter 3. HST observations of nuclear stellar disks
Figure 7 — Age/metallicity diagnostic diagram (B-V color vs.
Fe5270 index). Horizontal thick
solid lines are lines of constant
age [Gyr] and vertical thin lines
are lines of constant metallicity
[Fe/H]) of Vazdekis (1999) models.
The size of symbols is related to
the position of the slit: the smallest symbols are for the cen slits, intermediate for the pos slits, and the
biggest for the neg slits.
.
We wish to compare the line-strengths measured on the disk with the line-strengths
measured on the bulge using the three slit positions. The line-strength measurements
on the summed spectra show similarly high values as the spatially resolved measurements, although with relatively lower values due to the smaller spatial resolution. The
Mgb index values in NGC 4621 are particularly high. Comparing with the literature
we find similar values for Mgb and Fe 5270 index. Table 7 of Trager et al. (1998) list
values of the same indices for NGC 4621 and NGC 4570 (Mgb 5.50 and 4.65 Å , Fe5270
3.59 and 3.49 Å), which, keeping in mind the unknown offset to the Lick system and
the lower spatial resolution of Trager et al. (1998) data (aperture of 1 00 × 400 ), are in good
agreement with our findings.
Age and metallicity have similar effects on the integrated spectral energy distributions that we measure from unresolved sources due to a finely tuned conspiracy
between age and metallicity variations (Worthey(1994) ). Broad-band colors and many
line-strength indices are degenerate with respect to age and metallicity. This makes
the determination of the age and metallicities very difficult and ideally one would
like to use two indices which can break this degeneracy. Usually, one or more Balmer
lines (H β , H γ , H δ ) are used as age indicators, and Mgb or some Fe index (Fe5270,
Fe5335) as a metallicity indicator (González 1993; Fisher et al. 1996; Mehlert et al.
1998; Kuntschner 2000; Trager et al. 2000). The high index values of our measured
line-strengths also suggests the presence of non-solar abundances of elements. If not
properly treated, over-abundant indices can give wrong age and metallicity estimates
(Kuntschner et al. 2001). A way around this issue is to define metallicity indicators
which are insensitive to abundance ratios (González 1993; Thomas et al. 2003). The
preferred indicator includes a combination of Mgb, Fe5335 and Fe5270 indices, where
Fe5270 is the least sensitive to changes of [α/Fe] abundance ratios (Thomas et al.
2003). We were not able to construct such a metallicity indicator with the indices from
Section 4. Discussion
55
our spectral range, and we chose to use the least sensitive Fe5270 index alone as a
metallicity indicator. Since in our spectral range there are no age indicators, we decided to use a combination of broad-band B-V colors and Fe5270 index to construct
an age/metallicity diagnostic diagram (Fig. 7). The models presented by solid lines
are based on the Vazdekis (1999) single stellar population models: color values were
obtained from A. Vazdekis web site3 , while we measured the Fe5270 index from the
library spectra broadening them to the Lick/IDS resolution. The combination of red
colors and high metallicities puts the measured points on Fig. 7 on the top right of
the model grid, indicating old stellar populations and a large spread of metallicities
between the galaxies.
4 Discussion
In the two previous sections we presented the observational results of HST program
8667. They include photometric and spectroscopic observations of four galaxies with
nuclear stellar disks. Here we analyze and discuss the observations.
4.1 NGC 4128
The most distant galaxy in the sample is NGC 4128 (36 Mpc). It is an S0 galaxy and it
has not been detected in radio nor in IR. The isophotal parameters show that it is disky
between 35 and 530 pc. On 1 kpc scale it has boxy parameters and on larger scales it
becomes disky again.
The color image shows a red nucleus. The values for Fe5270 index measured with
an aperture bigger than the red nucleus are the smallest in the sample of galaxies. This
combination puts the points on Fig. 7 above the model grid. The difference in colors
and line-strengths between the two slit positions are small and within errors indicate
old stellar populations of ∼14 Gyr and metallicities between [Fe/H]=-0.38 and solar.
It is probable that the difference in the color between the nucleus and the rest of
the galaxy, as well as the higher metallicity detected in the nucleus is connected with
the unusual spatially resolved kinematic profiles (Fig. 8). The velocity dispersion is
flat in the center. The velocity curve also shows an unusual flattening in the central
0.00 2, measurements being positive on the both sides of the galaxy nucleus. Outside
this radii the galaxy rotates fast, as expected for a disk galaxy. Kinematics extracted
fitting to two different spectral regions are in a good agreement, confirming the results.
Having in mind the boxiness in the central tens of arcseconds, the extracted kinematic
indicates the existence of a small (∼35 pc in diameter) core, kinematically distinct from
the nuclear stellar disk.
The B-V color profile on the last panel of Fig. 8 shows a slightly shifted (∼17 pc from
the center) peak of the red nucleus. This supports the presence of a distinct component
in the nucleus. On the other hand, the spatially resolved line-strengths do not follow
this trend. The spectral observations of this galaxy have the smallest S/ N ratio, and
the significance of this discovery is just above 1σ . Deeper exposures of high spatial
resolution, preferably with an integral-field unit to cover the 2D structure, are needed
3
http://www.iac.es/galeria/vazdekis/
56
Chapter 3. HST observations of nuclear stellar disks
Figure 8 — Kinematic and linestrength profiles for NGC 4128.
From top to bottom: mean velocity, velocity dispersion, Mgb index,
Fe5270 index and B-V color profile. The color profile was extracted
along the slit position averaging
0.00 2 perpendicular to the slit. The
closed symbols represent measurement obtained by fitting the whole
spectral region. The open symbols
represent measurement by excluding the Mgb line from the fit.
to confirm this result.
4.2 NGC 4570
NGC 4570 is a well-studied galaxy with HST. The main result from previous studies is
that the inner region of the galaxy was shaped under the influence of a weak bar (van
den Bosch & Emsellem 1998). The colors reveal no difference between the disk and
the bulge, and a comparison with the stellar-population models indicate that the stars
in the galaxy are of intermediate age, but the FOS spectral data gave a very high H β
line-strength suggesting recent star formation (BJM98). One of the questions raised by
these studies is whether all double-disk structures are the result of bar-driven secular
evolution.
To the previous photometric and spectroscopic observations we add new spatially
resolved spectroscopic measurements with STIS (Fig. 9). The probed region corresponds to the nuclear disk and inner 200 . The velocity curve shows regular rotation
peaking at ∼ 0.00 15 from the nucleus. The velocity dispersion steeply rises and peaks
in the center. The kinematic profiles are similar to BJM98 ground based data, except
the STIS data have a steeper velocity curve and higher velocity dispersion. In contrast,
the FOS velocity dispersion from the same authors is about 50 km s−1 higher than STIS
measurements; however, considering the error bars of both measurement (their error
on sigma is ≈ 30 km s−1 ) and the fact that our slit was significantly (for the width of the
slit) offset from the galaxy nucleus, these measurements can be considered consistent
with each other.
In the case of NGC 4570, the central velocity dispersion is somewhat dependent
Section 4. Discussion
57
Figure 9 — Kinematic and linestrength profiles for NGC 4570.
From top to bottom: mean velocity, velocity dispersion, Mgb index,
Fe5270 index. The closed symbols represent measurement obtained by fitting the whole spectral
region. The open symbols represent measurement by excluding the
Mgb line from the fit.
on the spectral region used in the fit. Excluding Mgb region systematically lowers the
values by just over 1σ , but increases the difference between this and BJM98 results.
We also measure, within the errors, similar line-strengths to BMJ98, but with higher
spatial resolution and we can give an estimate of the spatial changes in the indices. As
can be seen from the Fig. 9, both measured indices show flattening in the central 0.00 5
(∼60 pc). At larger radii the metallicity drops. Also, the slits positioned on both side of
the center measure the smallest metallicity (Table 8) in the sample and the largest drop
in values with respect to the center. This measurement shows that the nuclear disk
consists of different stellar populations than the rest of the bulge, which is consistent
with bar-driven evolution.
4.3 NGC 4621
The closest galaxy of the four is NGC 4621 (7 Mpc). It is also the only galaxy classified
as an elliptical and is the only galaxy from the sample detected with IRAS (in the 12
µm band). In the investigated range the galaxy is disky. The b4 coefficient steadily rises
from the center to the distance of 140 pc when it drops, but never reaching negative
values. With increasing radius it rises again, implying an outer disk.
The color images reveal the most interesting features in the nucleus. The few central
pixels are clearly much bluer than the rest of the bulge (Table 4). Another striking
characteristic of the galaxy, mentioned in section 2.3.2, is the extended blue and red
features visible on B-I (Fig. 2) and V-I images. The blue feature makes an angle of
15◦ with the major axis. Although the red feature spreads generally in the east-west
direction (angle with major axis is 103◦ ), it is not as clearly defined as the blue feature.
58
Chapter 3. HST observations of nuclear stellar disks
Figure 10 — Kinematic and linestrength profiles for NGC 4621.
From top to bottom: mean velocity, velocity dispersion, Mgb index,
Fe5270 index and B-V color profile. The color profile was extracted
along the slit position averaging
0.00 2 perpendicular to the slit. The
closed symbols represent measurement obtained by fitting the whole
spectral region. The open symbols
represent measurement by excluding the Mgb line from the fit.
We conclude, examining all color images, that the shape and the extent of the two
features can be interpreted as a blue disk-like structure imbeded in the red bulge. The
position angle of the blue feature is unexpected for an axisymmetric galaxy with a
nuclear stellar disk. This significant structure perhaps can be explained considering
the kinematics of this galaxy.
The velocity and velocity dispersion panels in Fig. 10 clearly show the existence
of a kinematically decoupled core (KDC). This core was already detected by WEC02
who observed the galaxy with integral field spectrograph OASIS mounted on CFHT
and assisted by the PUEO adaptive optics system. Complementing their OASIS observations, WEC02 also extracted kinematics from an archival STIS observations in the
Ca triplet region, showing a peak in velocity dispersion 0.00 05 from the center as well as
confirming the KDC with the same spatial resolution as in the data presented here. The
difference between the WEC02 and our kinematic profiles is largest in the velocity dispersion profile, where our values lie systematically above the WEC02 measurements.
This difference is lower, but still present if we compare the kinematics extracted excluding the Mgb line from the fit (∼60 kms−1 for the velocity dispersion peak, but with
large error-bars in both cases). This discrepancy could arise from the different slit positions in the two studies, our slit being offset from the center and not covering the KDC
uniformly. The counter-rotation of the KDC could lower the overall measured dispersion if the slit is placed over its center, and, alternatively, if the slit misses the center of
the KDC the measured velocity dispersion will be higher.
The KDC on the WEC02 OASIS data is not aligned with the major axis and it has a
similar position angle as the blue feature on the color images presented here. Although
the extent of the KDC is smaller (total of ∼ 2 00 or 60 pc) than the blue feature on the B-
Section 4. Discussion
59
I image, the existence of two structures could be connected as a result of the same
formation process.
Both Mgb and Fe5270 line-strengths indices in NGC 4621 are the highest in the sample, also suggesting the over-abundance ratios of elements similar to trends for giant
ellipticals (Kuntschner 1998; Kuntschner et al. 2001). Our metallicity indicator, Fe5270,
also has high values, with the central slit being slightly more metal-rich than the side
slits as well as super-solar. Colors at the slit positions are red and the comparison with
the stellar population models indicates the age of the stars is between 10 and 14 Gyr
and the metallicity between solar and +0.2.
Our spatially resolved measurements of the indices, shown in Fig. 10, are higher
than in previous studies (e.g. Kuntschner et al. (2001) have central Mgb ∼ 5.21 with
aperture of 3.00 4), but our aperture is much smaller (∼ 0.00 05) than that of any previous
study, and the values outside the central arc-second approach the observed values from
the literature. The Mgb index follows to some extent the changes in colors, showing a
small dip in the center, while this can not be said for Fe5270 measurements.
The existence of the KDC and the blue features in the red bulge of the NGC 4621
indicate two possible evolutionary scenarios. The visible structures could be the result
of a hierarchical formation scheme (e.g. Kauffmann et al. 1994) involving a merger
followed by a starburst where the KDC is the remnant of the ejected stars that later
fell back in. These structures are relatively long lived, having a relaxation time of
∼1 Gyr (Binney & Tremaine 1987); however, this is not long enough to explain the
detected old age of the stars. Alternatively, the structure could be produced by weak
bar-driven evolution, as in the case of NGC 4570 (van den Bosch & Emsellem 1998),
where the observed double disk structure is the consequence of resonant frequencies
in the galaxy, while the blue feature and the KDC are the result of gas captured on
retrograde (‘anomalous’) orbits which are tilted with respect to the equatorial plane
(Pfenniger & Friedli 1991; Friedli & Udry 1993; Emsellem & Arsenault 1997). Of course,
a combination of both processes can also lead to the present situation.
Distinguishing between the two scenarios is also difficult because the galaxy has no
obvious merger companion and it is nearly edge-on, making the detection of a weak
bar more difficult. There are other cases of barred galaxies with similar properties to
NGC 4621: i.e. an edge-on system with double-disk structure, unusual photometric
and kinematic features and the difference in metallicity between the bulge and the
disk. An example of a similar, although boxier, galaxy with a strong bar is NGC 7332.
This galaxy was recently studied in detail by Falcón-Barroso et al. (2004). NGC 7332 is
classified as an S0 galaxy and has a double disk structure (Seifert & Scorza 1996). Examining their SAURON spectroscopic observations, Falcón-Barroso et al. find a counter
rotating stellar component within the central 250 pc. The galaxy also has complex gas
morphology and the line-strength maps show it is young everywhere. The authors
conclude that NGC 7332 is an S0 galaxy with a bar viewed close to edge on. NGC 4621
and NGC 7332 are similar in their morphologies, and, although different in the stellar content, it is possible that NGC 4621 went through a similar formation process as
NGC 7332.
60
Chapter 3. HST observations of nuclear stellar disks
4.4 NGC 5308
In many aspects NGC 5308 is different from the other galaxies in this study. Our photometry reveals the largest nuclear stellar disk in the sample of galaxies in this study.
Unlike in the other galaxies, the nuclear disk of NGC 5308 is very thin and bright. The
diskiness parameter, b4 , rises from the center and peaks at about 150 pc, dropping to
zero at ∼1 kpc and suggesting a distinction between the two disks. At large radii the
galaxy again becomes disky.
The stars in the disk of NGC 5308 rotate fast, reaching ∼100 km s−1 within 15 pc
from the nucleus (Fig. 11). The velocity dispersion has a peak of about 300 km s−1
in the center and is relatively flat in the inner 15 pc. This trend is also visible in the
kinematics measured excluding the Mgb line from the fit, although the right hand side
of the plot shows considerably lower velocity dispersion values. This is reflected in
the panel with Mgb values, which are slightly higher on the right hand of the plot. The
Mgb and Fe5270 index values have opposite trends. The small variations in the B-V
color along the slit, including the sudden blue dip in the center, are followed by the
line-strength measurements.
There is a big difference between the line-strengths measured on the different slit
positions (Table 8 and Fig. 7). The nucleus, being just below solar metallicity, is more
metal-poor than the bulge which has a non-solar abundance ratio of elements and the
highest metallicity in the sample. The nucleus and the investigated part of the bulge
also have different colors, with the center being redder. Comparing these results with
the stellar population synthesis models reveals an old stellar population in the nucleus
(14 Gyr), while the colors of the bulge suggest intermediate age stellar component (∼
5-10 Gyr).
The color difference between the bulge and the nucleus is measured because the
side slits were positioned in the region of the minor axis blue feature, especially visible
on B-I image. This region is also special for its high metal content. There are no hints
of specific morphological structures (such as a polar ring) along the minor axis and the
question is whether the rest of the bulge, especially the red feature, and the nuclear
stellar disk share the same metallicity. Unfortunately our spectral observations did not
cover the necessary areas and we can only speculate on the processes that created the
observed structures.
If the metallicity of the minor axis blue feature and the nuclear disk are the same, the
formation of these two structures has to be connected to the same formation scenario,
most probably involving a transportation of gas to the center, perhaps by a bar, for
which Seifert & Scorza (1996) found evidence in NGC 5308. If the metallicity of the
nuclear disk is lower than the metallicity of the minor axis blue feature, but similar to
the measured metallicity of the nucleus, the two blue features in NGC 5308 were not
created from the same infalling material, but they still can be from the same epoch. If
the metallicity of the minor axis blue feature is equal to the rest of the bulge, which
is redder and therefore older, then the younger stellar population in the blue feature
must have been induced by an internal process, perhaps ionization from the radiation
generated by the central black hole, which was turned on with the infall of the material
that made the blue disk, and later turned off with the stabilization of the disk (Loeb &
Section 5. Conclusions
61
Figure 11 — Kinematic and linestrength profiles for NGC 5308.
From top to bottom: mean velocity, velocity dispersion, Mgb index,
Fe5270 index and B-V color profile. The color profile was extracted
along the slit position averaging
0.00 2 perpendicular to the slit. The
closed symbols represent measurement obtained by fitting the whole
spectral region. The open symbols
represent measurement by excluding the Mgb line from the fit.
Rasio 1994).
In section 2.3.2 we showed that the major axis blue feature in NGC 5308 corresponds to the nuclear stellar disk. It is about 30 pc thick which strongly suggest the
galaxy is viewed very close to edge-on. Comparing with the vertical scalelength of
34 edge-on spirals presented by Kregel et al. (2002), which are between 0.2 and 1.4 kpc
thick, the disk in NGC 5308 is a remarkably thin disk. Note that our estimate of the disk
thickness can only be approximately compared with the vertical scalelength measurements of Kregel et al. It is also not possible to say much about the thickness of the other
nuclear disks, due to their inclination (not as edge-on as NGC 5308). Whether this nuclear disk resembles the disks from the group of “super-thin” galaxies, like UGC 7321
or IC 5249 (Matthews et al. 1999; Matthews 2000; van der Kruit et al. 2001), is an open
question. The sizes of the nuclear disk in NGC 5308 and known “super-thin” disks are
quite different as well as the surrounding environment (stellar bulges and dark matter
halos respectively). A proper way to compare the disks is to measure the radial and
vertical sizes in a consistent manner, which is beyond the scope of this paper.
The color and metallicity of the disk in NGC 5308 suggest the disk could be made of
a younger and more metal-poor stellar population than the rest of the galaxy, implying
it formed at a different epoch from accreted material.
5 Conclusions
We have presented photometric and spectroscopic observations of four nearby earlytype galaxies with nuclear stellar disks (NGC 4128, NGC 4570, NGC 4621, NGC 5308).
The observations consist of high resolution images with WFPC2 using the F450W and
62
Chapter 3. HST observations of nuclear stellar disks
F555W filters, and STIS high resolution spectra through the 52x0.2 long-slit with the
G430M prism.
The photometric analysis reveals similarities and differences between the galaxies.
Nuclear stellar disks are clearly visible and are photometrically disconnected from the
large scale disks. NGC 4128 shows boxy isophotes on the inner and outer edge of the
nuclear disk. NGC 4621, the only E galaxy in the sample, is everywhere disky, while
NGC 5308 has a razor-thin (∼ 30 pc) disk.
Color images reveal interesting and unexpected structures. NGC 4128 has a red
nucleus, while NGC 4621 has a blue nucleus. Prominent color features are visible on all
galaxies. The blue feature in NGC 4128 is analyzed in Appendix B. and is the signature
of a transient event. NGC 4621 has a blue feature at an angle of 15◦ with the major axis
on top of a red bulge. It is likely connected to the KDC discovered by WEC02. The
nuclear stellar disk in NGC 5308 is associated with the razor thin blue feature along
the major axis. NGC 5308 has another blue feature along the minor axis. The colors
of all three galaxies indicate old stellar populations except for the bulge of NGC 5308
where the combination of slightly less red colors and high metallicity lowers the age of
the stellar populations.
The high resolution spectroscopy was obtained at three positions on each galaxy.
One slit was positioned on the nuclear stellar disk, with the PA equal to the major
axis PA. Two additional slits were positioned on both sides of the central slit, ∼ 0.00 3
away from the disk covering the bulge. The central slits were used to extract spatially resolved kinematics and line-strengths. The S/ N permitted the extraction of the
mean stellar velocity and the velocity dispersion, as well as the measurement of linestrengths. The kinematics will be used in a separate paper to estimate the black hole
masses in the centers of the galaxies.
Considering the shape of the spatially resolved kinematic curves, the four galaxies
could be sorted in two groups: fast and kinematically disturbed rotators. NGC 4570
and NGC 5308 belong to the first group. Their rotation curves show clear signature of
the stellar disks. The rotation curves of NGC 4128 and NGC 4621 are much more complicated. In the case of NGC 4621 the unusual mean velocity and velocity dispersion
curves are consistent with the known KDC (WEC02) in the nucleus. Although based
on a 1σ detection, we report the discovery of a similar kinematically distinct core in
the case of NGC 4128.
Spatially resolved line-strength measurements along the disk indicate that all four
galaxies are more metal-rich in the inner 0.00 5 than outside this radius. Both measured
indices (Mgb and Fe5270) increase towards the center, except in the case of NGC 5308
where Fe5270 has an opposite trend to Mgb index. Non-solar abundance ratios of
[Mg/Fe], hinted by results of the extraction of kinematics, are present in NGC 4570
and NGC 4621, and to some extent also in NGC 5308.
The slits positioned on the bulges had low S/ N and no spatially resolved kinematics were extracted. However, by binning the spectra, it was possible to measure
the line-strengths at one position and compare them to the values of the nuclei. The
objects show various structure: NGC 4128 has similar metallicities at the different
slit positions, NGC 4570 and NGC 4621 have higher metallicity in the nucleus, while
NGC 5308 in the bulge. Generally, the galaxies show a spread in metallicity from sub-
Section 5. Conclusions
63
to super-solar.
This study shows the diversity within this class of objects, but also emphasizes the
similarities in the photometry and kinematics. The red color gradient in the nuclei of
NGC 4128 and the blue features in NGC 4621 and NGC 5308 suggest the existence
of different stellar populations on small scales (∼100-500 pc). The investigated galaxies were chosen as galaxies with specific nuclear morphologies: nuclear stellar disks.
However, except in the case of NGC 5308 the colors of the disks are not much different
from the bulge, as previously noted by Carollo et al. (1997b). The existence of other
color features is a surprise. In two galaxies (NGC 4128 and NGC 4621) these color
features are followed by the existence of a KDC. The other two galaxies do not show
any peculiarities in their kinematics. Also, if the KDC in NGC 4621 is connected to the
misaligned blue feature, we can conclude, similar to Carollo et al. (1997a), that KDCs
are not kinematic counterparts of the nuclear stellar disks. This gives credit to the complexity of formation scenarios that demands a separate study per galaxy, but there are a
few most likely frameworks, outlined also in Scorza & van den Bosch (1998), in which
the processes responsible for the observed structures operate.
The formation of nuclear disks, rings and double disk structures in early-type galaxies can be explained through secular evolution driven by weak bars as shown by Emsellem et al. (1996) and van den Bosch & Emsellem (1998) in the cases of M 104 and
NGC 4570, respectively. This mechanism, through the evolution of the bar, explains the
double-disk morphology. Support for this scenario comes from the fact that S0 galaxies
have high line-strengths (Fisher et al. 1996) and there are evidences of embedded bars
in early-type galaxies (e.g. M104, NGC 4570, NGC 7332, Scorza et al. 1998). This model
of bar-driven evolution is consistent with the observations in the presented galaxies,
even in the cases of the galaxies with KDCs, such as NGC 4621, but also NGC 4128,
which is additionally boxy and presents an interesting case. The time varying triaxial
potential of the bars offers exotic orbits that could explain the existence of kinematic
and photometric features. In this scenario, the KDCs are created from enriched material transported inwards (perhaps even gas acquired through a merger), which gets
frozen on retrograde orbits tilted with the respect to the equatorial plane.
Other possibilities involve a merger scenario (capture of gas that settles in the principle plane forming stars, and/or makes tidal inflows that create KDCs), or growth of
a central black hole (Loeb & Rasio 1994). A black hole stabilizes the disk and within
this scenario a connection to quasars can be made by stopping the fueling of the central engines with the formation of a stable disk. None of the previously investigated
nuclear stellar disk galaxies has an active nucleus, although they do harbor 108M−9 black
holes (Kormendy et al. 1996b; Kormendy et al. 1996a; Cretton & van den Bosch 1999).
This makes them descendants of quasars that spent their fuel (there is not much dust
or gas in most of these galaxies), or quasars that, through dynamical evolution, turned
off the central engine (stabilization of the disk due to the growth of the black hole,
disappearance of bars that transport the material to the center).
Nuclear disks are easier to find in edge-on systems; however, the influence of weak
bars is correspondingly more difficult to ascertain. Detailed spectroscopic studies with
two dimensional coverage of the major features (nuclei, stellar disks, KDC, photometric features) are necessary to chose between the present formation scenarios. A careful
64
Chapter 3. HST observations of nuclear stellar disks
investigation of the two-dimensional kinematic properties and their connection to the
distribution of line-strengths (metal content and age of stellar populations) can offer
decisive tools to deduce the nature and nurture of galaxies with nuclear stellar disks.
Acknowledgments
We are grateful to Michele Cappellari, Eric Emsellem, Richard McDermid, Gijs Verdoes
Kleijn, Frank van den Bosch, Zlatan Tsvetanov and Tim de Zeeuw for comments and
discussions. DK thanks Michele Cappellari and Harald Kuntschner for making available the pPXF and line-strengths measurement software, respectively. This research
has made use of the NASA/IPAC Extragalactic Database (NED) which is operated
by the Jet Propulsion Laboratory, California Institute of Technology, under contract
with the National Aeronautics and Space Administration. This work also used LEDA
database. DK was supported by NOVA, the Netherlands Research school for Astronomy.
Appendix A. Extracted kinematics
Appendix A. Extracted kinematics
radius
(1)
V
(2)
65
δ V σ δσ Mgb δ Mgb Fe5270 δ Fe5270
(3) (4) (5) (6)
(7)
(8)
(9)
NGC 4128
-0.95
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.15
0.25
0.50
1.25
2323.
2359.
2438.
2370.
2475.
2489.
2474.
2498.
2568.
2618.
2649.
2691.
29.
19.
24.
20.
20.
12.
13.
14.
14.
12.
18.
20.
168.
258.
283.
206.
253.
229.
230.
216.
191.
150.
203.
91.
46.
27.
27.
24.
31.
15.
14.
18.
11.
13.
27.
30.
3.6
5.3
4.3
5.1
4.1
4.6
5.6
5.6
4.6
4.7
5.7
4.1
0.9
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.7
0.8
1.0
4.1
4.3
3.6
2.5
3.5
2.9
2.8
3.4
3.3
1.7
1.5
2.2
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.4
0.5
0.7
1827.
1803.
1853.
1856.
1877.
1920.
1941.
1950.
1979.
1966.
1996.
1956.
13.
16.
9.
9.
8.
8.
8.
7.
7.
13.
10.
16.
138.
106.
136.
155.
169.
202.
167.
145.
123.
176.
133.
114.
13.
18.
9.
14.
8.
12.
9.
9.
10.
17.
10.
25.
2.0
2.0
4.1
4.3
4.8
4.8
4.5
4.7
4.3
4.5
3.3
3.2
0.5
0.6
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.6
2.4
2.2
2.6
3.3
3.4
3.6
2.7
3.3
3.3
3.0
2.2
2.1
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
583.
572.
546.
580.
609.
631.
594.
603.
588.
629.
605.
552.
19.
19.
13.
13.
12.
13.
13.
17.
24.
13.
12.
14.
335.
306.
315.
308.
332.
339.
356.
420.
395.
341.
283.
283.
23.
22.
14.
10.
14.
13.
15.
29.
34.
21.
10.
14.
4.5
5.4
5.9
5.9
6.2
5.4
5.8
6.4
6.2
5.7
5.5
5.0
0.5
0.5
0.4
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.4
0.4
3.7
3.5
3.0
3.0
3.4
4.0
4.0
3.8
3.8
4.0
4.0
3.2
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
2295.
2241.
2282.
2259.
2258.
2179.
2135.
2007.
2003.
1973.
1974.
1971.
16.
20.
11.
13.
12.
14.
13.
12.
11.
9.
8.
10.
162.
195.
221.
214.
279.
302.
311.
290.
182.
175.
147.
158.
23.
26.
15.
12.
17.
21.
16.
17.
23.
12.
10.
11.
4.1
3.4
4.5
4.1
4.6
5.0
4.9
5.6
5.1
5.0
4.8
4.4
0.6
0.6
0.4
0.4
0.4
0.3
0.3
0.3
0.4
0.4
0.5
0.5
2.2
3.8
4.0
3.0
3.4
2.6
2.9
2.9
2.6
3.0
3.3
3.3
0.4
0.3
0.2
0.3
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
NGC 4570
-0.70
-0.45
-0.25
-0.15
-0.05
0.00
0.05
0.10
0.15
0.30
0.50
0.80
NGC 4621
-0.95
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.20
0.35
0.65
NGC 5308
-0.90
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.20
0.30
0.55
Table A.1 — Measured kinematics and line-strengths for observed galaxies using full spectral region
in the fit. Notes – Col. (1): radius of measurement (arcsec); Col. (2): mean velocity ( km s −1 ); Col. (3)
mean velocity error ( km s−1 ); Col. (4): velocity dispersion ( km s−1 ); Col. (5): velocity dispersion error
( km s−1 ); Col. (6): Mgb index (Å); Col. (7) Mgb index error (Å); Col. (8) Fe5270 index (Å); Col. (9) Fe5270
index error (Å).
Chapter 3. HST observations of nuclear stellar disks
66
radius
(1)
V
(2)
δ V σ δσ Mgb δ Mgb Fe5270 δ Fe5270
(3) (4) (5) (6)
(7)
(8)
(9)
NGC 4128
-0.95
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.15
0.25
0.50
1.25
2294.
2378.
2431.
2398.
2545.
2512.
2495.
2520.
2603.
2674.
2657.
2688.
31.
25.
35.
30.
21.
19.
19.
19.
15.
15.
24.
23.
258.
275.
297.
228.
258.
229.
223.
223.
174.
118.
179.
74.
30.
34.
36.
25.
32.
24.
25.
29.
12.
15.
24.
33.
3.9
5.4
4.3
5.1
3.8
4.6
5.5
5.6
4.4
4.4
5.6
4.0
0.8
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.7
0.7
1.0
4.4
4.3
3.7
2.5
3.5
2.9
2.8
3.4
3.2
1.6
1.4
2.2
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.4
0.6
0.7
1805.
1815.
1853.
1872.
1889.
1921.
1942.
1957.
1993.
1985.
1995.
1988.
14.
21.
8.
9.
9.
11.
9.
8.
8.
14.
11.
17.
138.
131.
133.
142.
149.
176.
146.
118.
93.
142.
123.
111.
14.
23.
10.
15.
10.
18.
9.
8.
6.
16.
10.
25.
2.0
2.0
4.1
4.2
4.8
4.7
4.4
4.7
4.2
4.4
3.3
3.1
0.5
0.6
0.4
0.4
0.4
0.5
0.4
0.4
0.4
0.5
0.5
0.6
2.4
2.2
2.6
3.2
3.4
3.6
2.7
3.3
3.3
3.0
2.2
2.2
0.4
0.4
0.3
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
531.
569.
562.
612.
622.
663.
608.
589.
592.
659.
618.
531.
27.
19.
21.
18.
16.
15.
17.
26.
39.
17.
14.
24.
306.
203.
280.
278.
316.
323.
307.
379.
324.
288.
293.
286.
29.
20.
19.
13.
15.
14.
17.
30.
51.
20.
12.
20.
4.3
4.9
5.6
5.6
6.0
5.1
5.5
6.1
5.7
5.3
5.5
5.0
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.4
0.3
0.4
0.4
3.6
3.2
3.0
2.9
3.3
4.0
3.8
3.7
3.5
3.8
4.1
3.2
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
2333.
2188.
2256.
2270.
2261.
2173.
2122.
2001.
2042.
1954.
1965.
1955.
24.
22.
14.
12.
16.
22.
21.
14.
13.
9.
9.
10.
110.
266.
244.
181.
291.
290.
305.
221.
96.
123.
136.
115.
37.
21.
19.
10.
26.
32.
20.
42.
25.
13.
11.
16.
3.9
3.7
4.6
4.0
4.7
4.9
4.8
5.2
4.8
4.9
4.8
4.3
0.7
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.4
0.4
0.5
0.5
2.2
4.1
4.1
2.9
3.5
2.5
2.9
2.8
2.5
2.9
3.3
3.2
0.4
0.3
0.2
0.3
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
NGC 4570
-0.70
-0.45
-0.25
-0.15
-0.05
0.00
0.05
0.10
0.15
0.30
0.50
0.80
NGC 4621
-0.95
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.20
0.35
0.65
NGC 5308
-0.90
-0.50
-0.30
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.20
0.30
0.55
Table A.2 — Measured kinematics and line-strengths for observed galaxies excluding Mgb region from
the fit. Same as in Table A.1.
Appendix B. A transient in NGC 4128
67
Figure B.1 — Zoom-in on the WFPC2 images of the nucleus of the NGC 4128, in F702W (left) and F555W
band (right). Both images are oriented as on Fig. 2 (north is down and east to the right). Horizontal line
is 100 long. The left image was taken almost two years before the right one. The offset of the peak next to
the center on the right image is 0.00 143 west and 0.00 318 north from the center of the galaxy.
Appendix B. A transient in NGC 4128
Examining the HST – WFPC2 images of the nearby S0 galaxy NGC 4128, taken on May
14 2001 in the F450W and F555W filters, a peculiar source of light was discovered very
close to the center of the galaxy (Fig. B.1). The source is offset by 0.00 14 west and 0.00 32
north of the galaxy center on the WFPC2 images. In the HST archive there are images
of the galaxy taken on March 17 1999, with filter F702W, observed under PID 6357 (PI
Jaffe), which do not show any additional light source next to the nucleus of the galaxy.
This clearly indicates the appearance of a transient object in our data. In this Appendix
we try to deduce the origin of the transient. Section B.1 presents a new method of
extraction of the light contribution from the background galaxy and the photometric
analysis, followed by discussion on the nature of the object in section B.2.
B.1 Extraction of light and results
The general properties of NGC 4128 were described in the main text. Here we add that
the dust in the galaxy has not been detected (Tran et al. 2001). This ensures there is
no significant extinction although the object is almost in the center of the galaxy. The
galactic component of the reddening in the direction of the NGC 4128 is estimated to
be E(B − V) = 0.02 mag (Schlegel et al. 1998).
To determine the nature of the transient, it is necessary to accurately do photometry on the observed light. The first required step is to remove the contribution of the
galaxy light. Since there are no pre-transient observations of the galaxy in the two filters, it was not possible to use the standard technique of subtracting a suitable image of
the galaxy taken with the same instrumental set up (e.g. Filippenko et al. 1986; Hamuy
68
Chapter 3. HST observations of nuclear stellar disks
Figure B.2 — Contour maps of WFPC2 F450W (left) and F555W (right) images of NGC4́128. The images
show the inner 7.00 5. Superposed on the two images are the contours of the MGE surface brightness,
convolved with the WFPC2 PSFs for the corresponding filters. The transient was excluded from the fit,
but it is shown in the images for illustration.
et al. 1994). To overcome this problem a Multi-Gaussian Expansion (MGE) model of
the galaxy was constructed (e.g. Emsellem et al. 1994). The method and software provided by Cappellari (2002) were used. The MGE models of the galaxies were created
using only the PC1 chip and masking the region of the transient by a circular mask
with radius of 5 pixel (Fig. 9). For both MGE models, the total number of used Gaussians was increased until the minimum χ2 stopped decreasing. This approach yielded
the total number of 9 Gaussians and RMS error of about 2%.
The obtained models were subtracted form the original images. Figure B.3 shows a
horizontal cut through the observed image at the position of the transient and the corresponding MGE model. The light of the transient is clearly distinguishable from the
rest of the galaxy. Subtracting the MGE model of the galaxy from the observations it
is possible to recover the transient light contribution. The residuals are symmetric and
can be used to calculate the magnitude of the transient. Photometric measurements
were conducted using the IRAF task PHOT. Magnitude zero points for filters were obtained from Dolphin (2000). The values calculated in an aperture of 0.00 5 were corrected
to infinite aperture by adding 0.1 mag. The correction for geometrical distortion and
the CTE correction were not performed as their influence are of second order, compared to the uncertainty introduced by subtracting the model galaxy from the original
image. The final transient parameters, namely its position, apparent magnitude and
absolute magnitude in Johnson-Cousins system, are given in the Table B.1.
B.2 Discussion and conclusions
Lacking any spectra of the detected object as well as a longer period of observation, it
is difficult to determine the object’s true nature. Since it is not visible on the F702W
Appendix B. A transient in NGC 4128
69
Figure B.3
— Horizontal cuts through the
galaxy on the position
of the SN. The thick
line is the MGE model
and the thin line is
the observed light.
The lower plots show
residuals
obtained
subtracting the models
from the observations.
The transient is clearly
separable from the
rest of the galaxy by a
MGE model.
band image while it is quite bright on the F450W and F555W band images (taken 22
months later), it is most natural to conclude the object is a transient. There are a few
possibilities such as a solar system object, a nova or a supernova.
The duration of all four independent WFPC2 exposures is about 40 minutes. A solar
system object would show a noticeable movement between the different exposures,
except if moving directly toward an observer. If the object is at the distance of the
Kuiper belt it would move approximately a few arc seconds during the observations.
However, the relative position of the object (the distance between the object and the
center of the galaxy) changes by less than one pixel (< 0.00 0455), the movement being
less than measurement error. It seems reasonable to conclude the object is of extra-Solar
system origin.
Novae are known to have a maximum absolute magnitude less bright then -9 mag
(Cohen 1985). With the measured absolute magnitude of -13.6 (V band), this is ruled
out. Similarly, because it is very faint, the observed transient is also not likely a nova in
our galaxy (a compilation of novae light curves is given in van den Bergh & Younger
(1987)). The observed magnitude leaves the possibility that the object in NGC 4128 is
a supernova. The type of supernova is defined according to its spectrum, and here
again it is hard to establish anything specific. However, the host galaxy is an S0 galaxy,
and since supernovae of type II do not occur in early-type galaxies (Table 3. in Cappellaro et al. 1997b), the transient is probably a supernova of Type Ia. Comparing the
measured absolute magnitude to absolute magnitudes of supernova 1994D or 1992A
(Cappellaro et al. 1997a), which were also S0 galaxies, suggests that the supernova was
observed about 200 days after the explosion. The B − V color of the supernova is -0.11,
which is bluer then the expected color for a type Ia SN at B maximum. On the other
Chapter 3. HST observations of nuclear stellar disks
70
filter
(1)
ra
(2)
dec
(3)
δx
(4)
δy
(5)
counts
(6)
m
(7)
σm
(8)
M
(9)
F450W 12:08:34.84 68:46:57.15 0.142 0.315 20940.09 19.06 0.05 -13.7
F555W 12:08:34.84 68:46:57.25 0.143 0.318 18099.38 19.17 0.05 -13.6
Table B.1 — Summary of transient measurements. Col.(1): name of the filter; Cols.(2) and (3): position
of the supernova measured in (h,m,s) and (deg,arcmin,arcsec) on WFPC2 (J2000); Cols. (4) and (5): the
offset in arcsec of the transient from the intensity peak of the galaxy due west and north respectively;
Col. (6) total counts inside aperture of 0.00 5; Col. (7) magnitude of the supernova in Johnson-Cousins
system; Col. (8) the estimated error on the apparent magnitude; Col. (9) absolute magnitude using the
distance to NGC 4128 from Table 1.
had, it is consistent with the B − V light curve at the later time (around 200 days) of
the above mentioned reference supernovae (Salvo et al. 2001).
Private communication with the supernova-survey groups (D. Green from IAU Circulars and W. Li from LOTOSS survey) did not confirm the existence of the supernova.
They checked images from January to June 2001, and after galaxy subtraction there
was no signature of any transient object. However, the proximity to the nucleus of
NGC 4128 is a possible reason why ground-based automated search program might
have overlooked the supernova.
If the source of the light is a Type Ia supernova, it will be the first supernova discovered in NGC 4128 (Barbon et al. 1999)4 . Unfortunately, without other high resolution
available data it is impossible to determine the true nature of the object. Also, the estimate of the timing of the supernova in NGC 4128 is highly uncertain, since it depends
on precise classification and calibration. Type Ia supernovae are known to have different absolute magnitude light curves (e.g. Cappellaro et al. 1997a). If the transient
in the NGC 4128 is not a supernova of type Ia 200 days after explosion then its nature
remains unknown (a flaring second black hole, an asteroid on the trajectory to Earth).
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Chapter 4
Kinemetry: a method to quantify
kinematic maps
Davor Krajnović, Michele Cappellari, Yannick Copin, P. Tim de Zeeuw, to be submitted to
Monthly Notices of the Royal Astronomical Society
We present a general method for analysing and describing kinematic maps of
galaxies observed with integral-field spectrographs. It is based on a harmonic expansion of the maps along concentric rings in the plane of the sky, similar to the
expansions used to quantify observed HI, CO and Hα velocity fields, and analogous to standard surface-photometry methods for analysing broad-band imaging.
We call our method kinemetry. We analyse the kinematic moments (mean velocity,
velocity dispersion and higher-order Gauss–Hermite moments of the line-of-sight
velocity distribution) of a model elliptical galaxy, and discuss the meaning of the
amplitude coefficients and corresponding phases of the expansion. The observed
kinematic moments have certain symmetries in the plane of the sky, and we exploit
these to filter the maps. We present diagnostics for determining the consistency of
velocity maps with axisymmetric underlying geometry, based on the phase angles
of the first two odd terms of the expansion. We apply this method to SAURON observations of the galaxy NGC 4365 and quantify the departures from axisymmetry.
We consider kinemetric expansions along circular and elliptic annuli, and find that
expansion along suitably-chosen ellipses may be superior for maps of the mean velocity and the higher-order odd moments, while circles may be more suited for velocity dispersion maps and the higher-order even moments. We present evidence
that the velocity maps of some early-type galaxies closely resemble the observed
kinematics of inclined circular disks, but the generality of this result needs to be
investigated further.
1 Introduction
T
WO - DIMENSIONAL
velocity maps were, until recently, largely the privileged property of radio astronomers. The advantages of full two-dimensional spatial coverage
of extended astronomical objects are self-evident and are extensively used in e.g. HI
studies of disk galaxies. The advent of integral-field spectrographs (IFS) has brought
two-dimensional kinematic measurements to optical wavelengths.
The inclusion of optical wavelengths also broadens the variety of objects accessible
for study. The two-dimensional radio observations are dependent on the existence of
73
74
Chapter 4. Kinemetry: a method to quantify kinematic maps
gas, while optical observations probe both the stellar absorption- and gas emission-line
spectral features, which may co-exist in the same potential with very different spatial
distributions and dynamical structures. The wealth of features seen in the stellar kinematic maps of early-type galaxies (Emsellem et al. 2004) confirms the usefulness of
two-dimensional data, but also poses a problem of efficiently harvesting and interpreting the important features from the maps.
An approach using harmonic expansion was developed for the analysis of the twodimensional radio velocity maps. This method divides a velocity map into individual rings (the so-called tilted-ring method, Begeman 1987) with a harmonic expansion
along these rings (e.g. Binney 1978; Teuben 1991). Assuming that the velocity map is
generated by gas moving in a thin disk, it is possible to assign certain physical properties to the coefficients of the harmonic expansion: e.g. the first cosine term in the
expansion gives the circular velocity of the gas, assuming the gas moves in circular
orbits in the disk. The higher-order terms measure the departures from a simple disk
model (pure circular motion) caused by e.g. elongation of the potential. This approach
was pioneered by Franx et al. (1994) and Schoenmakers et al. (1997) who used it to
investigate the axisymmetry of spiral galaxies, based on the prediction for harmonic
coefficients coming from epicyclic theory. Recently Wong et al. (2004) used this method
as a diagnostic tool for measuring radial flows in spiral galaxies.
The harmonic expansion is a simple and straight-forward tool to extract information from two-dimensional maps, and is a natural method for harvesting information
from kinematic maps obtained by the new optical IFS. However, interpretation of the
results depends on the intrinsic nature of galaxies. The spheroidal distribution of stars
typical of early-type galaxies does not have the same dynamical properties as a gas
disk. To explore those intrinsic properties, we need a more general description of the
harmonic terms, without assumptions on geometry or dynamical state of the observed
system. In this paper we present such a method, which we call kinemetry due to its complementarity with surface photometry of early-type galaxies. In its basics, kinemetry
is a generalisation of the tilted ring harmonic expansion method for analysing velocity maps of gaseous discs to the kinematic observations of spheroidal systems such as
elliptical and lenticular galaxies.
In Section 2 we present the theoretical background on which kinemetry operates.
Section 3 presents the method and discusses two choices of expansion: along circles
and along ellipses. The meaning of the kinemetric coefficients for different kinematic
moments is presented in Section 4. In Section 5 we present the application of kinemetry
as a diagnostic tool for quantifying axisymmetry and kinemetric misalignments in triaxial systems, and we discuss the advantages of the expansion along ellipses. Section 6
summarises the conclusions.
2 Theoretical background and motivation
The dynamics of a collisionless stellar system is fully specified by its phase-space density or distribution function f = f (~
x, ~
v, t) (e.g. Binney & Tremaine 1987). However, this
quantity is not measurable directly. When observing external galaxies, we measure
properties that are integrated along the line-of-sight (LOS). The observables, which
Section 2. Theoretical background and motivation
75
reveal only the averages of properties of a large number of unresolved stars, are the
surface brightness and the full velocity profile (for a review see de Zeeuw 1994). An
additional complication is that the galaxies are viewed from a certain angle, and we
actually observe only the projected properties of the integrated distribution function.
Analysis of the projected surface brightness via (broad-band) imaging is called surface photometry. The surface brightness is, however, only the zeroth-order projected
moment of the distribution function. For a complete picture, the analysis has to include the full velocity profile, i.e. the line-of-sight velocity distribution (LOSVD):
L (v; x, y) =
Z
LOS
dz
Z Z
dvx dv y f (~r, ~
v),
(1)
where (x,y,z) are the three spatial coordinates, oriented such that the LOS is along the zaxis. Observations of the LOSVD are usually presented by its moments: mean velocity
V, velocity dispersion σ and higher-order moments commonly parametrised by GaussHermite coefficients, (van der Marel & Franx 1993; Gerhard 1993), h 3 and h4 being the
most commonly used.
The kinematic moments of stationary triaxial systems show a high degree of symmetry which can be expressed through their parity. The mean velocity is an odd moment, while velocity dispersion is an even moment. In practice, this means that a twodimensional map of a given moment shows corresponding symmetry. Maps of even
moments are point-symmetric, while maps of odd moments are point-anti-symmetric. In
polar coordinates this gives:
µe (r, θ + π ) = µe (r, θ ),
µo (r, θ + π ) = −µo (r, θ ),
(2)
where µe and µo are arbitrary even and odd moments of the LOSVD, respectively.
Furthermore, if the observed system is axisymmetric, the even moment of the LOSVD
will also be mirror-symmetric or, correspondingly, an odd moment will be mirror-antisymmetric:
µe (r, π − θ ) = µe (r, θ ),
µo (r, π − θ ) = −µo (r, θ ).
(3)
Unlike surface brightness images, analysis of maps of stellar kinematic moments
for early-type galaxies have not been extensively explored, due to the small number
of studies with full two-dimensional kinematics. On the theoretical front, there were
some studies of velocity maps of triaxial systems (e.g. Franx et al. 1991; Statler 1991,
1994a; Statler & Fry 1994; Statler 1994b; Arnold et al. 1994). The new observations with
the IFS SAURON (Bacon et al. 2001), and its survey of a representative sample of nearby
galaxies (de Zeeuw et al. 2002) yield high-quality maps of the kinematic moments of
early-type galaxies (Emsellem et al. 2004). The structures visible on these kinematic
maps are reflections of the intrinsic properties of the galaxies and kinemetry provides
an efficient method for quantifying the wealth of information seen on these maps. In
this way, kinemetry can be used as an analysis tool and a step between observations
and theoretical modelling.
Chapter 4. Kinemetry: a method to quantify kinematic maps
76
3 The method
In this section we present the details of the kinemetry method which exploits the high
degree of symmetry observed in early-type galaxies. The errors are treated in more
detail in Section 4.
3.1 Harmonic expansion
Fourier analysis is the most straightforward approach to characterise any periodic phenomenon. The periodicity of a kinematic moment can easily be seen by expressing the
moment in polar coordinates: K(x, y) → K(r, θ ). The map K(r, θ ) can then be expanded
as follows to a finite number (N + 1) of harmonic terms (frequencies):
K(r, θ ) = a0 (r) +
N
∑ cn (r) cos[n(θ − φn (r))].
(4)
n=1
The main advantages of this approach are: (i) linearity at constant r, and (ii) no a priori
assumptions about the kinematic maps of the observed galaxy.
Choice of the centre and geometry of the expansion is somewhat arbitrary. We fix
the centre of the polar coordinate grid at the central intensity peak in the nucleus of
the galaxy, which is usually well-defined in early-type galaxies. We assume this point
corresponds to the gravitational potential minimum.
We perform the expansion along a set of concentric circular annuli although in
principle any geometry can be used. The main advantage of circles is that they do
not introduce any a priori assumption about the structure of the kinematic maps (or
the underlying galaxy potential). Throughout this paper we use circles to explain the
basic features and properties of the kinemetric expansion, but in Sections 3.2 and 4.5
we consider expanding along elliptical annuli, with its specific application to velocity
maps only.
In practice, we rewrite eq. (4) in the form:
K(r, θ ) = a0 (r) +
N
∑
n=1
an (r) cos nθ + bn (r) sin nθ ,
(5)
where the coefficients an , bn are determined by a least-squares fit using singular value
decomposition with a basis {1, cos θ , sin θ ,...,cos N θ, sin N θ}. The amplitude and phase
coefficients (cn , φn ) of eq. (4) can be easily calculated from the a n , bn coefficients:
cn =
φn
a2n + b2n ,
b n
= arctan
.
an
p
(6)
In addition to measurement errors, there are two effects which limit the reliability
with which coefficients in the expansion can be determined: (i) the absolute number of
points sampled along the annulus, and (ii) the regularity with which these points sample the annulus as a function of angle, θ . Figure 1 shows an example of these effects
Section 3. The method
77
Figure 1 — Examples of kinematic profiles and kinemetric coefficients for the E4 galaxy NGC 2974 as
observed with SAURON. Top left panel: the kinematic profile of the innermost annulus (r = 0.00 8). Second
left panel: the kinematic profile of an annulus at r = 10 00 from the centre. Third left panel: the kinematic
profile of an outer annulus (r = 2200 ). In these panels, the observed data are indicated by field symbols.
The 1σ error bars are generally smaller than the symbols. The solid line is the fit to the data using
nmax = 4 terms. The dashed line is the fit using nmax = 7 terms. The dash-dotted line is the fit using
nmax = 2 terms. Top right panel: the amplitude of the c1 coefficient from the kinemetric expansion of the
full velocity map of NGC 2974. Open symbols and solid line were obtained using n max = 4 terms in the
expansion, while the dashed line using nmax = 7 and dash-dotted line using nmax = 2 terms. The bottom
right panel: c3 /c1 coefficient ratio from the two expansions: solid symbols and solid line for n max = 4
terms and dashed line for nmax = 7 terms.
and how they limit the number of terms which can be reliably fitted to the given kinematic profile1 . The figure is based on the observed SAURON velocity map of NGC 2974
shown on Fig.9 and described in more details in Chapter 5 of this thesis. In order to
prescribe the number of terms for the expansion we impose the condition that the corresponding half-wavelength of the highest term in the expansion has to be longer than
the maximum angular distance between the data points. This can be expressed by a
simple relation: nmax < π/∆θ , where nmax = N + 1 is the maximum number of terms
used in the expansion and ∆θ is the size of the largest distance between the data points
in the kinematic profile.
At small radii (top panel in Fig. 1), the annulus intersects only a few evenly-spaced
points, and nmax is correspondingly small (in this example nmax = 4). At intermediate
radii, (the second panel in Fig. 1), the kinematic profile is well sampled allowing more
1
In this study we use the term “kinematic profile” to describe the variation in the value of a kinematic
moment along annuli extracted from maps.
78
Chapter 4. Kinemetry: a method to quantify kinematic maps
higher-order terms. At large radii (the third panel in Fig. 1), the annulus can include
regions without data (sampling beyond the edge of the map), creating “holes” in the
kinematic profile. The angular size of the holes limits the number of terms that can be
used for the expansion (in this example nmax = 2).
In the right panels of Fig. 1 we show the dominant odd terms, c1 and c3 of the
harmonic expansion. The different lines correspond to the different number of terms
used in fitting the kinematic profiles on the first three panels. The dashed-dotted line
corresponds to nmax = 2. These two terms alone are clearly not sufficient to fit the data.
Adding more terms will increase the accuracy of the reproduction of the kinematic
moment, but if too many are added, the discreteness effects will become important.
The dashed line corresponds to nmax = 7 which is well justified at intermediate radii,
but in the central annulus and in the annuli at large radii (r > 20 00 ), it does not satisfy
the relation for maximum number of terms used in the expansion.
To combat the effects of sampling, the Fourier expansion in kinemetry is therefore
performed on concentric annuli of increasing width. In general, this is the consequence
of the rapidly falling signal-to-noise ratio of spectra as one goes away from the centre.
The kinematic maps are necessarily binned (e.g. using adaptive Voronoi binning (Cappellari & Copin 2003) as in the presented examples), and as the bins typically increase
in size with radius, the area of the annuli in which the kinematic values are selected
have to increase as well to uniformly sample the kinematic profile. However, by increasing the bin size, one loses the spatial resolution and the final size of the annuli
is a compromise of these two effects. We made a specific choice for the SAURON data,
where the width, ∆r, of a given annulus, j, is given by the expression ∆r j = s × q j−1 .
Here, s corresponds to the size of the smallest spatial element (0.00 8 for SAURON), and q
is a scale factor such that ∆r ≈ 200 at a radius of 2500
It should be noted that the number of terms required in the expansion depends also
on the purpose of the expansion, which can be to reproduce the map in detail using a
large number of terms (possibly enforcing a symmetry, as in Section 4.4) or to extract
a small number of coefficients to describe the main features of the map and obtain a
low-order approximation to the galaxy highlighting the key terms.
3.2 Expansion along elliptical annuli
In the previous section we discussed the kinemetric expansion of kinematic maps along
circular annuli which bring no assumptions about the galaxy. However, certain physical insight for the choice of the shape of the annuli may be well justified, as in the case
of surface photometry, or the analysis of velocity fields of ionised gas discs. In this
section, we turn in more detail to the alternative approach of expansion along elliptical
annuli. The kinemetric formalism described above remains unchanged and only the
selection of the data points changes from circular to elliptical annuli.
Surface photometry of early-type galaxies has the obvious choice to expand along
elliptical isophotes of the light distribution. The azimuthal surface-brightness profile
at a certain radius is fitted by an ellipse and the possible deviations are represented by
higher-order terms of a harmonic series. The existence and amplitude of the higherorder terms quantify the deviations of the ellipses, which have physical meaning and
describe the shape of the isophotes relative to the best-fitting ellipse (e.g Lauer 1985;
Section 4. Kinematic parameters and their meaning
79
Jedrzejewski 1987; Bender 1988).
Observed velocity maps of disc galaxies can be well fitted by circular motion. A
standard approach of the tilted ring method (Begeman 1987) in the analysis of the velocity maps of HI, CO and Hα discs is to decompose them in a number of separate
rings. Each ring is then described by six parameters: the centre coordinates, position
angle, inclination, systemic velocity and circular velocity. A harmonic analysis of the
rings can be performed, characterising the higher-order deviations from the pure circular motion (Franx et al. 1994; Schoenmakers et al. 1997; Wong et al. 2004).
Kinematic maps of early-type galaxies, having different symmetries and not necessarily being created by stars moving in a disc, do not offer such simply motivated geometries for the expansion. On the other hand, since their light distribution is elliptical
it is reasonable to assume that an expansion along ellipses will have some advantages
over the expansion along the circles. The choice of the actual ellipticity is somewhat
arbitrary. For example, it is possible to expand along the galaxy isophotes or along
ellipses that correspond to projected circles. In the first case, one follows the photometry and probes regions of the same projected surface brightness; while in the second
case, one samples locations with equal intrinsic radii. In the second case, however, it is
necessary to assume an inclination for the galaxy, which is usually difficult to estimate.
Also, assuming a constant ellipticity for the whole kinematic map may not be justified.
Let us assume that the velocity maps of early-type galaxies are created by stars
moving on circular orbits in thin discs. Following the tilted-ring approach, we can
then divide a velocity map into a number of separate rings. The extracted velocity
profile is fitted with a simple cosine function:
V(R, θ ) = V0 + VC cos θ,
(7)
where R is the mean radius of the ring in the plane of the galaxy, V0 is the systemic velocity, VC is the circular velocity not corrected for the inclination and θ is the azimuthal
angle in the plane of the galaxy, which is related to the axial ratio q of the ring’s major
and minor axes, and is measured from the kinematic position angle of the map. Varying the axial ratio, one can find the ring whose velocity profile is the most similar to the
circular velocity of a disc, with radius R and inclination cos i = q. In other words, the
axial ratio defines the ellipse on the sky, q = 1 − , with ellipticity , which corresponds
to a circle in the plane of the galaxy, describing the orbits of stars in the disc. These
independent rings are then analysed by means of harmonic expansion. This approach
effectively minimises the higher-order terms. If the assumption that the investigated
velocity maps are similar to disc velocity maps is satisfied, then it is to be expected that
the higher-order terms will be negligible. Sections 4.5 and 5.3 present an application of
this modified kinemetry approach on model and observed velocity maps, respectively.
4 Kinematic parameters and their meaning
Kinemetric analysis is possible for all measured kinematic moments. The properties
and meaning of the kinemetric coefficients will differ depending on the underlying
symmetry of the analysed map. The influence of the map symmetry on the coefficients
can be predicted and compared to the obtained kinemetric values. On the other hand,
Chapter 4. Kinemetry: a method to quantify kinematic maps
80
assuming a symmetry one can obtain the properties of the map by effectively filtering
the noise in the data. In this section we characterise the kinemetric coefficients for
odd and even kinematic moments, present the filtering capabilities of kinemetry and
discuss kinemetry along ellipses.
4.1 Model galaxy
We constructed a model galaxy to demonstrate the application of kinemetry. The
model is axisymmetric with a distribution function which depends only on the energy and one component of the angular momentum. The model was constructed using the Hunter & Qian (1993) contour integration method and following the prescriptions of Emsellem et al. (1999) to resemble the SAURON observations of NGC 2974:
surface-brightness distribution, kinematic observations, inclination, mass-to-light ratio and central black hole mass. The distribution function of the model yields the full
LOSVD from which the observable kinematics can be extracted. This was done on
a large 10000 × 10000 field by fitting a Gauss-Hermite series (V, σ , h3 and h4 ) to spatially binned data which resemble typical SAURON observations. In order to mimic the
real observations, we also assigned the typical error of the SAURON observations to
each model observable. These errors were used to add intrinsic scatter to the noiseless
model data by means of a Monte Carlo realisation. Further details on the construction
of the model galaxy and its kinematics are given in Section 5.1 of Chapter 5 of this
thesis.
This model is an example of an axisymmetric galaxy, with mirror-(anti)-symmetric
kinematic maps. Although kinemetric analysis of a more complicated model is also
possible (and equally straightforward), here we present a simpler example to clearly
quantify the main properties of the kinematic moment maps and the results of kinemetry.
4.2 Odd kinematic moments
In a Gauss-Hermite parameterisation of the LOSVD, the first two odd moments are
the mean velocity V, and the Gauss-Hermite coefficient h 3 . The maps of these moments look different and have different interpretations, but have the same underlying symmetry. Generally, maps of odd moments show point-anti-symmetry. Imposing
the point-anti-symmetry condition (eqs. 2–3) on the terms of the kinemetric expansion
(eq. 4), for the odd moments of LOSVD one has:
µo (−x, − y) = −µo (x, y)
⇒
a0 = c2n ≡ 0.
(8)
A map with additional mirror-anti-symmetry (an axisymmetric case) requires also:
µo (x, − y) = µo (x, y)
⇒
φ2n+1 = const ≡ PA.
(9)
Therefore, one can predict that in an observed odd moment map the even terms will
be considerably smaller than the odd ones, where the departures from zero are caused
by noise or possible lopsidedness (departures from the assumed symmetry).
Section 4. Kinematic parameters and their meaning
81
Figures 2 and 3 show the kinemetric expansion of the V and h3 maps of the model
galaxy. The errors were estimated using Monte Carlo simulations. The kinemetric coefficients were derived from 100 realisations of the moment map, where the moment’s
value in each spatial bin was taken from a Gaussian distribution with the mean of the
original moment and standard deviation given by the error assigned to the moment
in the bin. Each realisation of the map was expanded using kinemetry providing a
distribution of values from which we estimate the 1σ confidence limit.
The zeroth-order term, a0 , measures the mean level of the map. For the first kinematic moment, this is equivalent to the systemic velocity of the galaxy. In the case
of the model velocity field, the systemic velocity was zero by construction, and in an
observed galaxy, a0 will be non-zero. However, if the systemic velocity is properly subtracted (as it was assumed in eq. 8), a0 will be zero. Alternatively, using the kinemetric
expansion it is possible to determine a reliable systemic velocity using the information
of the whole velocity map. In the case of the observed h3 maps, which have mean level
equal to zero by construction, a0 will be small, and like other even terms, consistent
with zero.
The coefficient c1 gives the general shape and amplitude of the odd moment map
and is always the dominant term. Hereafter, we normalise the higher coefficients, c i>1 ,
in the kinemetric expansion of the velocity map by c1 , to simplify the comparison between the terms.
The first-order correction is given by the next odd term, c3 . This term can be named
the morphology term because it describes most of the additional geometry of the map.
Generally, the first two odd terms are enough to describe the velocity map, although
the kinemetric expansion can include higher terms as well, c 5 and even c7 . In Fig 2
and 3 we plot the c5 term for completeness. Although in some instances this term can
become significant (around 2000 in this case), it is generally very small, being at the level
of noise in the data.
Connected to the amplitude terms are the corresponding phase terms, φ n . They
determine the orientation of the map, but their contribution depends on the relative
strength of the amplitude terms. The first phase coefficient, φ 1 , gives the mean position
angle of the velocity map (measured from the horizontal axis, θ = 0). We name it the
kinematic angle. The angle that φ1 measures is the position angle of the maximum c1
term. This is, in general, slightly different from the positions of the maxima on the
map, which are also influenced by the contribution from higher-order terms. However,
it does give the global orientation of the map at a given radius to a good approximation
and can be used to describe the symmetry of the map (Section 5.1).
The angle φ3 is the phase angle of the third harmonic: the next significant term. For
a small amplitude of c3 , its contribution to the overall orientation will be small, and
the position of the maximum velocity will be given accurately by θ max = φ1 . For an
axisymmetric galaxy φ3 will have specific values, as we will see in Section 5.1.
The error bars plotted on Fig. 2 and 3 (as well as on Fig. 4 and 5 of the next section)
are typical for the SAURON observations of the nearby galaxies (Emsellem et al. 2004).
As expected, due to the discreteness, they are larger at small and large radii where the
sampling and edge effects play an important role. In the case of the velocity maps,
at intermediated radii with dense sampling of kinematic profiles, the typical intrinsic
82
Chapter 4. Kinemetry: a method to quantify kinematic maps
Figure 2 — Kinemetric expansion of the velocity map of the model axisymmetric galaxy. Panels of the
left column show the amplitude coefficients of the kinemetric expansion (from top to bottom): a 0 , c1 ,
c2 /c1 , c3 /c1 , c4 /c1 and c5 /c1 . The velocity map is presented in the upper right, while other panels in the
right column show the corresponding phase angles (from top to bottom): φ 1 , φ2 , φ3 , φ4 and φ5 . The relatively large errors to the even phase angles are not significant because the associated amplitude is zero.
Section 4. Kinematic parameters and their meaning
83
Figure 3 — Kinemetric expansion of the h3 map of the model axisymmetric galaxy. Panels of the left
column show the amplitude coefficients of the kinemetric expansion (from top to bottom): a 0 , c1 , c2 , c3 ,
c4 and c5 . The h3 map is presented in the upper right panel, while the other panels show the same phase
angles as in Fig 2, but for the h3 map.
84
Chapter 4. Kinemetry: a method to quantify kinematic maps
errors (not accounting for systematics) for the c1 and c3 coefficients are 0.5 km s−1 and
0.6 km s−1 , respectively; and for the φ1 and φ3 phase angles are 0.5◦ and 1◦ , respectively.
The larger errors on the phase angles of the even terms can be explained by the nearzero values of the corresponding amplitude coefficients. The same effect is visible
for the phase angles of the higher-order odd terms, when they have near-zero values.
Similar, but somewhat higher values are seen for the errors on the kinemetric terms of
higher-order kinematic moments (σ , h3 , h4 ).
The same description can be assigned to all terms of the kinemetric expansion of h 3
maps. The values of the amplitude coefficients ci are much smaller for the h3 moment
(ci < 1), and the rescaling of the higher terms with the dominant term is not very useful.
The h3 map is noisier than the mean velocity map. This is reflected in the recovered
errors of the coefficients, which are somewhat larger, even for the odd terms, than in
the case of the mean velocity map. The typical intrinsic errors of kinemetric expansion
of h3 maps for the c1 and c3 coefficients are 0.04 and 0.005, respectively; and for the φ 1
and φ3 phase angles are 3◦ and 4◦ , respectively.
4.3 Even kinematic moments
The even terms in the standard parametrisation of the LOSVD are the velocity dispersion σ , and the Gauss-Hermite coefficient h4 . In many ways, analysis of the even
moments is analogous to that for the odd moments, taking the proper parity into account. The maps of even moments show point-symmetry which translates to the terms
of the kinemetric expansion as:
µe (−x, − y) = −µe (x, y)
⇒
c2n+1 ≡ 0.
(10)
A map with additional mirror-symmetry requires:
µe (x, − y) = µe (x, y)
⇒
φ2n = const ≡ PA.
(11)
As anticipated, the odd kinemetric terms are expected to be consistent with zero on the
observed maps of even moments. This is clearly visible in Figs. 4 and 5, which show
the coefficients of the kinemetric expansion of the model velocity dispersion and h 4
maps. The 1σ confidence levels shown in the figures were obtained via Monte Carlo
simulations as in Section 4.2.
The dominant term of the even maps is a0 , and it describes the absolute level of the
map as a function of radius. The next important term in the expansion is c 2 , and it is the
morphology term of the even moment maps. As seen in Figs. 4 and 5 this term describes
more specific features of the maps. Features such as elongations along the minor axis
or “bow-tie” shapes, often seen in observed velocity dispersion maps (Emsellem et al.
2004), should leave signatures in this term. Specifically, for the velocity dispersion
maps the c2 term is mostly a few percent of the dominant a0 term, implying that these
maps have near-circular symmetry, and that the choice of circles for describing these
maps is a natural one.
The orientation of the morphologically distinct features are determined by the phase
angles of the amplitude coefficients. When there is a feature with a specific angular dependence, e.g. an oval elongation along the major axis, the position angle of the feature
Section 4. Kinematic parameters and their meaning
85
Figure 4 — Kinemetric expansion of velocity dispersion map of the model axisymmetric galaxy. Panels
on the left column show amplitude coefficients of the kinemetric expansion (from top to bottom): a 0 ,
c1 /a0 , c2 /a0 , c3 /a0 , c4 /a0 and c5 /a0 . The velocity dispersion map is presented in the upper right, while
other panels in the right column show the same phase angles as in Fig 2, but for the velocity dispersion
map.
86
Chapter 4. Kinemetry: a method to quantify kinematic maps
Figure 5 — Kinemetric expansion of the h4 map of the model axisymmetric galaxy. Panels on the left
column show amplitude coefficients of the kinemetric expansion (from top to bottom): a 0 , c1 , c2 , c3 , c4
and c5 . The h4 map is presented in the upper right panel, while the other panels show the same phase
angles as in Fig 2, but for the h4 map.
Section 4. Kinematic parameters and their meaning
87
Figure 6 — An example of kinemetric filtering on kinematic maps of the galaxy NGC 474. Rows from
left to right: mean velocity V, velocity dispersion σ , and Gauss-Hermite moments h 3 and h4 . Columns
from top to bottom: data, symmetrised data applying additional point-(anti)-symmetric condition (eqs. 8
and 10), data symmetrised applying additional mirror-(anti)-symmetric condition (eqs. 9 and 11). The
overplotted kinematic contours were obtained by interpolation between the bin generators and extrapolation to the edge of the maps.
is given by the φ2 phase angle of the c2 term. The phase angles of the odd terms, whose
amplitude coefficients are zero, have large errors, while the errors of the even phase
angles are generally smaller, although still high at certain radii, suggesting there is no
preferred direction of the features on the example maps. The typical intrinsic errors for
kinemetric expansion of the velocity dispersion maps are: 0.9 km s−1 and 1.1 km s−1 for
a0 and c2 coefficients, respectively, and 3◦ for the φ2 phase angle in the region where the
phase angle is well constrained. Similarly, for the expansion of the h 4 map we obtained
errors of 0.005, 0.006 and 5◦ for a0 , c2 and φ2 , respectively.
4.4 Filtering
Kinemetry can also be useful as a powerful filter of two-dimensional kinematic maps.
As already mentioned above, if the number of terms in the expansion is small, the
88
Chapter 4. Kinemetry: a method to quantify kinematic maps
map will be smoothed, taking away the higher-order harmonics from the data, which
may be caused by noise. However, kinemetry offers some other more specific filtering,
which makes assumptions of the underlying symmetries in the kinematic maps.
Following eqs. (8) and (9), one can filter a kinematic map by fixing certain terms
in the expansion to zero or to a constant value. Requiring point-anti-symmetry in the
kinemetric expansion for odd maps implies fixing the even terms to zero (in case of an
even map, the odd terms are set to zero).
Similarly, a more strict requirement that all non-zero phases are set to a constant
value will produce mirror-(anti)-symmetric maps. This symmetry removes twists of the
kinematic angle, creating what is sometimes called a bi-symmetric map. These filtering
criteria may also be applied to extract the relevant coefficients from maps with noisy
data.
Figure 6 gives an example of filtering, applied to the first four observed moments of
the LOSVD for SAURON observations of NGC 474 (Emsellem et al. 2004). The kinematic
maps of this galaxy are consistent with point-(anti)-symmetry and, applying this symmetry condition to the kinemetric expansion, removes much of the noise from the data.
However, in the following example, we set all (non-zero) phases to the median value
of the measured kinematic angle (≈ 60◦ ), enforcing additional mirror-(anti)-symmetry,
with which the galaxy kinematics are clearly not consistent. The results are axisymmetric kinematic maps (no kinematic twists), that, however, do not correspond to the
real galaxy, but show the full filtering power of kinemetry.
A draw-back of filtering such integral-field data with kinemetry comes from the
nature of the spatial bins. Generally, the bins are not symmetrically distributed around
the symmetry axes. Kinemetric filtering works in annuli and if the bins are not uniformly distributed in the annuli, it will not be possible to find symmetric pairs of bins
in all quadrants of the map and properly enforce the symmetry (e.g. K(−x, − y) =
− K(x, y) = − K(x, − y) = K(−x, y)). A way out is to interpolate the binned data on a regular grid and then symmetrise using kinemetry, although the best way of symmetrising
the maps of the kinematic moments is to impose symmetry during the extraction of the
kinematics from the observed data cube spectra.
4.5 Expansion of velocity maps using kinemetry along ellipses
At this point we turn again to the special case of kinemetry along ellipses. In Section 3.2
we suggested that the tilted-ring approach to the velocity maps of early-type galaxies,
although not physically founded, might give a better insight in the structure of maps.
Here we show an example of the kinemetric expansion of the velocity map of the model
galaxy discussed in Fig. 2 along ellipses best-fitting ellipses following the prescription
of Section 3.2.
We performed the expansion up to the third odd term (c1 , c3 and c5 ), where the c1
term is by construction identical to VC from eq. (7), while the higher-order terms describe the deviations of the velocity map from the projected circular motion. The result
is shown in Fig. 7. The first panel of the figure shows the axial ratio of the elliptical
rings used in the expansion. In the inner few arcseconds this ratio changes and then
drops to a constant value of relatively round value for the axial ratio of about q = 0.7.
Strikingly, the higher-order terms, plotted on the lower panels, are negligible, their
Section 5. Application
89
Figure 7 — Terms of kinemetric expansion of
the velocity map of the model galaxy along ellipses. From top to bottom: axial ratio of the
best-fitting ellipse, and the ratio of the c3 /c1
and c5 /c1 terms which measure the deviation
from the circular velocity assuming the velocity map was generated by stars moving along
circular orbits in a disc. The deviations are below the 1% level. See text for details.
contribution being mostly below the 1% level. This shows the power of this approach,
which can describe a velocity field with basically two parameters: the axial ratio of the
adopted ellipse and the first term of the harmonic expansion.
The underlying assumption of this application of kinemetry is that the velocity
maps of early-type galaxies are created by stars moving along circular orbits in a thin
disc. This, generally, is not true, and our intention here is only to qualitatively compare
the observed velocity maps of spheroidal systems with those of thin discs. In the example shown in Fig. 7, the higher-order terms are very small and the velocity map of
the model early-type galaxy seems to be consistent with a velocity map of an inclined
disc. Our comparison stops here, but it is an interesting finding, worth more detailed
investigation (see Section 5.3). Along the same lines, the axial ratio, q, from Fig. 7, does
not imply the intrinsic inclination of the galaxy. It can, however, be used to categorise
the velocity maps: velocity maps with small q are flat while velocity maps with high q
are round.
5 Application
In this section we consider the ability of kinemetry to quantify the underlying symmetries of kinematic maps of observed galaxies, as well as give examples of kinemetry
along ellipses for three early-type galaxies. For this purpose we focus on the velocity
maps.
Chapter 4. Kinemetry: a method to quantify kinematic maps
90
5.1 Prescription for axisymmetry
Two-dimensional velocity maps can be used to constrain the intrinsic shapes of earlytype galaxies (Franx et al. 1991; Statler 1994b), and kinemetry can serve as a tool for
extracting the necessary information from the maps. Here we consider conditions by
which one can distinguish between velocity maps of axisymmetric and more general
triaxial galaxies.
Axisymmetry is a special case of triaxiality, and triaxial galaxies, viewed under
certain inclination can have axisymmetric appearance (e.g Stark 1977; de Zeeuw &
Franx 1989). A galaxy is consistent with axisymmetry if the velocity map satisfies the
following three conditions:
1. The velocity map is truly point-anti-symmetric, and, hence, the even terms in kinemetric expansion are zero (or negligible), as given by (8).
2. The velocity map satisfies the condition (9), where all phase angles are constant.
3. All phase angles are equal to the photometric position angle. This condition can
be softened by requiring that the higher-order phase angles satisfy the relation:
φ1 − φi =
nπ
,
i
(12)
where n ∈ Z and φi is the i-th order term in the expansion.
The last condition can be easily derived considering that for an axisymmetric velocity field the position of the zero velocity curve, the curve along which the velocity
is zero on the map, is orthogonal to the kinematic angle given by φ1 . This means that
K(r, θ ) = 0, for θ = φ1 + π/2. Neglecting the higher order terms, (ci > c3 ), and substituting θ = φ1 + π/2 into eq. (4) one obtains the result of eq. (12).
Similarly, deviations from axisymmetry can be quantified following eqs. (4) and (12).
If K(r, θ = φ1 + π/2) = ∆V 6= 0, then one finds:
∆V
c3
= sin 3(φ1 − φ3 ),
c1
c1
(13)
where we express the relation as a ratio of the dominant term in the expansion. This
relation quantifies the contribution of the c3 term due to departures from axisymmetry
and can be generalised to other higher terms. In cases of large misalignments between
the kinematic and photometric position angles, φ1 should be replaced by the photometric PA in the above equation.
Fig. 2 shows the kinemetric expansion of a mirror-anti-symmetric velocity map and
it is clear that all three conditions for axisymmetry are satisfied.
5.2 A triaxial case
In the previous section we presented the prescriptions for axisymmetry which were
tested on an axisymmetric model velocity field. Here we turn to the wealth of the
SAURON observations and use an observed velocity field of a triaxial galaxy, in order
to show the departures from the conditions listed in the previous section. The velocity
field belongs to the well studied triaxial galaxy NGC 4365. The SAURON kinematics, as
Section 5. Application
91
Figure 8 — Kinemetric analysis of
NGC 4365.
The velocity map of
NGC 4365 is presented in the upper left
panel. The panels in the left column
show: odd amplitude coefficients: c1 ,
c3 and c5 . Higher order terms are presented as fractions of c1 , the dominant
term in the expansion. The first panel
on the right shows the contribution of
the c3 term to non-axisymmetry. Other
panels in the right column present the
phase angles: φ1 , φ3 and φ5 . Higher
order phase angles are compared to the
phase angle of the dominant terms φ1 by
subtraction. North is up and east to the
left on the velocity map and φ1 is measured east of north. Second panel on the
right also shows major (lower straight
line) and minor axis (upper straight line)
photometric PAs.
well as the distribution of line-strengths, for this object were presented in Davies et al.
(2001).
The velocity map of NGC 4365 (Fig. 8) shows a striking kinematically decoupled
component (KDC) in the central 500 . The structure and shape of this component led
several authors to conclude that NGC 4365 is intrinsically a triaxial body showing no
figure rotation (Surma & Bender 1995; Statler et al. 2004). We performed a kinemetric
analysis of the velocity map, expanding up to the fifth term (c5 ). The resulting coefficients and corresponding phase angles are shown in Fig. 8.
The KDC component is clearly evident in the dominant c1 terms as the fastest rotating component of the galaxy, with a well-defined radius. The main body of the
galaxy shows increasing rotation with increasing radius, but remains a slow rotator
(V /σ = 0.08, Surma & Bender 1995). The morphology term, c 3 , is very strong, contributing up to 50% to the velocity field, and is strongest at the transition radius between the
KDC and the main body of the galaxy. At larger radii, it slowly drops, but its relative
contribution (about 20%) stays high. In the last extracted term, c 5 , there is still considerable signal, again strongest in the transition region between the KDC and the rest of
the galaxy. The contributions from the higher order terms (ci , i ≥ 7) are on the order of
92
Chapter 4. Kinemetry: a method to quantify kinematic maps
a few per cent.
The amplitude coefficients accurately describe the map, but the phase angles are
useful for the determination of departures from axisymmetry. The kinematic angle, φ 1 ,
shows a clear twist of more then 100◦ over the map. The photometric major and minor
axis PAs are overplotted on the same panel with two horizontal lines. We measured the
PA on the reconstructed SAURON flux image obtained by integrating the spectra in each
bin. The kinematic angle of the KDC is aligned with the major axis PA, while the main
body of the galaxy rotates about an axis misaligned by about 10◦ from the major axis
PA of the galaxy, as previously noted by Davies et al. (2001). This is a clear signature of
non-axisymmetry. This conclusion is confirmed by the φ1 − φ3 profile, which changes
in step with φ1 , nowhere strictly satisfying the relation (12). The contribution of the
c3 term, expressed by eq. (13), and presented in the top left panel of Fig. 8, is high
everywhere, especially in the transition region between the KDC and the main body of
the galaxy.
5.3 Comparison of velocity fields of early-type galaxies with velocity fields of discs
We turn again to the case of kinemetry along ellipses. Repeating the analysis from
Section 4.5 we also analysed the velocity maps of three galaxies observed with SAURON
as part of the SAURON survey (de Zeeuw et al. 2002). The observations and the velocity
maps of NGC 524, NGC 2974 and NGC 4526 are presented in Emsellem et al. (2004).
We chose these three galaxies as characteristic examples due to their shape and the
pedagogical features of their velocity maps. NGC 524 is a roundish galaxy with an
“open” velocity map. NGC 2974 is a fast-rotating E4 galaxy, and NGC 4526 is an S0
galaxy with a prominent embedded disc which can be also seen on the velocity map as
a distinct component.
Fig. 9 presents the analysis of the three velocity maps. The analysis of the real
observations with ellipses is more complicated than the analysis with circles or the
analysis of the large model field (sampling issues), so, we had to rebin the velocity
map to a finer grid (4 times finer). This is especially important in the centres of the
field, where sampling can cause strong artifacts. The maps were also rotated such that
the photometric major axes are horizontal in Fig. 9. The maps are presented above each
corresponding set of kinemetric expansion terms. We summarise the main results as
follows:
NGC 524 has a velocity field with high axial ratio and hence we can label it as a
round velocity field. The higher-order terms c3 and c5 are small over the entire map,
with a relative contribution to the circular velocity of about 2% and 1% respectively.
NGC 2974 has a mean photometric flattening of ∼ 0.6 and the flattening of the
velocity field corresponds to this value (expressed as axial ratio q on the figure). This
velocity field is an example of a medium-flattened velocity field. The higher-order
deviations from the circular velocity are smaller than in the case of NGC 524, c 3 having
a relative contribution of ≈ 1% and c5 of ≈ 0.5%.
NGC 4526 is a more complicated map with its two kinematic components. The
central disc on the velocity map is clearly visible in the inner 10 00 . This structure is
reflected in the terms of the kinemetric analysis. The axial ratio is ≈ 0.2 in the inner 5 00 ,
while beyond that radius it is much higher and varies between 0.6 and 0.8. The velocity
Section 5. Application
93
Figure 9 — Kinemetric analysis along ellipses for velocity maps of three early-type galaxies observed
with SAURON. First row from left to right: velocity maps of NGC 524, NGC 2974 and NGC 4526. Second
row from left to right: axial ratio q of the best fitting ellipse describing the flattening of the velocity field.
Third and fourth rows from left to right: ratio of the terms in the kinemetric expansion: c 3 /c1 and c5 /c1 ,
respectively.
map in the inner few arcsec is clearly different from the rest of the map. The inner
part is quite flat, while the outer part has more round features, somewhere between
NGC 2974 and NGC 524. The higher-order terms are also different on this velocity
map. The relative contribution of c3 is much higher than in the two other examples (up
to ∼ 5 times), especially in the part where the velocity map is flat. The middle part of
the field is more similar to projected circular motion, with a small c 3 term. Towards the
end of the map, edge effects have an increasing influence on the expansion (Section 3).
At radii larger than 2000 , we only used the c3 term in expansion. The contribution of the
c5 term is smaller, but, interestingly, not negligible in the middle part of the map.
The similarities of the velocity maps of early-type galaxies with disc velocity maps
are striking. It might be the case that the three investigated galaxies have a strong disc
contribution which dominates the appearance of the velocity map, while the specific
94
Chapter 4. Kinemetry: a method to quantify kinematic maps
features are visible from the small departures of the higher terms. Similar result was
also seen in the model velocity field, which coressponds to a model galaxy with no disc
component. In analogy with photometry, the deviations of the higher-order terms are
also on the order of a few percent. This warrants a detailed study of a larger sample of
two-dimensional velocity maps, such as the 48 SAURON galaxies from Emsellem et al.
(2004).
6 Conclusions
We have presented a general method for analysing and describing two-dimensional
maps of the kinematic moments observed with integral-field spectrographs. The method is based on the harmonic expansion of velocity maps. It is particularly useful for
describing the maps of kinematic moments of early-type galaxies. We call our method
kinemetry.
Kinemetry is a straight-forward Fourier expansion of two-dimensional maps. Using the specific properties of the kinematic moments (symmetries) it can be used as a
powerful filter to the data. The results of kinemetry, the coefficients of the harmonic
expansion, can be used to parametrise trends and detect properties of galaxies. Maps
of odd kinematic moments are described only by the odd terms in the expansion. Similarly, maps of even moments are described only by the even terms.
In the case of odd maps, the first term is the most dominant term and gives the
overall shape of the map (the zeroth term can exist for velocity maps and gives the
systemic velocity). The third term describes the additional morphological shapes. In
some galaxies, higher terms can also be significant, although usually the first and third
term reproduce all important features of the map. The phase angle of the first term
gives the orientation of the map and it is called kinematic angle. Higher-order phase
angles are useful in detecting small departures from axisymmetry.
In the case of even maps, the zeroth term is the dominant term and it describes the
global shape of the map. The next important terms which describes the morphology
of the map in more detail, is the second term in the expansion. The zeroth term does
not have a phase angle, and the orientation of the features of the maps are given by the
phase angle of the second term.
The measured values of the kinemetric coefficients can be used to detect departures
from axisymmetry in the observed maps, and in this way, to quantify the intrinsic
shape of the galaxy. The necessary requirement for a velocity map to be consistent
with axisymmetry is that the even terms in the expansion are consistent with zero and
that the kinematic angle is constant and equal to the photometric position angle. We
present a diagnostic tool for determining the consistency of velocity maps with axisymmetry using the phase angles of the first two odd terms as well as quantifying the
departures from an axisymmetric velocity map. We apply this method to the triaxial
galaxy NGC 4365 as an obvious case of a non-axisymmetric object, with a decoupled
component and a strong kinematic twist.
Circular rings are the most natural choice for expansion, because they are simple,
general and can be uniformly used on maps of all kinematic moments. In some cases,
like for the velocity maps, it is necessary to expand the maps to a relatively large num-
Section 6. Conclusions
95
ber of terms (up to c5 or even c7 of the harmonic expansion judging from a preliminary
study of SAURON velocity maps (Emsellem et al. 2004)). In other cases, e.g. for the
velocity dispersion maps only a small number of terms (up to c2 ) are needed when the
expansion is performed along circles. We note that the maps of line-strengths, which
resemble the maps of the even moments (a line-strength is the zeroth moment of the
LOSVD), could also be analysed by kinemetry.
We also presented a preliminary study of kinemetry of velocity fields along ellipses
instead of circles. In this approach the number of terms needed to describe the field
is smaller than using circles (q and c1 versus, generally, c1 , c3 and c5 ). Also, the axial
ratio, q, provides a simple way of describing the global appearance of the velocity map,
which facilitates the use of illustrative terms such as flat or round. These terms are also
used to describe the surface-brightness distribution (note that q can be vary significantly from case to case), and this makes a natural connection between the different
moments of the distribution function.
The main assumption used when expanding along ellipses is that the velocity maps
of early-type galaxies are similar to the velocity maps generated by stars moving in circular orbits in a thin disc. Although we do not suggest this as a physical interpretation
for early type galaxies, it does provide an excellent low-order approximation to the
observed velocity maps. Indeed, in the presented examples we found that the velocity
maps of some early-type galaxies do resemble the velocity maps of discs. The presented preliminary results are encouraging and the next step is a detailed study of
the kinemetry of velocity maps along ellipses for a representative sample of early-type
galaxies.
Acknowledgments
We thank Eric Emsellem for providing a model axisymmetric galaxy. We thank Glenn
van de Ven for many useful discussions and Richard McDermid for a critical reading
of the paper.
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Chapter 5
Dynamical modelling of stars and gas in
NGC 2974: determination of
mass-to-light ratio, inclination and
orbital structure by Schwarzschild’s
method
Davor Krajnović, Michele Cappellari, Eric Emsellem, Richard M. McDermid, and P. Tim
de Zeeuw, submitted to Monthly Notices of the Royal Astronomical Society
We study the large-scale stellar and gaseous kinematics of the E4 galaxy NGC 2974,
based on panoramic integral-field data obtained with SAURON . We quantify the velocity fields with Fourier methods (kinemetry), and show that the large-scale kinematics is largely consistent with axisymmetry. We construct general axisymmetric
dynamical models for the stellar motions using Schwarzschild’s orbit-superposition method, and compare the inferred inclination and mass-to-light ratio with the
values obtained by modelling the gas kinematics. Both approaches give consistent results. However we find that the stellar models provide fairly weak constraints on the inclination. The intrinsic orbital distribution of NGC 2974, which
we infer from our model, is characterised by a large-scale stellar component of
high angular momentum. We create semi-analytic test models to study the ability of Schwarzschild’s modelling technique to recover the given input parameters
(mass-to-light ratio and inclination) and the distribution function. We also test the
influence of a limited spatial coverage on the recovery of the distribution function
(i.e. the orbital structure). We find that the models can accurately recover the input mass-to-light ratio, but we confirm that even with perfect input kinematics the
inclination is only marginally constrained. This suggests a possible degeneracy in
the determination of the inclination, but further investigations are needed to clarify this issue. We also show that the distribution function can be reliably recovered
by the modelling method inside the spatial region sampled by the integral-field
kinematics.
1 Introduction
T
internal dynamical structure of galaxies retains evidence of their evolution. The
internal dynamics, however, can only be interpreted through a combination of obHE
97
98
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
servational and theoretical efforts. From a theoretical point of view, one wants to know
how the stars are distributed in space and what velocities they have. From the observational point of view, one wants to determine the intrinsic structure of the observed
galaxies. The goals of both approaches are equivalent, and consist of the recovery of the
phase-space density, or distribution function (DF) of galaxies, which uniquely specifies
their properties. An insight into the DF is possible by the construction of dynamical
models which are constrained by observations. There are several modelling methods established in the literature, of which Schwarzschild’s orbit-superposition method
is perhaps the most elegant (Schwarzschild 1979, 1982). In the past few years it has
been applied successfully to a number of galaxies (van der Marel et al. 1998; Cretton
& van den Bosch 1999; Cappellari et al. 2002; Gebhardt et al. 2003); but recent observational advances in spectroscopy with integral-field units offer for the first time full
two-dimensional constraints on these dynamical models (Verolme et al. 2002; Copin,
Cretton & Emsellem 2004).
This paper presents a case study of the early-type galaxy NGC 2974. It is one of the
few elliptical galaxies known to contain an extended disc of neutral hydrogen in regular rotation (Kim et al. 1988). It also hosts extended Hα emission (Buson et al. 1993;
Plana et al. 1998), and belongs to the “rapid rotators” (Bender 1988). The total absolute
magnitude of MB = −20.32 puts NGC 2974 near the transition between giant ellipticals and the lower-luminosity objects which often show photometric and kinematic
evidence for a significant disc component (e.g. Rix & White 1992). Emsellem et al.
(2003, hereafter EGF03), combining WFPC2 imaging with TIGER integral-field spectroscopy of the central few arcseconds, discovered spiral structure in the Hα emission
in the inner few arcseconds, and concluded that the galaxy contains a nuclear stellar
bar. The general properties of NGC 2974 are listed in Table 1.
The availability of both stellar and gaseous kinematics makes NGC 2974 a very interesting case for detailed dynamical modelling. Cinzano & van der Marel (1994) made
dynamical Jeans models of the gaseous and stellar components additionally introducing a stellar disc in order to fit their long-slit data along three position angles. They
found that the stellar and gaseous discs were kinematically aligned and the inclination of both discs was consistent with 60◦ . This prompted them to suggest a common
evolution, where the gas could be ionised by the stars in the stellar disc. Using more
sophisticated two-integral axisymmetric models, which assume the DF depends only
on the two classical integrals of motion, the energy E and the angular momentum with
respect to the symmetry axis L z , EGF03 were able to reproduce all features of Cinzano
& van der Marel (1994) data as well as their integral-field TIGER data (covering the
inner 400 ). The models of EGF03 did not require a thin stellar disc to fit the data.
In this study we construct axisymmetric models for NGC 2974 based on Schwarzschild’s orbit superposition method. This method allows the DF to depend on all
three isolating integrals of motion. All previous studies with three-integral models
concentrated on the determination of the mass-to-light ratio, ϒ, and mass of the central
black hole, MBH . Based on the observed stellar velocity dispersion, the MBH − σ relation
(e.g. Tremaine et al. 2002) predicts a central black hole mass of 2.5 × 10 8 M , which at
the distance of NGC 2974 (21.48 Mpc, Tonry et al. 2001) has a radius of influence of 0.00 2.
Our observations of NGC 2974, with the integral-field spectrograph SAURON (Bacon
Section 2. Observations and data reduction
Table 1 — Properties of NGC 2974. Listed properties are taken from the Lyon/Meudon Extragalactic
Database (LEDA). Distance modulus is from Tonry
et al. (2001).
99
Parameter
Value
Morphological type
M B [mag]
effective B-V [mag]
PA [degrees]
Distance Modulus [mag]
Distance scale [pc/arcsec]
E4
-20.46
1.00
42
31.66
52.1
et al. 2001), do not have the necessary resolution to probe the sphere of influence of
the central black hole. The dynamical models presented here are, therefore, aimed at
determination of the ϒ, the inclination, i, and the internal orbital structure. The stellar
and gaseous kinematics also provide independent estimates of ϒ and i, which can be
used to cross-validate the results from the two approaches.
The results of the dynamical modelling are influenced by the assumptions of the
models, but also by the specifics of the observations. The spatial coverage of the kinematics is one example. The two-dimensional coverage is an improvement over a few
slits often used in other studies. Similarly, increasing the radial extent of the data could
change the results. Another issue, associated with the modelling techniques, is the ability of the three-integral models to recover the true distribution function of the galaxy.
This is very important for the investigation of the internal dynamics, since the recovered orbital distribution must represent the observed galaxy if we want to learn about
the galaxy’s evolutionary history. In this paper we present tests designed to probe
these issues and, in general, to determine the robustness of our three-integral method.
This paper is organised as follows. Section 2 summarises the SAURON spectroscopy
and the photometric ground- and space-based data. The analysis of the velocity maps,
used to quantify the presence and influence of possible non-axisymmetric motions as
well as a brief discussion on bars in NGC 2974, is presented in Section 3. The threeintegral dynamical models for the stellar motions are discussed in Section 4. Section 5 is
devoted to tests of the three-integral method involving the determination of the model
parameters (ϒ, i), influence of the radial extent of the data and the recovery of the DF.
The modelling of the emission-line gas kinematics and comparison with the results of
the stellar dynamical modelling is presented in Section 6. Section 7 concludes.
2 Observations and data reduction
The observations of NGC 2974 used in this work consist of ground- and space-based
imaging, and ground-based integral-field spectroscopy. The imaging data were presented in EGF03 and the absorption-line kinematics of the SAURON observations in
Emsellem et al. (2004,hereafter E04) as part of the SAURON survey (de Zeeuw et al.
2002). In this study we also use the SAURON emission-line kinematics of NGC 2974.
2.1 SAURON spectroscopy
NGC 2974 was observed with the integral-field spectrograph SAURON mounted on the
4.2-m William Herschel Telescope (WHT) in March 2001. The observations consisted
100
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Field of view
Aperture size
Final spatial sampling
Spectral range
Spectral sampling
Spectral resolution
# of field lenses
# of sky lenses
# of exposures
Exposure time per pointing
Instrumental dispersion(σ )
Median seeing (FWHM)
3300 × 4100
0.00 94
0.00 8
4810 - 5300 Å
1.1 Å pixel−1
4.2 Å (FWHM)
1431
146
8
1800 s
108 km s−1
1.00 4
Table 2 — The SAURON instrumental
characteristics and exposure details of
the observations of NGC 2974 obtained
in March 2001 at the WHT. The sky
apertures are pointed 1.0 9 away from the
main field.
of eight exposures divided equally between two pointings, each covering the nuclear
region and one side of the galaxy. The individual exposures of both pointings were
dithered to obtain a better estimate of detector sensitivity variations and avoid systematic errors. The instrumental characteristics of SAURON and a summary of the observations are presented in Table 2.
The SAURON data were reduced following the steps described in Bacon et al. (2001)
using the dedicated software XSauron developed at CRAL-Observatoire. The performed reduction steps included bias and dark subtraction, extraction of the spectra
using a fitted mask model, wavelength calibration, low frequency flat-fielding, cosmicray removal, homogenisation of the spectral resolution over the field, sky subtraction and flux calibration. All eight exposures were merged into one data cube with a
common wavelength range by combining the science and noise spectra using optimal
weights and (re)normalisation. In this process we resampled the data-cube to a common spatial scale (0.00 8 × 0.00 8) with resulting field-of-view of about 4500 × 4500 . The data
cube was spatially binned to increase the signal-to-noise (S/ N) ratio over the field,
using the Voronoi 2D binning algorithm of Cappellari & Copin (2003). The targeted
minimum S/ N was 60 per aperture, but most of the spectra have S/ N ratio high (e.g.
[S/ N]max ≈ 420) and about half of the spatial elements remain un-binned. The final
data cube of NGC 2974 and the detailed reduction procedure was presented in E04.
2.2 Absorption-line kinematics
The SAURON spectral range includes several important emission lines: Hβ , [OIII]λλ
4959,5007 and [NI]λλ5198,5200 doublets. These lines have to be masked or removed
from the spectra used for the extraction of the stellar kinematics. The method most suitable for this is the direct pixel-fitting method operating in wavelength space, which
allows easy masking of the emission lines. We used the penalised pixel-fitting algorithm (pPXF) of Cappellari & Emsellem (2004), following the prescriptions of E04. The
line-of-sight velocity distribution (LOSVD) was parametrised by the Gauss-Hermite
expansion (van der Marel & Franx 1993; Gerhard 1993). The 2D stellar kinematic maps
of NGC 2974, showing the mean velocity (V), the velocity dispersion (σ ), as well as
Section 2. Observations and data reduction
101
Figure 1 — Distribution of Hβ and [OIII] emission-lines and gas kinematics observed by SAURON. Gas
intensities are in mag arcsec−2 with arbitrary zero points. Gas mean velocity V and velocity dispersion σ
are in km s−1 . Overplotted isophotes are levels of the reconstructed total intensity from the full SAURON
spectra.
higher order Gauss-Hermite moments h3 and h4 , were presented in E04, along with the
kinematics of 47 other elliptical and lenticular galaxies. In this study we expand on the
previously published kinematics by including two more terms in the Gauss-Hermite
expansion (h5 and h6 ) to make sure all useful information was extracted from the spectra and tighten the constraints on the dynamical models. The extraction of additional
kinematic terms was performed following the same procedure as in E04. The new extraction is consistent with the published kinematics (except that now the LOSVD is
parameterised with 6 moments) and we do not present them here explicitly (but see
Fig. 11).
We estimated the errors in the kinematic measurements by means of Monte-Carlo
simulations. The parameters of the LOSVD were extracted from a hundred realisations
of the observed spectrum. Each pixel of a Monte-Carlo spectrum was constructed
adding a value randomly taken from a Gaussian distribution with the mean of the
observed spectrum and standard deviation given by a robust-sigma estimate of the
residual of the fit to the observed spectrum. All realisations provide a distribution of
values from which 1σ confidence levels were estimated. During the extraction of the
kinematics for error estimates, we switched off the penalisation of the pPXF method
in order to obtain the true (unbiased) scatter of the values (see Cappellari & Emsellem
2004 for a discussion).
2.3 Distribution and kinematics of ionised gas
NGC 2974 has previously been searched for the existence of emission-line gas. Kim
et al. (1988) reports the detection of HI in a disc structure aligned with the optical
isophotes. The total mass of HI is estimated to be 8×108 M , rotating in a disc with
an inclination of i ≈ 55◦ . Buson et al. (1993) detected Hα emission distributed in a
flat structure along the major axis. Assuming a disc geometry, the inferred inclination
is ≈ 59◦ , and the total mass of HII was estimated to be ≈ 3×104 M . Similar results
are found also by Plana et al. (1998). Deep optical ground-based imaging studies suggested the existence of “arm-like” spiral structures, visible in filamentary distribution
of ionised gas outside ∼ 500 (Bregman et al. 1992; Buson et al. 1993). The recent high-
102
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
JKT
Filter band
Exposure time (s)
Field of view (arcsec)
Pixel scale (arcsec)
Date of observations
HST/WFPC2
I
F547M & F814W
60
700 & 250
380×350
32×32
0.3106
0.0455
16.04.1993
16.04.1997
Table 3 — Summary of the
ground- and space-based
observations of NGC 2974.
The exposure times of the
HST/WFPC2
observations
are averages of all frames
used to produce the WFPC2
association images.
resolution HST imaging in Hα+[NII] revealed the presence of a gaseous two-arm spiral
in the inner ∼ 200 pc, with a total mass of 6.8 × 104 M (EGF03).
The strongest emission line in the SAURON spectra of NGC 2974 is the [OIII] doublet.
There is also considerable emission in Hβ and some emission from the [NI] lines. Measurement of the emission-line kinematics followed the extraction of the absorption-line
kinematics. For each spectrum in the data-cube we performed three steps:
(i) The pPXF method provided the model absorption spectrum that yielded the best
fit to the spectral range with the emission lines ([OIII], Hβ and [NI]) excluded.
(ii) We then subtracted the model absorption spectrum from the original observed
spectrum. This resulted in a “pure emission-line” spectrum which was used to
extract the gas kinematics.
(iii) Each emission line was approximated with a Gaussian. The fit was performed
simultaneously to the three lines of [OIII] and Hβ , not using the mostly negligible
[NI] doublet.
This procedure assumes that the velocity and velocity dispersion of the different
emission lines are equal. Preforming the simultaneous fit to the lines while allowing
them to be kinematically independent yields similar results (Sarzi et al. in preparation). Following Osterbrock (1989) we assumed a 1:2.96 ratio for the components of
the [OIII] doublet, while leaving the intensity of the [OIII] and Hβ lines independent.
The flux maps of [OIII] and Hβ lines as well as the maps of the [OIII] emission-line
mean velocity and velocity dispersion are presented in Fig. 1.
Both the Hβ and [OIII] emission lines are present over the whole extent of the maps
on Fig. 1, but their intensity drops off approximately exponentially with distance from
the centre. The [OIII] emission is stronger over the entire SAURON field with the [OIII] to
Hβ line-ratio being ≈1.7. The shape of the gas distributions are very similar, although
Hβ follows the stellar light isophotes more precisely. The [OIII] distribution shows
departures from the stellar isophotes in two roughly symmetric regions, positioned at
approximately 45◦ from the vertical axis on Fig. 1. The nature of these dips in the [OIII]
flux are discussed in Section 3.3.
2.4 Ground- and space-based imaging
In this study we used the existing ground- and space-based images of NGC 2974. The
already reduced wide-field ground-based I-band image of NGC 2974 was taken from
Goudfrooij et al. (1994), obtained at the 1.0-m Jacobus Kapteyn Telescope (JKT). We
also retrieved the Wide Field and Planetary Camera 2 (WFPC2) association images
Section 3. Quantitative analysis of velocity maps
103
Figure 2 — V-I colour versus the elliptical
radius of every pixel in the inner 1500 of
the WFPC2/PC1 images of NGC 2974. The
straight line presents the best fit to the points
obtained by minimising the absolute deviation. Notice the excess of red pixels between
0.00 3 and 2.00 5 caused by dust.
of NGC 2974 from the Hubble Space Telescope (HST) archive (Program ID 6822, PI
Goudfrooij). The details of all imaging observations are presented in Table 3.
A major complication in the derivation of the surface brightness model needed for
the dynamical modelling is the existence of dust, clearly visible on the high resolution
images. We considered two possible approaches: masking the patchy dust areas and
excluding it from the calculation of the model, or constructing a dust-corrected image.
We decided to adopt the latter approach to determine the stellar surface brightness.
We derived the correction of dust absorption using the F547M and F814W WFPC2
images, following the steps listed in Cappellari et al. (2002). The process consists of
construction of a colour excess map E(V-I), from a calibrated V-I colour image. The
colour excess map is used to correct the pixels above a given E(V-I) threshold using the
standard Galactic extinction curve. We assumed that the dust is a screen in front of the
galaxy and that dust-affected pixels have the same intrinsic colour as the surrounding
unaffected pixels. Figure 2 shows the calibrated V-I colour of pixels in the inner part
of the PC images. The best fit to the colours was obtained by minimising the absolute
deviation of the pixel values. This fit, represented by a line in Fig. 2, was used to calculate the colour excess by subtracting the measured colour from the fit. The resulting
E(V-I) image is shown in the second panel of Fig. 3. The other panels on the same figure present the inner parts of the F814W PC image before and after the correction of
dust absorption. The colour excess image highlights the dust structure visible also on
Fig. 3 of EGF03 and suggests a non-uniform distribution of dust in the central region
of NGC 2974.
3 Quantitative analysis of velocity maps
Two-dimensional kinematic maps offer a large amount of information and are often
superior to a few long-slit velocity profiles. The two-dimensional nature of these data
motivates us to quantify the topology and structure of these kinematic maps, just as is
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
104
Figure 3 — Dust correction on the F814W WFPC2 image of NGC 2974. From left to right: observed
F814W image; colour excess E(V-I) obtained as described in the text; dust corrected F814W image. The
arrow points to the north and associated dash to the east. All images were constructed using histogram
equalisation. Lighter shades represent brighter regions. The E(V-I) map is stretched between -0.1 (dark)
and 0.2 (bright) magnitudes.
commonly done for simple imaging. We have developed a new technique to deal with
kinematic maps based on the Fourier expansion, and, due to its similarity to the photometry, we named it kinemetry (Copin et al. 2001). This method is a generalisation of
the approach developed for two-dimensional radio data (Franx et al. 1994; Schoenmakers et al. 1997; Wong et al. 2004). The aim of the method is to extract general properties
from the kinematic maps of spheroidal systems (early-type galaxies) without assuming
a specific intrinsic geometry (e.g. thin disc) for the distribution of stars. This changes
the interpretation and the approach to the terms of the harmonic expansion from the
case of cold neutral hydrogen or CO discussed in the above mentioned papers. In this
section we briefly present the method and apply it to the stellar and gaseous velocity
maps. The detailed treatment of kinemetry with examples and tests is presented in
Chapter 4 of this thesis.
3.1 Harmonic Expansion
The kinemetry method consists of the straightforward Fourier expansion of the lineof-sight kinematic property K(r, θ ) in polar coordinates:
K(r, θ ) = a0 (r) +
N
∑ cn (r) cos[n(θ − φn (r))].
(1)
n=1
The expansion is done on a set of concentric circular rings (although other choices are
possible), and its main advantage is linearity at constant r. The expansion is possible
for all moments of the LOSVD, but in this paper we restrict ourselves to the mean
velocity maps.
The kinematic moments (moments of LOSVD) of triaxial galaxies in a stationary
configuration have different parity, e.g., mean velocity is odd, while the second moment hv2 i, is even. The parity of a moment generates certain symmetries of the kinematics maps. More generally, the maps of odd moments are point − anti − symmetric,
Section 3. Quantitative analysis of velocity maps
or:
V(r, θ + π ) = −V(r, θ ).
105
(2)
If axisymmetry is assumed, in addition to the previous relation, maps are mirror −
anti − symmetric, or:
V(r, π − θ ) = −V(r, θ ).
(3)
These symmetry conditions translate into the requirement on the harmonic expansion
(eq. 1) that for point-anti-symmetric maps the even coefficients in the expansion are
equal to zero, while in the case of mirror-anti-symmetry, additionally, the odd phase
angles have a constant value, equal to the photometric position angle (PA) of the galaxy
in the case of a true axisymmetric galaxy. This means that to reconstruct the mean
velocity map of a stationary triaxial galaxy, it is sufficient to use only odd terms in the
expansion.
These properties of the velocity maps enable certain natural filtering (point-(anti)symmetric - eq. (2), and mirror-(anti)-symmetric - eq. (3)) using the harmonic expansion with coefficients set to zero or phase angles fixed at certain values. For (visual)
comparisons of the data with the results of axisymmetric modelling it is useful to apply
the axisymmetric filtering to the data, as we will see below (Section 6).
3.2 Kinemetric analysis of velocity maps
We wish to know the intrinsic shape of NGC 2974 and, in particular, whether it is
consistent with axisymmetry, which would permit the construction of three-integral
axisymmetric dynamical models of the galaxy. In order to obtain the necessary information we applied the kinemetric expansion to the observed stellar velocity map. If
NGC 2974 is an axisymmetric galaxy, the kinemetric terms should have odd parity
(even terms should be zero) and the kinematic position angle should be constant and
equal to the PA.
The amplitude and phases of the first five terms in the expansion are presented in
Fig. 4. The first panel presents the dominant term in the expansion, c 1 , which gives the
general shape and amplitude of the stellar velocity map. The correction to this term
is given by the next significant term, c3 , which is already much smaller than c1 and
is presented in the second panel as a fraction of c1 . Even terms in the expansion, c2
and c4 , are also plotted on the same panel, and are much smaller (∼ 1% of c 1 )1 . For
comparison, the fifth term in the expansion, c5 , is also plotted and is larger than both
c2 and c4 . The SAURON pixel size is ∼ 100 and measurement of higher-order terms at
radii smaller than 200 cannot be trusted. Clearly, the velocity map in NGC 2974 can be
represented by the first two odd terms in the expansion. Neglecting all higher terms
results at most in a few percent error.
The lower two panels in Fig. 4 present the phases of the dominant terms. The φ 1
phase is defined as the kinematic angle of the velocity map, here measured east of
north. This angle is compared with measurements of two important angles: (i) the
PA measured on the WFPC2/PC F814W dust-corrected image using the IRAF ellipse
fitting task ellipse and (ii) the PA measured on the reconstructed SAURON flux image
1
The zeroth term, a0 , gives the systemic velocity of the galaxy and is not important for this analysis.
106
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 4 — Kinemetric expansion
of the stellar velocity field as a
function of radius. From top to
bottom: (a) first amplitude coefficient in the harmonic expansion c1 ;
(b) ratios of amplitude coefficients
presented by:
triangles c2 /c1 ,
diamonds c3 /c1 , squares c4 /c1
and plusses c5 /c1 ; (c) important
position angles: phase angle φ1
representing the kinematic position
angle (diamonds), photometric
position angle as measured on
WFPC2/PC1 F814W image (asterisks) and adapted value for
photometric position angle measured from the integrated SAURON
flux image (dashed straight line);
(d) difference between the first and
third phase from the kinemetric
expansion.
obtained by integrating the spectra in each bin. The agreement between the different
angles measured on the SAURON observations is excellent, with slight departures in
the inner 300 . The PA measured on the high resolution WFPC2 image suggests a small
photometric twist in the inner 1000 of ≈ 3◦ , which can be also seen in Fig. 9.
The phase angle φ3 is the phase of the third term in the kinemetric extraction. It
is easy to show, if the galaxy is axisymmetric (requiring in eq. 1, K(r,θ ) = 0 for θ =
φ1 + π/2), and the higher terms can be neglected, that the phases φ 1 and φ3 satisfy the
relation:
nπ
φ1 − φ3 =
(4)
3
where n ∈ Z. The last panel in Fig. 4 shows this phase difference. The condition given
by eq.( 4) is satisfied along the entire investigated range with a small deviation in the
inner 300 . Summarising all the above evidence, we conclude that the observed stellar
kinematics in NGC 2974 is consistent with axisymmetry.
We repeated the kinemetric analysis2 on the emission-line gas velocity maps and
present the results in Fig. 5. While the amplitude coefficients, c i , are similar to the
stellar coefficients (small values of all terms higher than c3 ), the behaviour of the phase
angles is quite different.
The last panel of Fig. 5 is perhaps the best diagnostic tool. The dashed line presents
the required value for the difference between the phase angles, φ 1 − φ3 , assuming axisymmetry. Deviations are present in the inner 4 00 and, although much smaller, between 900 and 1100 . These deviations indicate departures from axisymmetry, which are
2
A similar analysis approach for a gas disc would be using the Schoenmakers et al. (1997) harmonic
analysis on a tilted-ring model of the gas disc, interpreting the results within epicycle theory (see also
Wong et al. 2004).
Section 3. Quantitative analysis of velocity maps
107
Figure 5 — Same as Fig 4, but for
the gas velocity map.
strongest in the central few arcsecs.
3.3 Signature of bars in NGC 2974
In previous section, we quantified the signatures of non-axisymmetry on the gas velocity maps, especially strong in the inner 400 . Inside this radius, EGF03 discovered a
two-armed spiral and explained it by a weak bar with the corotation resonance (CR)
at 4.00 9 and outer-Lindblad resonance (OLR) at 8.00 5. These scales are consistent with
the observed departures from axisymmetry in our SAURON maps. Assuming that the
emission-line velocity field is generated by gas in a disc, the change in the phase difference and the crossing of the “axisymmetric” value can be interpreted as evidence of
the influence of the bar-potential, where the streaming of the gas changes direction as
one crosses the corotation radius.
As mentioned above, the distribution of the [OIII] emission-line intensity (Fig. 1)
exhibits an elongated structure in the central 5 00 . Similarly, around 800 − 1000 [OIII] is also
elongated, but this time approximately perpendicular to the first elongated structure.
Following this, the [OIII] map has a plateau between 12 00 and 1500 . The end of the
plateau is followed by a dip in the [OIII] distribution with a possible turn up at radii
larger than 2000 .
Although the central structure and kinematics of the [OIII] distribution are influenced by the inner bar, the large-scale structure (beyond ≈ 10 00 ) is not likely to be influenced by this weak inner bar. On a more speculative basis, we can infer the existence of
a large-scale bar. The primary (large-scale) bar should be 5 to 10 times bigger than the
secondary (inner) bar (Erwin & Sparke 2002, 2003), therefore, between ≈ 12.00 5 and 2500 .
A more precise, although still approximate, estimate of the properties of the pri-
108
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 6 — Diagram of resonances
in NGC 2974, derived from the
potential of the best-fitting stellar dynamical model. The upper horizontal line is the pattern speed of the nuclear (secondary) bar from EGF03 study
(Ωsp = 700 km s−1 kpc−1 ). The lower
horizontal line shows the position
of the inferred pattern speed of
p
the large-scale primary bar (Ω p =
−
1
−
1
700 km s kpc ). The vertical lines
show the assumed radial positions
of important resonances of the primary bar. From left to right: ILR
(CR of the secondary bar), UHR,
CR and OLR.
mary bar can be obtained from the resonance curves of NGC 2974. Using the potential of the best-fitting stellar dynamical model (see Section 4) we constructed the resonance diagram presented in Fig. 6. We calculated profiles of Ω, Ω − κ/2, Ω + κ/2 and
Ω − κ/4, where Ω is the angular velocity, V /r, and κ is epicyclic frequency, defined as
2
+ 4Ω2 . Assuming that the resonances of the primary and the secondary bar
κ2 = r dΩ
dr
are coupled to minimise the chaos produced around the resonances (Friedli & Martinet
1993; Pfenniger & Norman 1990), where the inner Lindblad resonance (ILR) of the primary bar is the CR of the secondary bar, we can estimate the main resonances of the
primary bar (indicated by the vertical lines on Fig. 6). The pattern speed of the primary
component is then ≈ 185 km s−1 kpc−1 , ILR is at 4.00 9, ultra harmonic resonance (UHR)
at ≈ 12.00 5, CR at ≈ 18.00 6 and OLR at ≈ 27.007. The size of the primary bar can be taken
to be 80% of its CR, so about 1300 to 1400 .
These size estimates are only approximate, but indicative, since the presented analysis is strictly valid only for an axisymmetric potential with an infinitesimal bar perturbation. We see several features in the [OIII] distribution and velocity maps that support
the assumption of a large-scale primary bar: the dip in the gas velocity map around
1200 , the plateau between 1200 and 1500 in [OIII] distribution as well as the dip in the [OIII]
distribution around 1800 . The last one corresponds to the position of the CR, which is a
chaotic region devoid of gas, consistent with the observed lower flux in that region.
3.4 Case for axisymmetry in NGC 2974
The alignment of the gaseous and stellar component, previously detected and also confirmed in this study, suggests that NGC 2974 is an axisymetric galaxy. However, the
gaseous component shows signatures of non-axisymmetric perturbations. The contri-
Section 4. Stellar Dynamical Modelling
109
Figure 7 — Contribution of the
non-axisymmetric motion to the
stellar and gaseous velocity fields,
as a fraction of the dominant term
in the kinemetric expansion, c1 . Diamonds present the emission-line
gas velocity contribution, while triangles present the stellar velocity
contribution.
bution of the non-axisymmetric motion, ∆V /c1 (see Chapter 4 for details), to the total
velocity field can be quantified from the phase difference φ3 − φ1 . If the condition in
eq. (4) is not satisfied then:
∆V
c3
= sin 3(φ1 − φ3 ),
(5)
c1
c1
which is presented in Fig. 7 for both stellar and gaseous velocity maps. At ∼ 3 00 , ∆V /c1
for the emission-line gas is ≈ 0.1 and at ∼ 10 00 it is ≈ 0.04, confirming that the nonaxisymmetric contribution is significant in the centre of the emission-line velocity map.
Its influence on the stellar velocity is not significant over the SAURON field. Emissionline gas is a more responsive medium and unlike the stars, due to the viscosity of the
gas particles, shows evidence of weak non-axisymmetric perturbations. It is possible
that other early-type galaxies with disc-like components harbour such weak and hidden bar systems.
Summarising, the stellar velocity map is mirror-anti-symmetric, supporting an axisymmetric shape for NGC 2974. On the other hand, the gaseous velocity map shows
strong deviations from mirror-anti-symmetry in the centre and the distribution of [OIII]
emission lines supports the weak inner bar found by EGF03 and suggests the existence
of a weak large-scale bar. However, since the bar perturbations on the axisymmetric
potential are weak and do not influence the stellar kinematics, we ignore them in the
remainder of the paper, and describe NGC 2974 with an axisymmetric potential.
4 Stellar Dynamical Modelling
In order to investigate the orbital structure of NGC 2974 we construct fully general axisymmetric models of the galaxy’s stellar component. The three-integral models presented here are based on Schwarzschild’s orbit superposition method (Schwarzschild
1979, 1982), further developed by Rix et al. (1997), van der Marel et al. (1998) and
Cretton et al. (1999), and adapted for more general surface-brightness distributions by
Cappellari et al. (2002,hereafter C02) and Verolme et al. (2002,hereafter V02), similarly
as in Cretton & van den Bosch (1999). The three-integral modelling technique is widely
used for constructing dynamical models of axisymmetric galaxies, and has been thoroughly described in the literature by the aforementioned authors as well as by other
groups (e.g. Gebhardt et al. 2003; Valluri et al. 2004). It is most commonly used to determine the masses of the central black holes in nearby galaxies and investigate the
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
110
j
Gj
σk (arcsec)
1
2
3
4
0.352
0.531
0.082
0.035
0.024
0.072
0.365
0.908
Table 4 — The MGE parameters
HST/WFPC2/F814W filter.
j
I j (L pc−2 )
σ j (arcsec)
qj
L j (×109 L )
1
2
3
4
5
6
7
8
9
10
11
190297.
44170.6
24330.8
27496.3
23040.6
10299.6
5116.29
1902.25
388.278
139.447
16.9405
0.0378596
0.0945030
0.185143
0.340087
0.591227
1.15500
3.41758
8.67562
17.5245
43.9864
82.9488
0.580000
0.800000
0.800000
0.583279
0.720063
0.777448
0.658664
0.597636
0.677645
0.580000
0.800000
0.0108
0.0215
0.0455
0.1264
0.3952
0.7279
2.6820
5.8305
5.5060
10.663
6.3538
of
the
circular
PSF
of
Table 5 — The parameters of
the MGE model of the deconvolved I-band WFPC2 surface brightness of NGC 2974.
Columns present (from left to
right): number of the twodimensional Gaussian, central intensity of the Gaussian,
width (sigma) of the Gaussian,
axial ratio of the Gaussian, total intensity contained in the
Gaussian.
internal orbital structure of the galaxies. The SAURON observations of NGC 2974 do
not have the necessary resolution to probe the sphere of influence of the central black
hole and we therefore restrict ourselves to the determination of the mass-to-light ratio
ϒ and the inclination i of the galaxy, as well as the internal orbital structure.
4.1 The Multi-Gaussian Expansion mass model
The starting point of the stellar dynamical modelling is the determination of the gravitational potential of the galaxy. The potential can be obtained by solving the Poisson
equation for a given density distribution which can be derived by deprojecting the observations of the 2D stellar surface density. In this work we used the multi-Gaussian
expansion (MGE) method (Emsellem et al. 1994), following the approach of C02 and
V02.
In order to get the MGE model, we simultaneously fitted the ground-based I-band
image and the dust-corrected PC part of the WFPC2/F814W image using the method
and software developed by Cappellari (2002). The dust correction (Section 2.4) successfully removed the dust contamination from the high-resolution image of the nucleus,
but the large-scale image was badly polluted by several stars, with a particularly bright
one almost on the galaxy’s major axis. We masked all stars inside the model area to exclude them from the fit. The ground-based image, used to constrain the fit outside
2500 , was scaled to the WFPC2/PC1 image. We computed the PSF of the F814W PC1
image at the position of the nucleus of NGC 2974, using TinyTim software (Krist &
Hook 2001), and parametrised it by fitting a circular MGE model with constant position angle as in C02. Table 4 presents the relative weights G j (normalised such that
Section 4. Stellar Dynamical Modelling
111
Figure 8 — Left Panels: Comparison between the combined WFPC2/F814W and ground-based photometry of NGC 2974 (open squares) and the MGE model (solid line) in seven angular sectors as function of
radius. The individual convolved Gaussian are also shown. Right panels: radial variation of the relative
error along the profiles.
112
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 9 — Contour maps of the ground-based I-band and dust corrected WFPC2/F814W images. The
brightest star on the ground-based image as well as four additional stars covered by the model were
masked out and excluded from the fit. Superposed on the two plots are the contours of the MGE surface
brightness model, convolved with the WFPC2 PSF.
their sum is equal to unity) and the corresponding dispersions σ of the four Gaussians.
Table 5 gives the parameters of the MGE model analytically deconvolved from the PSF.
Following the prescription of Cappellari (2002), we increased the minimum axial ratio
of the Gaussians, q j , until the χ2 significantly changed, in order to make as large as
possible the range of allowed inclinations by the MGE model. The upper limit to the
q j was also constrained such that the MGE model is as close as possible to a density
stratified on similar ellipsoids. Although the deprojection of an axisymmetric density distribution is non-unique (Rybicki 1987), our ‘regularisation’ on the MGE model
produce realistic intrinsic densities, while preventing sharp variations, unless they are
required to fit the surface brightness. We verified that the MGE model used in this
study is consistent with the MGE model presented in EGF03.
The comparison between the MGE model and the photometry along different angular sectors is shown in Fig. 8. The profiles are reproduced to within 3%, and the RMS
error is about 2%. The fluctuation of the relative error (right-hand panel in Fig. 8) at
larger radii is caused by the light pollution of the bright star on the major axis of the
galaxy and can be better understood by looking at the comparison of the convolved
model and the actual observation. Fig. 9 presents both ground- and space-based images and the MGE model. On the WFPC2/PC image there is a slight deviation from
the model (of constant PA) about 1000 from the nucleus. The deviating structure is
point-symmetric and reminiscent of a spiral perturbation. as suggested by other studies (Bregman et al. 1992; Buson et al. 1993; EGF03). Except for this slight departure
from the model the galaxy surface brightness is well represented by the MGE model
and we use it to calculate the representative gravitational potential.
Section 4. Stellar Dynamical Modelling
113
Figure 10 — A grid of
inclination angle versus
M/ L ratio.
Contours
present constant ∆χ2 ,
measuring the goodness
of fit of the dynamical
models. Every symbol
corresponds to a threeintegral
axisymmetric
model with given inclination angle, i, and ϒ
ratio.
The best-fitting
model for each inclinations are presented with
grey symbols. The first
three contours show the
formal 68.3%, 95.4% and
99.73% (thick contour)
confidence regions for
two degrees of freedom.
The best-fitting model on
the grid is constructed
for inclination of 65◦ and
ϒ = 4.5 M / L .
4.2 Construction of three-integral models
Briefly, Schwarzschild’s method can be divided in four steps. In the first step, one
derives the stellar potential assuming the shape of the potential (axisymmetry) and
stellar mass-to-light ratio, ϒ (free parameter), through deprojection of a parametrisation of the surface density (in this case MGE parametrisation which can be deprojected
analytically). The second step involves the construction of a representative orbit library by integrating the orbits in the derived potential. Each orbit is specified by three
integrals of motion (E, L z , I3 ), where E is the energy, L z the component of the angular
momentum along the z symmetry axis, and I3 is a non-classical integral, which is not
known analytically. The integral space is constructed on a grid that includes >99% of
the total luminous mass of the galaxy. The next step consists of projecting the orbits
onto the space of observables (x 0 , y0 , vlos ), where (x0 , y0 ) are in the plane of the sky and
vlos is the line-of-sight velocity given by the observations. In our implementation, this
is done taking into account the PSF convolution and aperture binning. The final step
of the method is to determine the set of weights for each orbit that, when added together, best corresponds to the observed kinematics in the given spatial bin as well as
reproducing the stellar density. In our implementation of the method, this best-fitting
set is found by solving a nonnegative least-squares (NNLS) problem using the routine
written by Lawson & Hanson (1974).
The software implementation used here is similar to that used in the V02 and C02
studies, but it has evolved substantially since. The improvements are described in
114
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
detail in Cappellari et al. (in prep.). We verified that the results from the new code are
the same as from the old one if identical settings are adopted. An application to the
elliptical galaxy NGC 4473 was presented in Cappellari et al. (2004). Here we give a
quick overview of the changes with respect to the description in C02:
1. The method requires that the orbits sample a three-dimensional space of integrals
of motion, the energy E, L z and I3 . In the new scheme (see Cretton et al. 1999 for
details of the previous approach), at each E, we construct a polar grid of initial
starting positions on the meridional plane (linear in angle and in radius), going
from R = z = 0 to the curve defined by the thin tube orbits (to avoid duplication)
which is well approximated by the equation R2 + z2 = R2c (E), where Rc (E) is the
radius of the circular orbit at energy E. The orbits are released with v R = vz = 0
and Lz 6= 0. In this way we sample the observable space by uniformly distributing
the position of the orbital cusps (see Cappellari et al. 2004) on the sky plane.
2. Improved treatment of seeing effects and instrumental point spread function
(PSF) by a Monte Carlo method. The PSF can be considered as the probability
that an observed photon arriving at a detector will be displaced from its original
position by a given amount (specified by the PSF characteristics). The projected
orbital points (results of the orbit integration and projection onto the sky-plane)
are stored in the apertures in which they landed after applying a random displacement taken from the Gaussian probability distribution defined by the PSF.
3. Generalisation of the projection of the orbits into the space of the observables.
The bins of the optimal Voronoi binning of the two-dimensional integral-field
data have non-rectangular shapes. The orbital observables now can be stored on
apertures of any shape that can be represented by polygons.
4.3 Stellar dynamics - modelling results and discussion
Our stellar kinematic maps of NGC 2974 consist of 708 Voronoi bins. Each bin contributes with 6 kinematic observables to which we also add the intrinsic and projected
mass density observables, resulting in a grand total of 5664 observables. The largest
orbit library that was computationally possible for the given number of observables,
consists of 2 × 41 × 10 × 10 = 8200 orbits (for each of the 41 different E we construct
a polar grid of starting points sampling 10 angles and 10 radii). With this choice of
orbit library, the number of observables is smaller than the number of orbits, and the
NNLS fit will not have a formally unique solution. Moreover the recovery of the orbital
weights for the orbits from the observations is an inverse problem, and as such is intrinsically ill-conditioned. For these reasons a direct solution of the problem generally
consists exclusively of sharp isolated peaks. It is unlikely for the DF of real galaxies to
be very jagged, since (violent) relaxation processes tend to smooth the DF. Moreover
observational constraints on the smoothness of the DF, at least for the bulk of the stars
in a galaxy, come from the smoothness of the observed surface brightness, down to the
smallest spatial scales sampled by HST.
A standard mathematical approach to solve inverse problems is by regularising
(e.g. Press et al. 1992,Chapter 18). This has been generally applied by all groups involved in this modelling approach (e.g. Rix et al. 1997; Gebhardt et al. 2003; Valluri et al.
2004; Cretton & Emsellem 2004). Regularisation inevitably biases the solution, by forc-
Section 4. Stellar Dynamical Modelling
115
Figure 11 — Comparison of the symmetrised observation of NGC 2974 (first row) and four orbital superposition models with best mass-to-light ratio ϒ, for a given inclination i. From second row to bottom:
(i , ϒ) = (55, 4.4), (65, 4.5), (75, 4.7), (89, 4.8). From left to right each panel presents: mean velocity V,
velocity dispersion σ , and Gauss-Hermite moments: h 3 , h4 , h5 and h6 . Isophotal contours of total light
are shown with elliptical solid lines. The overploted kinematic contours were obtained by interpolation
between the bin generators and extrapolation to the edge of the maps.
ing most orbits to have a non-zero weight. The key here is to apply the right amount
of regularisation. Previous tests with the Schwarzschild code suggested a value of the
regularisation parameter ∆ = 4 (see Cretton et al. 1999; V02). After initial testing we
also adopted this value. For more details on regularisation, see McDermid et al. (in
prep.).
The models are axisymmetric by construction. In order to avoid possible systematic
effects we additionally symmetrise the stellar kinematics as usually done in other studies. The symmetrisation uses the mirror-(anti)-symmetry of the kinematic fields, such
that kinematic values from four symmetric positions ((x, y), (x, − y), (−x, y), (−x, − y))
were averaged. However, the Voronoi bins have irregular shapes and they are not
equally distributed with respect to the symmetry axes of the galaxy (minor and major
axes). In practice, we average the four symmetric points, and, if for a given bin there
are no bins on the symmetric positions, we interpolate the values on those positions
116
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 12 — Integral space of the best fitting orbit superposition model for NGC 2974. Each panel
plots the meridional plane (R,z) with the starting positions of orbits (dots) for the given energy. Orbital
starting positions correspond to the position of cusps (v R = v z = 0). Overplotted is the fraction of mass
assigned to orbits at constant energy, labelled by the radius of the circular orbit in arcseconds (printed
at the upper left corner of each panel). The radius of the circular orbit is the size of the horizontal axis
(measured from the centre). Negative values are obtained by sign reversal, since orbits can be prograde
and retrograde. Orbits with high angular momentum are found in the right and left corner respectively
on the plots. We show only the radii constrained by the data. The last three panels have the size of the
SAURON field overplotted for comparison (grey rectangle). The area inside the rectangle is constrained
by the kinematic data. Brighter colour correspond to higher mass weights.
and then average them.
Finally, we fitted axisymmetric dynamical models to symmetrised observations of
velocity, velocity dispersion and Gauss-Hermite moments (h3 − h6 ) while varying the
mass-to-light ratio ϒ and the inclination i. Figure 10 shows a grid of our models with
overplotted ∆χ2 contours. The best-fit parameters are ϒ = 4.5 ± 0.1 (in the I band)
and i = 65◦ ± 2.5◦ . The data – model comparison for these values is given in Fig. 11
(symmetrised data are shown in the first row and the best-fitting model in the third
row). In the same figure we present the best-fitting models for the given inclinations.
The formal statistical analysis firmly rules out (with 3σ confidence) all inclinations
outside i = 65◦ ± 2.5◦ . The differences between the models are only marginally visible
on Fig. 11. However, comparing the models with the top row of symmetrised data, it is
noticeable that the velocity dispersion is less well fitted with increasing inclination. On
the other hand, the fit to h3 improves with higher inclinations. Higher-order moments
change similarly and the final χ2 is the result of this combined effect. Surprisingly,
the difference between the best-fit model and the data are bigger than the difference
between the other models and the best-fit model, provoking a question whether the
determination of the inclination is robust.
Recently, EGF03 used two-integral f (E, L z ) dynamical models and found a best fit
for an inclination 60◦ but also stated that models with 58◦ ≤ i ≤ 65◦ fit equally well.
Our three-integral models have a larger freedom in fitting the observations and it is
unknown whether these models can uniquely constrain the inclination. Our obtained
inclination is close to the previous measurements in the literature (references in Sections 1 and 2), and also to the inclination measured from gas and dust. NGC 2974 is
Section 5. Tests of Schwarzschild’s orbit-superposition models
117
perhaps a special case (in terms of its intrinsic structure and geometry) for which threeintegral models are able to give a stronger constraint on the inclination. We return to
this issue in Section 5.2.
The integral space of the best-fitting model, (i.e. the space defined by the isolating integrals of motion (E, L z , I3 ) that define the orbits and the DF f = f (E, L z , I3 )),
is shown in Fig. 12. Each panel presents mass assigned to orbits of constant energy,
parameterised by the radius of the circular orbit. This orbit also has the maximum
angular momentum and circular orbits of negative and positive angular momentum
are in the bottom left and right corner of each plot, while the low angular momentum
orbits are close to the symmetry (y) axis. An interesting feature appears on the panels
for radii between 5.00 97 and 17.00 7. A high fraction of mass is assigned to orbits with high
angular momentum. This indicates that the bulk of the stars rotate with high angular
momentum. A possible physical interpretation is that a large fraction of the stars orbit
in a disc. Cinzano & van der Marel (1994) argued that NGC 2974 has an embedded
stellar disc and in their two-integral Jeans models they were not able to fit the stellar
kinematics without introducing a disc with ≈ 7% of the total galaxy light. On the other
hand, the two-integral models of EGF03 did not need to invoke a stellar disc component to fit data consisting of their TIGER data and the three long slits of Cinzano & van
der Marel (1994). The integral space presented here suggests that the three-integral
models need orbits with high angular momentum, but the selected orbits also have
different values of I3 , and therefore do not represent a very thin stellar disc as assumed
by Cinzano & van der Marel (1994), but a somewhat flattened distribution of stars like
in a normal S0. The relative light contribution of the high-angular momentum orbits is
≈ 10%, which corresponds to a total stellar mass of 1.5 × 1010 M assuming the best-fit
model inclination and ϒ.
5 Tests of Schwarzschild’s orbit-superposition models
In the previous section we used three-integral models to recover the inclination, massto-light ratio and the internal structure of NGC 2974. Surprisingly, we find that the
inclination is tightly constrained by χ2 contours (Fig. 10), although the difference between the models (Fig. 11) are smaller than the difference between formally the bestfitting model and the data. In this section, we wish to test the robustness of those
results as well as the general ability of the three-integral models to recover the given
parameters. For this purpose we constructed an axisymmetric model mimicking NGC
2974 using two integrals of motion: the energy E, and the z-component of the angular momentum, Lz . This two-integral galaxy model has the advantage of a known DF,
f = f (E, Lz ), everywhere, which we want to compare with the results of the threeintegral modelling. There are three issues we wish to test:
1. Recovery of the input parameters of the two-integral model galaxy. This is a
general test to show whether the three-integral method can recover the parameters used in construction of a test model. We wish to be consistent with the
observations and consider only the recovery of the input mass-to-light ratio and
inclination, especially in light of the results from the Section 4.
2. Influence of the spatial coverage. The SAURON kinematic observations of NGC
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
118
2I model Full field SAURON field
(1)
(2)
(3)
ϒ
i
4.6
60◦
4.6 ± 0.1
60◦ ± 5◦
4.4 ± 0.1
65◦ ± 5◦
Table 6 — The properties of two-integral
models and comparison to three-integral bestfit results. Col.(1): parameters of the twointegral model of NGC 2974; Col.(2): recovered parameters using the Full field spatial
coverage (10000 × 10000 effectively) of kinematic
constraints; Col.(3): recovered parameters using the SAURON field spatial coverage (4000 ×
4000 effectively) of kinematic constraints.
2974 roughly cover one effective radius. This is also the typical size of most kinematic observations of other early-type galaxies from the SAURON sample. Here
we want to test the influence of the limited extent of the kinematic coverage on
the recovery of the orbital distribution. We do this by comparing the difference
between models using a limited and a full spatial kinematic information provided
by the two-integral galaxy model.
3. The recovery of the input DF. We wish to test the ability of our three-integral models to correctly recover the true input (two-integral) DF. Similar tests were also
presented by Thomas et al. (2004) for their implementation of Schwarzschild’s
method. Cretton et al. (1999), Verolme & de Zeeuw (2002) and Cretton & Emsellem (2004) described similar tests using two-integral Schwarzschild models.
5.1 The input two-integral test model
An f (E, Lz ) model of NGC 2974 was constructed using the Hunter & Qian (1993) contour integration method (hereafter HQ, see also Qian et al. 1995). We used the mass
model from Section 4.1 parameterised by MGE. This approach follows in detail Emsellem et al. (1999), and, due to the properties of Gaussian functions, simplifies the
numerical calculations significantly. Given the density of the system, the HQ method
gives the unique even part of the DF, f e = 21 [ f (E, Lz ) + f (E, − Lz )] (even in Lz ). The odd
part can be calculated as a product of the even f e and a prescribed function h = h(L/ L z ).
The magnitude of the function h is chosen to be smaller than unity, which ensures that
the final DF, f = f e + f o , is physical (i.e. non-negative, provided that f e >> 0 everywhere). In practice, the odd part is chosen to fit the observed kinematics (mean streaming) by flipping the direction of orbits with respect to the symmetry axis (photometric
minor axis).
The two-integral model of NGC 2974 was computed using i = 60◦ and ϒ = 4.6.
In order to construct a realistic DF we also included a black hole with mass M BH =
2.5 × 108 M , from the MBH − σ relation. The MGE model, constructed from a finite
spatial resolution HST WFPC2 image, has by construction an unrealistic flat asymp< 0.0002) and therefore we
totic density profile well inside the central observed pixel (r ∼
assumed a cusp with a power-law slope of 1.5 (ρ = r−1.5 ) inside that radius, following
the prescription of Emsellem et al. (1999). The final two-integral DF was computed
on a fine adaptive grid (i.e. more points in the region of strongly-changing DF with
E/ Emax < 2, where Emax is the value of the central potential of the model excluding the
black hole) of 140 × 79 points in (E, L z ). A fine grid of LOSVDs was computed from
this DF. These LOSVDs were used to compute the observable LOSVDs on 3721 posi-
Section 5. Tests of Schwarzschild’s orbit-superposition models
119
tions, two-dimensionally covering one quadrant of the sky plane (50 00 × 5000 ), accounting for the instrumental set up (size of SAURON pixels) and atmospheric seeing (which
matched the observations of NGC 2974 and was used for the three-integral models in
Section 4.2). The parameters of the two-integral model of NGC 2974 are listed in the
first column of Table 6.
In order to mimic the real observations (as well as to reduce the number of observables in the fit) we adaptively binned the spatial apertures using the Voronoi tessellation method of Cappellari & Copin (2003) as it was done for the observations, assuming
Poissonian noise. The final LOSVDs were used to calculate the kinematic moments (V,
σ , h3 to h6 ) by fitting a Gauss-Hermite series (first row on Fig. 14). These values were
adopted as kinematic observables for the three-integral models. From these data we
selected two sets of kinematic observables:
• The first set consisted of all 513 spatial bins provided by the two-integral model.
In terms of radial coverage this Full field set extended somewhat beyond two
effective radii for NGC 2974.
• The second set had a limited spatial coverage. It was limited by the extent of the
SAURON observations of NGC 2974, approximately covering one effective radius.
We call this observational set of 313 bins the SAURON field.
5.2 Recovery of input parameters
Our two-integral models are axisymmetric by construction and all necessary information is given in one quadrant bounded by the symmetry axes (major and minor photometric axes). Hence, the inputs to the three-integral code covered only one quadrant
of the galaxy. Although only one quadrant was used for the calculations we show all
maps unfolded for presentation purposes.
The three-integral models were constructed in the same way as described in Section 4.2. For both (Full field and SAURON field) sets of kinematic data we created orbit
libraries of 2 × 41 × 10 × 10 orbits and constructed models on grids of (ϒ, i). As for the
real data, we used a regularisation parameter ∆ = 4. The resulting grids are presented
in Fig. 13, and the best-fitting models are listed in the Table 6. The three-integral models
were able to recover the true input parameters within the estimated errors, although
the SAURON field models were less accurate.
The kinematic observables computed from the two-integral models are noiseless,
without errors nor intrinsic scatter typical of real measurements. For each kinematic
observable we assigned a constant error, but representative to the SAURON observations
of NGC 2974: 1σ errors for V, σ , h3 , and h4 . . . h6 were 4 km s−1 , 7 km s−1 , 0.03 and 0.04
respectively.
As we wanted to test an ideal situation we computed the kinematic observables
from the two-integral model without adding noise (intrinsic scatter) typical for real
measurements. However, given the fact that the input model is noiseless, the χ 2 levels
computed from the fit to the kinematics are meaningless. In order to have an estimate
of the uncertainties in the recovery of the parameters we computed half a dozen Monte
Carlo realisations of the kinematic data, introducing the intrinsic scatter to the noiseless
data. For each Monte Carlo data sets we constructed a three-integral model grid like
120
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 13 — Three-integral model grids of inclination angle versus M/ L ratio, ϒ. Contours present
constant ∆χ2 , measuring the goodness of fit of the models. Every symbol corresponds to a three-integral
axisymmetric model with given inclination angle and ϒ. The red symbols indicate the best fitting
models at a given inclination. The top grid presents models using the Full field set of kinematic
constraints. The global minimum is for the model with i = 60◦ and ϒ = 4.6. The bottom panel presents
models using the SAURON field set of kinematic constraints. The global minimum here is for the model
with i = 65◦ and ϒ = 4.4.
in Fig. 13. Due to time limitations we calculated parameter grids (ϒ, i) of models with
smaller orbit libraries (2 × 21 × 7 × 7 orbits) of both Full field and SAURON field data sets.
In this case we also applied regularisation ∆ = 4. Approximate 3σ confidence levels
assigned to the best-fitting parameters are listed in Table 6. Setting the regularisation
to zero, we observed similar trends.
The numbers in Table 6 suggest that the inclination is formally recovered by threeintegral models, as seen in the case of the observation (Section 4.3). We repeat the
exercises of plotting a sequence of models with different inclinations (using the Full
field kinematics). They are presented in Fig. 15 and we can see a very similar trend
as in Fig. 11: there appears to be little difference between the models, although by
scrutinising the details, it is possible to choose the best model by eye.
The smoothness of the data of the two-integral test model helps in recognising
the best-fit model. The models with lower inclination (towards face-on) are generally
smoother than the higher inclination (towards edge-on) models, which systematically
show radial structures. These “rays” visible on Fig. 15 are artifacts of the discreteness
of our orbit library. The starting points of the orbits correspond to the positions of orbital cusps, which carry the biggest contribution to the observables. The total number
of cusps is determined by the number of orbits, and the finiteness of the orbit library is
reflected in the discrete contributions of the cusps to the reconstructed observables (see
Fig. 1.2 of Cappellari et al. 2004). The projection effects, however, increase the smooth-
Section 5. Tests of Schwarzschild’s orbit-superposition models
121
Figure 14 — Comparison between two-integral analytical model kinematics and three-integral models.
First row: two-integral model used as input to the three-integral code. Second row: best fitting threeintegral model (i = 60◦ , ϒ = 4.6) using the Full field set of kinematic constraints. Third row: best-fitting
three-integral model (i = 65◦ , ϒ = 4.4) using the SAURON field set of kinematics. The spatial extent of this
set is marked by white squares on the maps. From left to right each panel presents: mean velocity V,
velocity dispersion σ , and Gauss-Hermite moments: h 3 , h4 , h5 and h6 . Isophotal contours of total light
are shown with the elliptical solid lines.
ness by spatially overlapping different cusps; hence, models projected at e.g. i = 60 ◦
will be smoother than models viewed edge on. We believe this effect could influence
the χ2 , favouring the lower inclination models.
Although present, this effect does not provide the only constraint on the inclination.
When examined more closely, models with low inclination do reproduce better certain
features. For example: the shape and amplitude of the velocity dispersion in the central
2000 , h3 and h4 at the larger radii (towards the edge of the field), the central 10 00 of h5
and h6 . In all cases the model with i = 60◦ reproduces these features better than other
models. Comparing the models, the most significant contribution to the χ2 comes from
the velocity dispersion, but generally, individual observables have slightly different χ 2
values, which increase with the inclination moving away from 60◦ and is visible only
as a cumulative effect. This explains the similarities of the different models to the eye,
although they are formally significantly different.
The difference in the model observables (which include moments up to h 6 ) are below the level of the systematics in the data (e.g. template mismatch), or in the models
(e.g. regularisation or variations in the sampling of observables with orbits). In the case
of NGC 2974, using high signal-to-noise two-dimensional data, the difference between
the models themselves are smaller than between the best-fitting model and the data,
implying that the inclination is only weakly constrained. This result suggests a fundamental degeneracy for the determination of inclination with three-integral models,
which is contrary to indications from previous work by Verolme et al. (2002). Theoret-
122
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 15 — Sequence of three-integral models for different inclinations fitting the (Full filed of kinematic observables. First row: two-integral test model. Subsequent rows: three-integral models for
i = (55◦ , 60◦ , 70◦ , 80◦ , 89◦ ). Columns from left to right present moments of the LOSVD: v, σ , and from h 3
to h6 . Isophotal contours of total light are shown with elliptical solid lines.
ical work and more general tests on other galaxies are needed for a better understanding of this issue.
5.3 Effect of the field coverage on orbital distribution
The next step is to compare in more detail the three-integral models using the two different kinematic data sets. The kinematic structures of the best-fitting models are presented in Fig. 14. In the region constrained by the kinematic data both models reproduce equally well the input kinematics. As expected the regions outside the SAURON
Section 5. Tests of Schwarzschild’s orbit-superposition models
123
Figure 16 — Comparison of the integral spaces of the f (E, L z ) test models. Upper five rows belong to
the model constrained by the SAURON field kinematics and the lower five rows to the model constrained
by the Full field kinematics. The meaning of each panel is the same as in Fig. 12. In the region constrained
by the both kinematic sets the two integral spaces are indistinguishable.
field are not reproduced well. It is more interesting to compare the phase spaces of the
models. In particular, we wish to see whether the mass weights assigned to the orbits
(represented by the integrals of motion) are the same for the two models.
The corresponding integral-spaces are shown in Fig. 18. Red rectangular boxes
represent the extent of the kinematics used to constrain the models. In the regions
constrained by both kinematic sets, the two integral spaces are identical: both models
recover the same orbital mass weights. The differences appear at larger radii (beyond
2000 ), outside the area constrained by the SAURON field kinematic set. Putting this result
in the perspective of observations, the resulting phase space (in the region constrained
by the observations) does not depend on the extent of the radial coverage used to constrain the model. This result strengthens the case of the NGC 2974 modelling results,
where we have integral-field observations reaching ≈ 1 re . The recovered integral space
and its features would not change if we had a spatially larger observational field.
124
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 17 — Moments of the velocity ellipsoid for the two-integral test galaxy recovered by the threeintegral model (constrained by the Full field kinematic set). The left panel presents the ratio of the radial
and longitudinal moments. The right panel shows the ratio of the radial and tangential moment as
defined in the text. Different lines show the ratio of the moments in the meridional plane at different
position angles, starting from the major-axis to the minor axis. In a true two-integral galaxy, all three
moments of the velocity ellipsoid have to be equal. Note that the deviation inside 1 00 are expected since
the data do not constrain the model in that region.
5.4 Recovery of the internal moments
We wish to see if the best-fitting three-integral model to the f (E, L z ) test galaxy model
is consistent with the input, i.e., whether three-integral models will recognise the true
structure of the test galaxy. A first estimate can be achieved by investigating the internal structure of the resulting model galaxy, specifically the shape of the velocity
ellipsoid. We define the tangential dispersion as σ t = [ 21 (σθ2 + σφ2 )]1/2 . Note that σφ
includes only random motion so that for an isotropic distribution, under the given
definition, the radial (σr ) and tangential dispersion are equal. Since two-integral models are isotropic in the meridional plane per definition, we expect to recover that σ r is
equal to σθ and the cross-term σ Rθ is equal to zero. In Fig. 17 we show the ratios of the
moments of the velocity ellipsoids at different positions in the meridional plane and
at different radii from the model constrained by the Full field kinematics. One can see
that σr = σθ within ≈ 5%, confirming that our three-integral model recovers the true
internal moments. Also, computing the cross-terms σ Rθ , we verified that it is negligible everywhere. Similar results are also recovered from the SAURON field model: in the
constrained region the ratio of σr and σθ moments are consistent with unity.
5.5 Recovery of the distribution function
The previous result shows that the constructed three-integral model is a consistent representation of the input f (E, L z ) model. A more conclusive test, however, is to compare
the distribution functions.
The results of the three-integral Schwarzschild method are orbital mass weights,
0
γ3I
(E, Lz , I3 ), for each set of integrals of motion (E, L z , I3 ), which define an orbit. The
DF is related to the mass weights via the phase-space volume (for a detailed treatment
Section 5. Tests of Schwarzschild’s orbit-superposition models
125
Figure 18 — Comparison of the
mass weights from the two-integral
model (upper panel) and the results of the three-integral modelling (lower panel) using the twointegral model as input. The galaxy
centre is on the left side. The
first bin containing the contribution
of the black hole was not plotted,
since the resolution of the models
do not allow for its recovery. The
two vertical lines enclose the region
constrained by the kinematic data.
see Vandervoort 1984):
γ (E, Lz , I3 ) dEdLz dI3 = f (E, Lz , I3 ) ∆V(E, Lz , I3 ) dEdLz dI3 ,
where
∆V(E, Lz , I3 ) =
Z
J (~
x, E, Lz , I3 )d3 x,
(6)
(7)
Ω
and J (~
x, E, Lz , I3 ) is the Jacobian of the coordinate transformation from (~
x, ~
v) to (~
x, E,
Lz , I3 ), and Ω is the configuration space accessible to an orbit defined by the integrals
(E, Lz , I3 ). Unfortunately, I3 is not known analytically, so the above relation can not be
explicitly evaluated, except for separable models. For this reason we limit ourselves to
test the consistency of our three-integral mass weights with the input two-integral DF.
This is possible, since if the recovered three-integral DF is equal to the input DF, then
the mass γ2I (E, Lz ) assigned to the stars in a given range of (E, L z ) by the three-integral
model has to be equal to the mass in the same range of the input model.
There exists a precise relation between the input two-integral DF, f = f (E, L z ), and
the corresponding orbital mass weights, γ2I (E, Lz). The total mass of the system is the
integral of the DF over the phase-space. Using this, Cretton et al. (1999) derived the
expression for the mass weights in Appendix B of their paper (eq. B4):
γ2I (E, Lz ) =
Z
Ω
with
dM
= f (E, Lz ) ×
dEdLz
dM
dEdLz
dEdLz
I
ZVC(E, L z )
(Rdz − zdR)
(8)
(9)
126
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
where the contour integral yields the area of the zero velocity curve (ZVC). Before
applying eqs. (8) and (9) on the two-integral DF we rebinned it to the same grid of ∆E
and ∆Lz as the three-integral mass weights. Finally, we approximate the integral (8) by
multiplying the mass fraction in each grid cell by ∆E∆L z .
For our comparison we defined as the energy intervals the set of energies used in
the construction of the three-integral models (total of 41). The interval in angular momentum was defined as a step of 0.1 of L z / Lmax
from −1 to +1 (total of 20) for a given
z
energy. The resulting grid of orbital weights is relatively coarse, but is representative
of the model. The agreement between the two sets of mass weights is shown in Fig. 18.
The main features of the given two-integral test model are reproduced quite accurately
by the three-integral model. Again, the mass weights should be compared in the region
constrained by the data (between the vertical lines in the figure). The mass weights of
the three-integral model are relatively noisy which is mostly the consequence of imposed discreteness as well as the numerical nature of the method.
We conclude that the Schwarzschild method provides accurate dynamical models
for galaxies when constrained by two-dimensional kinematics out to an effective radius.
6 Modelling of emission-line gas
Clearly, with its prominent gas component, NGC 2974 is an unusual elliptical galaxy.
The observations indicate the morphological similarity between the small (HII) and
large scale (HI) gas discs. Also, long-slit measurements of stellar and gas motions
detect similarities between the stellar and gas kinematics (Kim 1989; Cinzano & van der
Marel 1994). In this section we investigate the inclination of the gaseous component as
well as construct dynamical Jeans model of the gas disc similar to one used by Cinzano
& van der Marel (1994), in order to compare them to the results of the stellar dynamical
modelling.
6.1 Inclination of the gas disc
The existence of the emission-line gas disc in NGC 2974 can be used to infer the inclination of the galaxy assuming an equilibrium dynamical configuration. This has been
attempted before and in all studies the inclination of the gas disc was consistent with
55◦ − 60◦ (Amico et al. 1993 55◦ ; Buson et al. 1993 59◦ ; CvdM94 57.5◦ ; Plana et al. 1998
60◦ ). The high quality of the two-dimensional SAURON kinematics allows us to estimate
the inclination of the emission-line gas disc more accurately.
We assume the motion of the emission-line gas is confined to a thin axisymmetric
disc. We neglect the deviations from axisymmetry discussed in section 3. Using the
kinemetric expansion, we symmetrised the observed velocity field applying mirror(anti)-symmetric filtering (using the first six terms) on the coefficients of the expansion
(eq. 3), interpolating onto a regular grid. We set all phase coefficients to the mean kinematic angle, φ1 , of the emission-line gas velocity field. This velocity field is an axisymmetric representation of the observed field, which can be compared to an axisymmetric
model of the disc velocity field. Constructing the full two-dimensional velocity field
requires only the kinematic major axis velocity profile v m j . The entire field is then given
Section 6. Modelling of emission-line gas
127
Figure 19 — ∆χ2 as a function of inclination
obtained by comparing the symmetrised data
for NGC 2974 and the model gas disc velocity
map described in 6.1.
by the standard projection formula:
v LOS (x0 , y0 ) = vφ
x0 sin i r
= vm0 j
x0 r
,
(10)
where r2 = x02 + (y0 / cos i)2 and i is the inclination of the disc. It is clear from this
formula that for a given observed major-axis velocity, the velocity field is just a function
of inclination. From the first three odd coefficients (c1 , c3 and c5 ) of the kinemetric
0
expansion we construct the velocity profile vm
j along the major axis (θ = φ1 ). Using the
major axis velocity profile, we created a set of disc velocity fields inclined at different
values of i, and compared them with the symmetrised velocity field. We did not correct
for the influence of the PSF as this effect is small and is confined to the central few
arcseconds, which we excluded from the comparison. We also compared the models
with the non-symmetrised velocity map and the results were in very good agreement,
but with a slightly larger uncertainty range.
Figure 19 presents the ∆χ2 obtained by subtracting the disc model velocity field
from the symmetrised measurements. The best-fitting inclination is i = 58◦ ± 5◦ (at one
σ level). Fig. 20 shows a comparison between the symmetrised and model velocity
fields for a few representative inclinations. The differences between the model fields
are mostly in the opening angle of the iso-velocity contours, which change with the
inclination of the field. The model for i = 58◦ has this angle the most similar to the
observed velocity field and this significantly lowers the χ2 of the fit.
The best-fit inclination of 58◦ for the emission-line gas is in excellent agreement
with literature values determined from the various gas components. This suggests
the gas is in the principal plane of the galaxy. Our best-fitting three-integral stellar
dynamical model was obtained for an inclination of 65◦ with 3σ uncertainty of 2.5◦ .
This inclination is close to the inclination of 58◦ presented in this section, suggesting
a good agreement between the stellar and gaseous models. There is, however, the
concern that the agreement may not be as significant as it seems in light of the tests
and results from Section 5.2.
128
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 20 — Comparisons between observed and model gas disc velocity fields. From left to right:
observations (symmetrised), model fields for inclination of 45◦ , 55◦ (best-fitting), 65◦ . Isophotal contours
of total light are shown with elliptical solid lines.
6.2 A simple dynamical model for the disc
At large scale, the gas kinematic maps are consistent with the assumption that the
emission-line gas is moving in a thin disc. This assumption clearly breaks down in the
inner few arcseconds, but at this point we neglect this effect. The observed gas velocity
dispersion is high everywhere in the disc and is much larger than the thermal velocity
dispersion which should be σthermal ∼ 10 km s−1 only (Osterbrock 1989). Clearly, in
addition to the thermal dispersion, the gas has another source of motion, which is
not presently understood, but is seen in many galaxies (Bertola et al. 1995). Several
studies (e.g. van der Marel & van den Bosch 1998; Verdoes Kleijn et al. 2000) assumed
that the non-thermal gas velocity dispersion is the result of ‘local turbulence’, without
describing the details of the underlying physical processes. In this assumption, the
gas still rotates at the circular velocity and the invoked turbulence does not disturb
the bulk flow of the gas on circular orbits. The alternative to this assumption is that
the non-thermal velocity dispersion component comes from collisionless gravitational
motion of the gas, where the gas acts like stars: clumps of gas move on self-intersecting
orbits. This is, perhaps, not very physical for gas in general, but it can be applied
to estimate the difference between the circular and streaming velocity (and including
the projection effect on the observed velocity) of the gas. Several studies used this
approach successfully (e.g. Cinzano & van der Marel 1994; Cretton et al. 2000; Barth
et al. 2001; Aguerri et al. 2003; Debattista & Williams 2004). Presently, the role and
importance of the asymmetric drift remains an unresolved issue.
In constructing our simple disc model we assumed that the emission-line gas is
moving in individual clumps that interact only collisionlessly. The clumps move along
ballistic trajectories in a thin disc, under the influence of the galaxy potential given
by the stellar distribution (Section 4). The gas kinematics are determined by solving
the Jeans equations for radial hydrostatic equilibrium. Following Binney & Tremaine
(1987,eq. 4-33), the streaming velocity of gas can be written in cylindrical coordinates
as:
h
d ln ρ
d ln σ R2
σ2 i
v̄2φ = Vc2 − σ R2 − R
−R
− (1 − R2 ) ,
(11)
dR
dR
σφ
Section 6. Modelling of emission-line gas
129
Figure 21 — Fit to the surface density profile of the [OIII] emission lines. Dashed
lines present individual exponentials given
by eq.(12).
where we have assumed the distribution function depends on the two classical integrals of motion, fp
= f (E, Lz ), which implies σ R = σz and v R vz = 0. In eq. (11), Vc is the
circular velocity ( R(dΦ/dR)), Φ is the total potential of the galaxy obtained from the
MGE fit assuming inclination i, σ R and σφ are the radial and azimuthal velocity dispersions, and ρ(R) is the spatial number density of gas clouds in the disc. Lacking any
alternative, we use the surface brightness of the gas to estimate ρ(R). Instead of using
the actual measured values of the [OIII] and Hβ flux, we parametrise the emission-line
surface brightness with a double exponential law,
ρ = ρ0 e
− RR
0
R
+ ρ 1 e − R1 ,
(12)
in order to decrease the noise. The parameters are obtained from the fit to the [OIII]
data shown in (Fig. 21), where the two-dimensional surface brightness was collapsed
to a profile by averaging along ellipses of constant ellipticity (ellipticity of the galaxy)
and position angle (PA of the galaxy). The errors are standard deviations of the measurements along each ellipse.
The relation between radial and azimuthal velocity dispersions can be obtained
using the epicyclic approximation. This gives (following eq. 4-52 in Binney & Tremaine
1987):
σφ2
1
d ln Vc = 1+
,
(13)
σ R2
2
d ln R
This approximation is valid for small values of the asymmetric drift v φ − Vc , or, in
other words, in the limit of a cold disc with small velocity dispersion, σ Vc . This is
marginally the case in NGC 2974, clearly violated in the central < 5 00 , but it is acceptable
in most of the observed regions (Fig. 22).
The observed quantities can be obtained from the calculated intrinsic properties
projecting at an inclination angle i. The projected two-dimensional line-of-sight (LOS)
velocity field is given by eq. (10). Within these assumptions of the disc model, the
projected LOS velocity dispersion is:
x0 sin i 2
2
2
2
σ LOS = (σφ − σ R )
+ σ R2 .
(14)
r
130
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
Figure 22 — Ratio σ R / VC for the best-fitting
model to the emission-line gas data.
We constructed the asymmetric drift models of the emission-line gas in NGC 2974 using the MGE parametrisation of the potential, ϒ=4.5, inclination i = 58◦ , and simultaneously accounting for the atmospheric seeing and pixel size of the SAURON observations
(see Qian et al. 1995 for details). In the process we assumed an exponential law for the
radial velocity dispersion:
R
σ R = σ0 + σ1 e− Rσ ,
(15)
and varying σ0 , σ1 , and Rσ we constructed gaseous disc models of NGC 2974. The
best-fitting model was obtained for σ0 = 90 ± 5 km s−1 , σ1 = 190 ± 10 km s−1 , and Rσ =
5 ± 100 . Comparison of this model with the symmetrised observations is presented in
Fig. 23.
Summarising, the asymmetric drift model can reproduce the general properties of
the emission-line gas disc. Using the circular velocity obtained from the stellar potential, the model is able to reproduce the bulk of the streaming velocity as well as
the significant non-zero velocity dispersion of the emission-line gas. A similar finding
was reported by Cinzano & van der Marel (1994). The simple asymmetric drift model,
however, is not able to reproduce several details: the velocity field in the centre, the
decrease of velocity at ∼ 1000 , and the minor axis elongation of the velocity dispersion. This is not surprising since those features are signatures of non-axisymmetry in
NGC 2974 and cannot be represented by simple axisymmetric models.
7 Concluding remarks
This paper presents a case study of the early-type galaxy NGC 2974, which was observed in the course of the SAURON survey of nearby E/S0 galaxies.
Kinematic position angles of the stellar and gaseous kinematics of this galaxy are
on average well aligned. The stellar kinematic maps exhibit mirror-(anti)-symmetry,
with the kinematic angle equal to the photometric PA, and are consistent with an axisymmetric intrinsic shape. The gaseous velocity map is more complicated, with clear
departures from axisymmetry in the centre of the galaxy (< 4 00 ). At larger radii, the
gas kinematic angle is not constant, although is largely consistent with the photomet-
Section 7. Concluding remarks
131
Figure 23 — Bottom Panels: Asymmetric drift model for the best fitting parameters compared to Top
Panels: the symmetrised (mirror(anti)-symmetric filtering with 6
terms) mean velocity (first column) and velocity dispersion (second column). Overplotted elliptical
solid lines represent typical total intensity isophotes.
ric PA, showing deviations of a few degrees. The SAURON observations of NGC 2974
confirm the existence of non-axisymmetric perturbations consistent with a nuclear bar
(EGF03) as well as a possible large-scale bar. The departures from axisymmetry are not
visible in the stellar kinematic maps and therefore are likely to be weak. This allows us
to construct axisymmetric models of NGC 2974.
We constructed self-consistent three-integral axisymmetric models based on the
Schwarzschild’s orbit superposition method, varying mass-to-light ratio and inclination. The observed surface brightness was parameterised by multi-Gaussian expansion model on both ground- and space-based imaging. The models were compared
with the SAURON kinematic maps of the first six moments of the LOSVD (v, σ , h 3 - h6 ).
The best-fitting model has ϒ = 4.5 ± 0.1 and i = 65◦ ± 2.5◦ . The inclination is formally
well constrained, but there are several indications that the recovery of the inclination is
uncertain: (i) differences between the models are on the level of systematics in the data
(e.g. template mismatch); (ii) difference between the best-fit model and the data are
bigger than differences between other models and the best-fit model; (iii) limitations
of the models (discreteness of the cusps) may artificially constrain the inclination.
The internal structure of NGC 2974 (assuming axisymmetry) reveals the existence
of a rapidly rotating component contributing with about 10% of the total light. This
component is composed of orbits allowing the third integral and does not represent a
cold stellar disc, although suggests a flattened structure similar to an S0 galaxy.
The results of the stellar dynamical models were compared with the results of modelling the gas component. The inclination of the gas disc, calculated from the emissionline velocity map is i = 58◦ ± 5◦ , in agreement with the formally constrained stellar
inclination. A simple model of the gas disc in the same potential used for the stellar
modelling (ϒ = 4.5, but i = 58◦ ) was able to reproduce the characteristics of the gas
kinematics (v and σ ) on the large scale, but failed in the centre, as expected.
We performed a set of tests of our implementation of the Schwarzschild’s orbit
132
Chapter 5. Dynamical modelling of stars and gas in NGC 2974
superposition method. For this purpose we constructed a general two-integral model
of NGC 2974, and used the reconstructed kinematics as inputs to the Schwarzschild’s
method. We tested (i) the influence of the radial coverage of the kinematic data on
the internal structure, (ii) the recovery of the test model parameters (ϒ,i), and (iii) the
recovery of the test model DF. The tests show that:
1. Increasing the radial coverage of the kinematic data from 1r e to 2re does not
change the internal structure within 1re . The results of the dynamical models of
the SAURON observations of NGC 2974 would not change if the radial coverage
would be increased by a factor of 2.
2. We find that three-integral models can accurately recover the mass-to-light ratio.
Although the models are also able to constrain the inclination of the test model
formally, the apparent differences between the models are small (as in the case of
the real observations). Under careful examination, it is possible to choose the best
model by eye, but the decisive kinematic features are below (or at the level) of the
systematics in the data (e.g. template mismatch) and might be influenced by the
uncertainties in the models (e.g. regularisation or variations in the sampling of
observables with orbits). This suggest a degeneracy of models with respect to the
recovery of inclination. More general tests on other galaxies and theoretical work
is needed for a better understanding of this issue.
3. Three-integral models constrained by integral-field kinematics out to an effective
radius are able to recover the true input DF, to the level of the discreteness effects
in the models.
Acknowledgments
We thank Glenn van de Ven for fruitful discussions about the recovery of the DF. DK
was supported by NOVA, the Netherlands Research school for Astronomy. MC acknowledges support from a VENI grant award by the Netherlands Organization of
Scientific Research (NWO).
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Nederlandse samenvatting
Het begrijpen van de wereld
D
E drang om de wereld te begrijpen en te beschrijven is karakteristiek voor mensen.
Een gedenkwaardig voorbeeld van deze drang is op de omslag van dit proefschrift te zien. Dit keramisch vat, met een geordende volgorde van verschillende
symbolen, is ongeveer 4500 jaar oud. Het is door een handwerksman van de Vučedol
cultuur gemaakt en is opgegraven in 1978 in de stad Vinkovci in Oost- Kroatië. De
klassieke Vučedol cultuur is in de tijd van het Europese Neolithicum ontwikkeld door
het nieuw opkomende Indo-Europese volk. Deze wijd verspreide cultuur is genoemd
naar zijn archeologisch centrale lokatie gelegen aan de rivier de Donau. De betekenis van de symbolen op het vat was tot voor kort een mysterie, totdat de archeoloog
Aleksander Durman een verband ontdekte. De symbolen vertonen de dominerende
sterrenbeelden aan de Europese hemel van vijfduizend jaar geleden. Dit halfgebroken vat is waarschijnlijk de oudste Europese kalender, gebruikt door de mensen van
Vučedol voor de organisatie van hun alledaagse leven.
Vijfduizend jaar geleden keken veeboeren van de Panonische vlakte naar de nachtelijke hemel. Ze ontdekten regelmatigheden en ontwikkelden een ingewikkeld systeem voor het meten van tijd. Op deze manier konden ze een belangrijk aspect van
de wereld beschrijven, met het gebruik van primitieve maar direkte sterrenkundige
waarnemingen. Vandaag is de sterrenkunde een wetenschap, die de weg heeft afgelegd
van het voorspellen van de toekomst door de eerste astrologen tot het verklaren van de feiten
door astronomen, geholpen door het waarnemen met moderne telescopen en instrumenten en het gebruik van natuurkundige wetten. In het hart van de sterrenkunde als
wetenschap ligt dezelfde wens die de Vučedol mensen leidde: beschrijven, begrijpen
en temmen van de wereld rondom ons.
Onze methoden zijn verder ontwikkeld, maar ook de astronomische thema’s zijn
veranderd. De sterrenkunde had een kenmerkende invloed op de mensen van de
Vučedol cultuur, en schonk hen de kalender. Het was een bron van belangrijke informatie voor het leven. In tegenstelling tot sommige andere wetenschappen heeft de
sterrenkunde tegenwoordig geen direkte invloed op ons alledaagse leven meer. Het
moderne sterrenkundig onderzoek is gericht op de processen die het Heelal vorm
geven: van de Zon, haar buren, de Melkweg en andere sterrenstelsels, tot de verre
quasars en de overblijfselen van de Oerknal. In bredere zin is de sterrenkunde vandaag een geı̈dealiseerde zoektocht naar de kennis van het Heelal. In aanvulling hierop
legt de sterrenkunde de menselijke perceptie van de wereld vast. De vooruitgang in
de sterrenkunde reflecteert zich in de veranderingen in de filosofie en cultuur.
In de jaren zestig van de vorige eeuw veranderde de grootte van het Heelal bijna
ieder dag met de ontdekkingen van verre quasars. Het is nu alleen nog een kwestie van
135
136
Nederlandse samenvatting
Figuur 1 — Het Hubble diagram. Het diagram is een classificatie van sterrenstelsels op basis van hun
vorm. Aan de linker kant liggen de elliptische stelsels, die verschillende afplattingen (ellipsvormen)
hebben: van de ronde E0 tot de platste E7. Daarna volgen lensvormige stelsels, die de overgang naar
schijfvormige sterrenstelsels kenmerken. Schijfvormige stelsels hebben indrukwekkende spiraalarmen
(rechtsboven), maar er zijn ook schijven met een balk tusen de spiralen (linksonder). Aan het einde van
het diagram ligt een groep van alle andere sterrenstelsels, zonder een bepaalde vorm.
tijd tot de eerste planeet vergelijkbaar met de Aarde ontdekt zal worden1 . De volgende
stap is de zoektocht naar leven op zo’n planeet. De sterrenkunde is ons venster naar de
complexiteit van het Heelal. Dit proefschrift richt zich op een speciaal thema binnen
de sterrenkunde: de vorming en evolutie van sterrenstelsels.
De “vroeg-type” sterrenstelsels
Sterrenstelsels zijn het elegantste beschreven door Immanuel Kant in de 18de eeuw
als “eilanden universa”. Noch hij noch iemand anders wist destijds wat deze “eilanden universa” waren: ze lijken op nevels aan de hemel, maar waarvan ze gemaakt
zijn en hoe ver ze van de Aarde af staan was onbekend totdat de sterrenkundigen
van de 20ste eeuw nieuwe ontdekkingen deden. De waarnemingen met de 100 inch
telescoop op Mount Wilson toonden aan wat de nevels werkelijk waren. Ze zijn opgebouwd uit sterren en bevinden zich op grote afstand van ons eigen “eiland universum”, de Melkweg. Er zijn veel verschillende soorten sterrenstelsels en ze worden
meestal geclassificeerd in vier groepen op basis van hun schijnbare vorm (Figuur 1).
De classificatie werd geı̈ntroduceerd door Edwin Hubble in het jaar 1936 en is vandaag bekend als het Hubble diagram (Hubble reeks of Hubble’s stemvorkdiagram zijn
ook vaak gebruikte uitdrukkingen). Het diagram begint met elliptische sterrenstelsels,
die er eenvoudig uit zien. Aan de andere kant liggen de schijfvormige sterrenstelsels,
met hun indrukwekkende spiraalstrukturen. Ze worden daarom vaak spiraalstelsels
1
Meer dan honderd planeten vergelijkbaar met Jupiter zijn al gevonden rond andere sterren.
137
Figuur 2 — Een tijdserie van de simulatie
van een botsing van twee gelijke schijfstelsels.
De tijd (in miljarden jaren) is rechtsonder van
de beelden geprint. Toen de stelsels voor de
eerste keer dicht bij elkaar kwamen, zorgde
de zwaartekracht voor de opvallend open
spiralen. Na de ontmoeting zijn de sterren
en het gas van de schijven uitgeworpen in
de vorm van getijdestaarten. Aan het einde
van de botsing zijn de schijven vernietigd en
het stelsel vormt een bolvormige verdeling
van gas en sterren die er bijna als een elliptisch sterrenstelsel uitziet. Met dank aan V.
Springel, MPA.
0.80
0.90
1.00
1.10
1.20
1.30
1.50
1.70
1.90
2.05
2.20
2.40
genoemd. De lensvormige stelsels (aangeduid met S0) liggen tussen de elliptische en
spiraalstelsels in. Ze hebben een prominente schijf, zonder de kenmerkende spiraal
struktuur, verzonken in een bolvormige verdeling van sterren. De vierde groep van
sterrenstelsels bestaat uit de stelsels zonder bepaalde vorm: de onregelmatige stelsels.
Hubble interpreteerde het diagram in termen van evolutie: de spiraalstelsels, met
hun gecompliceerde en duidelijk zichtbare struktuur, waren de logische kandidaten
voor ingewikkelde en ontwikkelde systemen, terwijl de elliptische stelsels voorbeelden
waren van eenvoudige systemen. De lensvormige stelsels waren een tussenvorm van
deze twee soorten sterrenstelsels. Alhoewel deze verklaring niet meer aannemelijk is
en de evolutie van sterrenstelsels waarschijnlijk in de andere richting van het Hubble
diagram “verloopt”, worden de elliptische en lensvormige stelsels nog steeds “vroegtype” stelsels genoemd en zijn de spiraalstelsels bekend als “laat-type” stelsels.
Sterrenstelsels zijn niet alleen uit sterren opgebouwd. Ze bevatten ook gas en stof
in verschillende hoeveelheden, afhankelijk van het Hubble type: de vroeg-type stelsels
hebben minder gas en stof dan de laat-type stelsels. In de zeventiger jaren van de
twintigste eeuw werd een nieuw bestanddeel van spiraalstelsels ondekt: deze sterrenstelsels zijn omringd door donkere materie. Men neemt aan dat alle sterrenstelsels
omgeven zijn door halo’s van donkere materie, maar de waarnemingen voor het bewijs
van donkere materie rondom elliptische stelsels geven nog geen uitsluitsel. De samenstelling van donkere materie is nog steeds niet bekend, maar de waarnemingen wijzen
erop dat het de dominante vorm van materie in het Heelal is. Een theorie van de vorming en evolutie van sterrenstelsels moet alle waargenomen feiten kunnen verklaren.
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Nederlandse samenvatting
Helaas is de leeftijd van een sterrenkundige veel korter dan de evolutietijd van sterrenstelsels. De sterrenkundigen werken dus als detectieven op zoek naar aanwijzingen
van de processen die een rol spelen in de vorming en evolutie van sterrenstelsels. De
vroeg-type stelsels zijn belangrijk, want ze bevatten maar kleine hoeveelheden van gas
en stof en vormen geen nieuwe sterren: ze hebben de blauwdrukken van hun vorming
bewaard.
Een korte gids over de vorming en evolutie van sterrenstelsels
Sterrenstelsels zijn ontstaan uit schommelingen in de dichtheid van de donkere materie in het vroege Heelal. Gebieden met een grotere dichtheid verzamelen door hun
zwaartekracht stof en vormen kleine objecten. Door botsingen van de kleine objecten
vormen zich grotere strukturen. De donkere materie domineert deze systemen, die
vaak schijven van gas in hun middelpunt hebben. Onder bepaalde voorwaarden vormt
het gas sterren, die het Heelal verlichten en de nieuwe sterrenstelsels zichtbaar maken.
Het botsen van de kleine sterrenstelsels gaat door en als twee schijfstelsels dicht genoeg bij elkaar komen, kunnen ze versmelten en een elliptisch stelsel vormen. Figuur 2
toont een simulatie van een botsing van twee schijfstelsels. Het eindresultaat, na 2.5
miljard jaar, is een elliptische verdeling van gas en sterren. De elliptische stelsels zijn
niet het eind van de evolutie. Een elliptisch stelsel kan weer een schijfstelsel worden als
zij genoeg intergalactisch gas invangt, dat opnieuw een schijf van sterren kan maken.
Dit spel tussen botsing en invangen wisselt vaak, maar dat zijn niet alle mogelijke
processen die de evolutie van sterrenstelsels beı̈nvloeden. In sterrenstelsels vinden
ook langzamere processen plaats (“secular processes”). Deze processen zijn het resultaat van een specifieke toestand in de sterrenstelsels, zoals hun vorm, vorm van hun
zwaartekracht potentiaal (de vorm van de donkere materie halo), de hoeveelheid gas
en de wisselwerking met aangrenzende (en kleinere) stelsels. De vorming van spiraalstrukturen, balken, ringen van gas en jonge sterren zijn typische gevolgen van deze
langzame evolutie.
Het waarnemen van vroeg-type sterrenstelsels
Sterrenkunde is een observationele wetenschap die verschilt van andere wetenschappen, omdat de astronomische objecten niet aangepast kunnen worden voor experimenten en het niet mogelijk is ze van alle kanten te bekijken.
Gelukkig zijn er ontelbaar veel sterrenstelsels in het Heelal en met waarnemingen
van ver weg gelegen stelsels kijken we naar het verleden, naar een jonger Heelal. Dit
betekent dat met onderzoek van een groter aantal sterrenstelsels het mogelijk is om
hun vorming en evolutie te verklaren. Om dat te doen is het belangrijk veel gegevens
te verzamelen van verschillende bronnen. Voor een onderzoek naar de struktuur en
dynamica van elliptische sterrenstelsels bijvoorbeeld, zijn gegevens over de verdeling,
kinematica en soorten van sterren nodig, evenals de verdeling van gas en stof. Daarom
is dit proefschrift gebaseerd op veel verschillende waarnemingen, vanaf de grond en
vanuit de ruimte, van radio tot optische golflengten.
De verdeling van sterren kan bepaald worden door het afbeelden van sterrenstelsels.
Eind 19de eeuw veroorzaakte het fototoestel een revolutie binnen de sterrenkunde.
139
Figuur 3 — Links: Hubble Space Telescope (HST) in zijn baan. De instrumenten van HST werden in
dit proefschrift gebruikt (hoofdstuken 2 en 3). Rechts: SAURON, de twee-dimensionale spektrograaf,
gemonteerd onder het focus van de 4.2m William Herschel Telescope op La Palma. De waarnemingen
met SAURON werden in hoofdstuk 4 en 5 van dit proefschrift gebruikt. Met dank aan NASA en het
SAURON team.
Ook de verschijning van digitale detectors, zoals CCD’s in de jaren zeventig van de
20ste eeuw, heeft een enorme vooruitgang van onderzoek naar de objecten in het Heelal mogelijk gemaakt. Maar de grootste stap in het onderzoek naar sterrenstelsels was
de lancering van de Hubble Space Telescope (HST) in een baan rondom de Aarde.
Figuur 3 toont de HST in de ruimte. Het licht dat is verzameld met de spiegel van de
HST gaat niet door de atmosfeer, die de baan van het licht verstoort en de informatie
van de hemellichamen filtreert.
Waarnemingen met de HST hebben ons beeld van de “eenvoudige “ elliptische
stelsels drastisch veranderd: ze hebben gecompliceerde strukturen met ontkoppelde
kernen en schijfjes van stof en sterren in hun centra.
De bewegingen en soorten sterren in een sterrenstelsel worden onderzocht met
waarnemingen van hun spectra. De sterren produceren het licht van een sterrenstelsel.
Maar alleen in de dichtstbijzijnde (op minder dan 3 miljoen lichtjaar2 ) sterrenstelsels
is het mogelijk waarnemingen aan individuele sterren te doen. Dat betekent dat het
licht van sterrenstelsels het gezamenlijke licht van alle sterren langs de gezichtslijn
is. We kunnen daarom alleen de gemiddelde eigenschappen van grote aantallen sterren meten. Het is ook nodig om te weten waar in een stelsel het waargenomen spectrum vandaan komt. De moderne technologie heeft het fabriceren van speciale tweedimensionale spectrografen mogelijk gemaakt. Deze spectrografen nemen de spectra
waar en registreren ook de plaats aan de hemel waar het licht vandaan komt. Het eind
resultaat is een drie-dimensionale dataset met informatie over de ruimtelijke positie
en de golflengte (x, y, λ). SAURON (Figuur 3) is zo’n spectrograaf. Hij bevindt zich aan
de William Herschel Telescoop op het Canarische eiland La Palma en wordt gebruikt
voor onderzoek naar de struktuur en kinematica van vroeg-type sterrenstelsels en de
soorten van sterren waaruit ze bestaan.
2
Een lichtjaar is de afstand die het licht in een jaar aflegt, en komt overeen met tienduizend miljard
km. Sterrenkundigen gebruiken vaak de eenheid parsec: 1pc ∼ 3.3 lichtjaar.
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Nederlandse samenvatting
Gids door dit proefschrift
De theorie van de vorming en evolutie van sterrenstelsels is ingewikkeld en bestaat
uit veel stukken die begrepen moeten worden en in een samenhangend geheel moeten
worden gegoten. Ieder hoofdstuk van dit proefschrift legt zich toe op een onderdeel
van de theorie van de vorming en evolutie van sterrenstelsels. Het onderzoek beschreven in dit proefschrift concentreert zich op de activiteit, struktuur, kinematica en dynamica van nabije3 vroeg-type sterrenstelsels.
Actieve sterrenstelsels
De kernen van veel vroeg-type sterrenstelsels zenden straling uit die niet van sterren
afkomstig is. Deze kernen worden actieve kernen genoemd. De theorie van de activiteit
in deze kernen is op het zwarte gaten paradigma gebaseerd. Volgens dit paradigma
bevindt zich in de kernen van (bijna) alle sterrenstelsels een massief object: een zwart
gat, met zo veel massa dat niets, zelfs niet het licht, kan ontsnappen aan de invloed
van zijn zwaartekracht. In het verre Heelal liggen krachtige actieve kernen: quasars en
radio sterrenstelsels zijn voorbeelden hiervan. Daarentegen vertonen de kernen van
nabije sterrenstelsels geen, of in ieder geval niet veel, activiteit. Als we bedenken dat
de nabije “slapende” kernen nakomelingen zijn van “wakkere” verre sterrenstelsels,
dan moeten nabije sterrenstelsels ook in hun kernen zwarte gaten herbergen4 . Eén van
de mogelijke redenen van het ontbreken van activiteit in de nabije sterrenstelsels is dat
er geen materiaal (brandstof) is, die in de zwarte gaten (machine) valt en de activiteit
op gang brengt.
Activiteit in nabije sterrenstelsels wordt onderzocht in hoofdstuk twee van dit
proefschrift. Een groep sterrenstelsels met en zonder stof is waargenomen met de
Very Large Array radio interferometer en met de HST. Het resultaat van de waarnemingen is dat, hoewel de sterrenstelsels met stof vaker actief zijn, de sterrenstelsels
zonder stof ook actieve kernen hebben. Dat betekent dat de aanwezigheid van stof,
dat waarneembaar is met de HST, niet nodig is voor het bestaan van actieve kernen in
nabije sterrenstelsels.
Nucleaire stellaire schijfjes
De waarnemingen met de HST tonen het bestaan van stellaire schijfjes in de centrale
delen van nabije vroeg-type sterrenstelsels aan. Deze schijfjes zijn extra dun (30 pc
vergeleken met de 300 pc van de dunne schijf in onze eigen Melkweg) en soms op
3
Nabij is een heel relatieve term in de sterrenkunde. De Andromedanevel, een sterrenstelsel lijkend
op onze Melkweg, ligt op een afstand van circa 3 miljoen lichtjaar. De sterrenstelsels in dit proefschrift,
die “nabij” worden genoemd, bevinden zich op een afstand van 20 tot 100 miljoen lichtjaar. De sterrenkundigen gebruiken deze term ook voor objecten die zich 10 keer verder weg bevinden. Hierachter
begint het verre Heelal.
4
Zwarte gaten zijn indirect ontdekt in zo’n 30 nabije sterrenstelsels op basis van hun invloed op de
beweging van het gas en de sterren in hun nabijheid. De massa van het zwarte gat blijkt gerelateerd aan
de grootte van het sterrenstelsel, en tot nu ontdekte massa’s zijn tussen de miljoen en een paar miljard
zonsmassa’s. Er bestaan ook stellaire zwarte gaten van slechts enkele zonsmassa’s, die uit exploderende
sterren zijn onstaan. Het is niet bekend hoe de zwaarste zwarte gaten in de kernen van sterrenstelsels
ontstonden.
141
een bepaalde manier verbonden met grotere schijven die ook kunnen voorkomen. Nucleaire sterschijfjes zijn heel interessante strukturen, die ons informatie over centrale
dichtheden, mogelijke zwarte gaten en over de evolutie van sterrenstelsels kunnen
opleveren.
Er zijn twee mogelijke scenario’s die beschrijven hoe de stersschijfjes onstaan zijn.
Eén is verbonden met de botsing van twee sterrenstelsels, waarvan één veel groter is
dan de andere. Dan valt het gas van het kleine stelsel in de put van de zwaartekracht
potentiaal, dus tot in de kern van het grotere stelsel, en onder gunstige condities wordt
een schijf gevormd. In de wisselwerking met het centrale zwarte gat stabiliseert het
schijfje zich en vormt het sterren. In het tweede scenario kunnen sterschijfjes het resultaat zijn van één van de langzame processen, bijvoorbeeld als gevolg van een instabiliteit van de veel grotere schijf, waar gas uit de buitendelen van het sterrenstelsel
naar binnen wordt getransporteerd. Het is ook mogelijk dat een combinatie van de
processen de nucleaire stellaire schijfjes vormt. In ieder geval, als de evolutie van de
schijfjes anders is dan in de rest van het sterrenstelsel, kunnen we verwachten dat er
verschillen zijn in de chemisch struktuur en leeftijd van de sterren.
Het derde hoofdstuk beschrijft waarnemingen van vier nabije sterrenstelsels met
bekende nucleaire stellaire schijfjes (NGC 4128, NGC 4570, NGC 4621 en NGC 5308).
De sterrenstelsels werden met twee instrumenten op de HST waargenomen. Het resultaat zijn spectra en afbeeldingen met de grootste resolutie tot nu toe (0.00 05 en 0.00 04555
respectievelijk). De waarnemingen hebben verschillende en enigszins onverwachte
strukturen in de kernen ontdekt, die niet noodzakelijk met de schijfjes zijn verbonden. De sterren in de onderzochte sterrenstelsels zijn oud, maar met een verschillende
chemische samenstelling. Het is waarschijnlijk dat sterschijfjes zich vormen als een
combinatie van zowel snelle als langzame processen. In beelden van sterrenstelsel
NGC 4128 is een tijdelijk verschijnsel ondekt. Dit is misschien de eerste supernova
beschreven voor NGC 4128, maar de werkelijke oorsprong blijft onbekend.
Twee-dimensionele kinematische kaarten
Als er zich geen objecten voor en achter het waargenomen sterrenstelsel bevinden,
is het mogelijk met spectroscopische waarnemingen de kinematische eigenschappen
vast te stellen. De snelheid van een ster is met spectraalanalyse vast te stellen, maar
de gemeten spectra van sterrenstelsels bestaan uit spectra van vele sterren langs de
gezichtslijn. Deze sterren hebben verschillende snelheden en het gevolg is dat de spectraallijnen veel breder zijn dan die van een enkele ster. Dat betekent dat het gezamelijke spectrum van de sterren langs de gezichtslijn de informatie over de verdeling van
snelheden bevat.
Twee-dimensionele kinematische kaarten zijn de resultaten van waarnemingen met
twee-dimensionale spectrografen. Deze kaarten laten zien hoe een kinematische parameter, zoals snelheid, verandert met de positie in het sterrenstelsel geprojecteerd
aan de hemel. De kaarten zijn indrukwekkend, maar het is ook nodig ze goed te
analyseren. In het vierde hoofdstuk van dit proefschrift wordt een methode voor
5
Een handbal balancerend op de torenspits van de kathedraal van Zagreb, gezien vanaf een terrasje
in Leiden, heeft een afmeting van ongeveer 0.00 04.
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Nederlandse samenvatting
de analyse van twee-dimensionele kinematische kaarten beschreven. De methode is
gebaseerd op de harmonische analyse van de kaarten langs concentrische ringen en lijkt op de methoden van oppervlakte helderheid fotometrie en op de analyse van de
snelheidskaarten van radio waarnemingen. Op grond hiervan is het kinemetry genoemd. De methode is voor modellen en echt gemeten kinematische kaarten (van
SAURON waarnemingen) beschreven, getest en gebruikt. Het verrassende eerste resultaat is dat de twee-dimensionale snelheidskaarten van elliptische sterrenstelsels heel
veel lijken op de snelheidskaarten van sterren die zich in schijven bewegen, hoewel de
sterren in elliptische sterrenstelsels zich niet in schijven bevinden.
Dynamische modellen
Het compleet begrijpen van de intrinsieke vormen en strukturen van sterrenstelsels is
alleen mogelijk door gedetaileerd dynamisch modelleren. Het maken van dergelijke
modellen is een theoretische onderneming, die op natuurkundige wetten is gebaseerd
en ideeën en veronderstellingen omvat over de te onderzoeken objecten (of processen).
Alle modellen die waarnemingen reproduceren kunnen beschouwd worden als fysisch. De theoretisch samenstellingen worden alleen begrensd door de menselijke fantasie, maar de wereld rondom ons is uniek. Om die te verklaren, moet de theorie
kloppen met de waarnemingen.
Het vijfde hoofdstuk van dit proefschrift presenteert de gedetaileerde dynamische
studie van sterren en gas in elliptische sterrenstelsel NGC 2974. De waarnemingen
bestaan uit metingen met grond- en ruimtetelescopen en met de SAURON spectrograaf.
Ze worden gebruikt voor het bouwen en het controleren van de theoretische modellen.
NGC 2974 is een ongewoon elliptisch sterrenstelsel, omdat ze grote hoeveelheden gas
bevat, dat geı̈oniseerd is door de straling van de sterren. De dynamische modellen van
het gasbestanddeel zijn gebaseerd op de veronderstelling dat het gas zich in een dunne
schijf bevindt, die onder een bepaalde hoek wordt waargenomen. Het gas beweegt in
hetzelfde zwaartekrachtsveld als de sterren en het resultaat kan vergeleken worden
met de resultaten van de modellen van de sterbewegingen.
De waargenomen verdeling van sterren in het sterrenstelsel NGC 2974 is consistent met een drie-dimensionale struktuur met axiale symmetrie. De modellen van het
sterrenstelsel moeten dan ook axisymmetrisch zijn. Een elegante methode voor het
bouwen van sterrenstelsels is de Schwarzschild methode van superpositie van sterbanen. In deze methode worden de sterrenstelsels opgebouwd als een verzameling van
sterbanen, die zich onafhankelijk gedragen, en niet als een verzameling van sterren
die bewegen door onderlinge zwaartkrachtsinvloeden. De banen beschrijven dan de
beweging van verzamelingen van sterren en in plaats van 1011 sterren is een sterrenstelsel opgebouwd uit 104 sterbanen. Gebruik makend van kinematische waarnemingen van NGC 2974 worden Schwarzschild modellen voor de bewegingen van sterren
gebouwd. De resultaten van deze dynamische modellen kloppen met de resultaten
van de gasmodellen, maar er is ontdekt dat de modellen niet precies de inclinatie van
het sterrenstelsel kunnen vaststellen.
Deze studie wordt ook voor het gedetaileerd testen van de Schwarzschild methode
gebruikt. De tests worden aan een theoretisch sterrenstelselmodel gedaan waarvan
alle eigenschappen bekend zijn. De methode is succesvol, omdat het mogelijk is alle
143
parameters van het model te reproduceren, ook de interne struktuur en de verdeling
van de sterbanen. Maar de testen hebben laten zien dat de inclinatie van sterrenstelsels
met de huidige waarnemingen niet met zekerheid kan worden vastgesteld.
Blik naar de toekomst
De fundamentele concepten van de vorming en evolutie van sterrenstelsels, alsook
hun kosmologische achtergrond, kunnen we als bekend beschouwen. Ze zijn in een
nieuw paradigma van de moderne sterrenkunde vastgelegd. Maar er zijn nog veel
onopgeloste raadsels, die ons uitdagen en op ons antwoord wachten.
Het onderzoek beschreven in dit proefschrift heeft een basis gelegd voor het toekomstige werk aan twee-dimensionale kinematische kaarten. De volgende stap is het toepassen van kinemetrie en dynamische modellen op een grotere verzameling van sterrenstelsels om hun struktuur en eigenschappen, die het gevolg zijn van evolutie processen, te analyseren.
In het algemeen is vooruitgang mogelijk in zowel de waarnemingen als in het
bouwen van theoretische modellen. De modellen van sterrenstelsels gebruiken nu
de informatie van de positie en kinematica, maar niet van de soort van sterren. De
sterrenstelsels zijn verzamelingen van sterren met verschillende leeftijden en chemische samenstellingen. Deze informatie moet ook in de modellen gebruikt worden om
precies de evolutie van de sterrenstelsels te bevatten. Aan de andere kant zullen de
modellen ook sterrenstelsels met triaxiale symmetrie gaan beschrijven. De leden van
het SAURON team zijn al begonnen aan deze ideeën te werken.
Gezien vanuit de observationele kant openen de opkomst van 8 - 10m telescopen
met technologie van adaptieve optiek, die de invloed van de atmosfeer corrigeert, en
ook een breed gebruik van twee-dimensionale spektrografen nieuwe waarneemmogelijkheden. Deze gaan nieuw licht werpen op de struktuur, kinematica en de soorten
van sterren in nabije sterrenstelsels, en ook inzicht in de eigenschappen van verre kosmologisch objecten waaruit sterrenstelsels zijn ontstaan.
Hrvatski sažetak
Razumijevanje svijeta
P
ORIV za spoznajom i opisom svijeta osnovna je karakteristika čovjeka. Znamenit
primjer tog poriva nalazi se na naslovnici ove disertacije. Keramički lonac, ukrašen
uskladenim nizom znakova, star je otrpilike 4500 godina. Izradio ga je zanatlija Vučedolske kulture, a iskopan je 1978. godine u Vinkovcima. Klasičnu Vučedolsku kulturu
razvili su tokom europskog neolitika novodošli Indo-europljani. Ova raširena kultura nazvana je po svom središnjem lokalitetu na rijeci Dunav u istočnoj Hrvatskoj.
Značenje znakova na loncu bilo je do nedavno nepoznato kada je arheolog Aleksandar Durman predložio da oni predstavljaju sazviježda koja su dominirala europskim
nebom prije pet tisućljeća. Polurazbijeni lonac iz Vučedola je vrlo vjerojatno najstariji
Europski kalendar, kojeg su ljudi iz Vučedola koristili za organizaciju svakodnevnog
života.
Prije pet tisuća godina, stočari Panonske nizine gledali su u noćno nebo. Primijetili
su pravilnosti i stvorili složen sustav mjerenja vremena. Na taj način mogli su opisati
bitnu značajku svijeta koristeći primitivna, ali direktna astronomska opažanja. Danas
je astronomija znanost, koja je prošla put od proricanja budućnosti prvih astrologa do
objašnjavanja činjenica suveremenih astronoma, opažanih modernim teleskopima i instrumentima koristeći zakone fizike. Ipak, u središtu astronomije kao znanosti čući ista
želja koja je vodila ljude iz Vučedola: razumijeti, opisati i ukrotiti svijet oko nas.
Naše metode su puno složenije, no i astronomske teme su se promijenile. Astronomija je imala značajan utjecaj na ljude Vučedolske kulture podarivši im kalendar. On je bio izvor informacija važnih za život. Za razliku od nekih drugih znanosti
u sadašnje vrijeme, astronomija ne utječe izravno na naš svakodnevni život. Moderna astronomska istraživanja su usmjerena na procese koji oblikuju Svemir, počevši
od Sunca, njegovih susjeda, Mliječne staze, i drugih galaksija, do udaljenih kvazara
i ostataka Velikog Praska. U širem smislu, astronomija danas je idealizirana potraga
za spoznajom Svemira. Sukadno s tim, astronomija bilježi ljudsko poimanje svijeta.
Napretci u astronomiji se odražuju u promjenama u filozofiji i kulturi. U 1960tima
veličina Svemira se mijenjala gotovao svakog dana otkrićima sve udaljenijih kvazara.
Sada se čini samo pitanje vremena kada će prva planeta nalik Zemlji biti otkrivena
van Sunčevog sustava1 . Slijedeći korak biti će potraga za životom na takvoj planeti. Astronomija ne mijenja izravno naše živote, ali ima dugotrajan utjecaj na ljudsko
društvo. Astromija je naš prozor u složenost Svemira. Ova disertacija usredotočena je
na posebnu temu astronomije: nastanak i evoluciju galaksija.
145
146
Hrvatski sažetak
Slika 1 — Hubblov niz galaksija. Hubblov niz je osnova klasifikacije galaksija. Galaksije su klasificirane
prema svom obliku. Na lijevoj strani nalaze se eliptične galaksije koje se medusobno razlikuju prema
svojoj prividnoj spljoštenosti (eliptičnosti). Gotovo okrugle galaksije su nazvane E0, a najspljoštenije
su E7. Nakon njih slijede lentikularne galaksije koje označavaju prijelaz od eliptičnih do disk galaksija.
Disk galaksije imaju znamenite spiralne krakove (gore), ali postoje i spiralne galaksije s tzv. prečkama
koje prolaze centrom i povezuju krakove spirala (dolje). Na samom kraju nalaze se nepravilne galaksije.
U tu skupinu spadaju sve galaksije bez odredenog oblika.
Galaksije ranog-tipa
Galaksije je vjerojatno najelegantnije opisao Immanuel Kant u 18. stoljeću kao “svemirske otoke”. Ni on niti itko drugi nije znao što su ustvari ti “svemirski otoci”. Izgledaju
poput maglica na nebu, ali od čega su izgradeni i koliko su udaljeni od Zemlje bilo
je nepoznato do početka 20. stoljeća. Opažanja s 100 inčnim teleskopom na Mount
Wilsonu pružila su prve naznake prave prirode galaksija. One su sastavljene od zvijezda i nalaze se daleko od našeg “svemirskog otoka”, Mliječne staze. Mnogo je različitih vrsta galaksija i obično su klasificirane prema svom prividnom obliku u četiri
istaknute skupine (Slika 1). Razredovanje galaksija uveo je Edwin Hubble 1936. godine, a danas je poznato kao Hubblov niz galaksija (Hubblov dijagram ili Hubblova
tonska vilica su takoder često upotrebljavani izrazi). Niz započinje sa eliptičnim galaksijama koje se čine vrlo jednolike i jednostavne. Na drugom kraju su disk galaksije,
sa svojim vrlo upadljivim spiralim kracima. One se obično nazivalju spiralnim galaksijama, da se naglasi njihova uočljiva struktura. Lentikularne galaksije (često kratko
zvane S0), koje nalikuju lećama, izgledaju kao prijelazni objekti izmedu eliptičnih i spiralnih galaksija. One imaju istaknuti disk, bez značajne spiralne strukture, uronjen u
skoro potpuno sferičnu raspodjelu zvijezda. U četvrtu skupinu galaksija pripadaju sve
ostale galaksije bez pravilnog oblika, koje su prikladno nazvane nepravilne galaksije.
Izradujući niz Hubble je razmišljao o evoluciji galaksija. Spiralne galaksije, sa svojom
zamršenom i lako uočljivom strukturom, bile su prirodni kandidati za složene i razvi1
Poznato je više od stotinu planeta sličnih Jupiteru u orbitama oko drugih zvijezda.
147
Slika 2 — Vremenski niz simulacije sudara dviju
jednakih disk galaksija. Vrijeme (u milijardama
godina) je označeno u doljnjem desnom kutu
svake slike. Kada se galaksije približe po prvi
put gravitacijske sile stvaraju izražene otvorene
spirale. Nakon susreta, zvijezde i plin iz galaksija su izbačeni u obliku plimnih repova. Na
kraju sudara diskovi su uništeni i pretvoreni
u sferičnu nakupinu zvijezda i plina, pomalo
nalik na eliptičnu galaksiju. S dopuštenjem V.
Springela, MPA.
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jene sustave, dok su eliptične galaksije bile primjer jednostavnih sustava. Lentikularne
galaksije su pak bile stepenica izmedu tih dviju vrsta galaksija. Iako ovo objašenjenje
nije više prihvatljivo i evolucija galaksija ustvari “ide” u suprotnom smjeru na Hubblovm dijagramu, eliptične i lentikularne galaksije se još uvijek zovu galaksije ranogtipa, a spiralne su galaksije sukladno poznate kao galaksije starog-tipa.
Galaksije se ne sastoje samo od zvijezda. One takoder sadrže plin i prašinu u
različitim količinama, ovisno o Hubblovim tipu: galaksije ranog-tipa sadrže manje
količine u odnosu na galaksije starog-tipa. U 1970tima otkrivena je nova sastavna komponenta spiralnih galaksija: ove galaksije su okružene tamnom materijom. Vjeruje
se da su sve galaksije uronjene u haloe tamne tvari, ali opažački dokazi za tamnu
tvar oko eliptičnih galaksije nisu potpuni. Neovisno o tome, priroda tamne tvari još
uvijek nije poznata, iako opažnja jasno upućuju da je većina materije u Svemiru upravo ta tamna tvar. Teorija nastanka i evolucije galaksija mora moći objasniti sve ove
opažalačke činjenice. Nažalost, životni vijek astronoma je puno kraći od vremena
potrebnog za evoluciju galaksija. Astronomi stoga djeluju poput detektiva tražeći
dokaze procesa koji su sudjelovali u nastajanju i daljnjem razvoju galaksija. Galaksije ranog-tipa posebno su tome pogodne jer sadrže male količine plina i prašine i, ne
stvarajući nove zvijezde, sačuvale su nacrte svog nastanka.
Kratki vodič kroz nastanak i evoluciju galaksija
Galaksije potječu od fluktuacija u gustoći tamne tvari u ranom Svemiru. Područja veće
gustoće, gravitacijski djelujući na okolinu, sakupljaju materiju starajući tako malene
kozmičke objekte. Manji objekti se medusobno sudaraju i spajaju stvarajući sve veće
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Hrvatski sažetak
objekte. Oni su definirani gravitacijskim utjecajem tamne tvari, a u središtu se često
nalazi plin u obliku diska. Pod odredenim uvjetima, iz plina nastaju zvijezde koje
obasjavaju prostor i otkrivaju novo nastale disk galaksije.
Sudaranje galaksija se i dalje odvija i ukoliko se dvije disk galaksije dovoljno približe spojit će se, a kao produkt nastat će eliptična galaksija. Slika 2 prikazuje simulaciju sudara dvije disk galaksije. Konačni rezultat, nakon nekoliko milijardi godina,
je sferična raspodjela zvijezda. Medtim, eliptične galaksije nisu kraj evolucijskog puta
galaksija. Eliptična galaksija može ponovo postati diks galaksija ukoliko uhvati plin
iz medugalaktičkog prostora, koji će iznova stvoriti disk zvijezda. Ova igra sudara
i hvatanja dešava se naizmjenice, ali ne opisuje sve procese koji utječu na evoluciju
galaksija. Uz gore navedene brze, u galaksijama, djeluju i polaganiji procesi, koje
se stoga i naziva sporim procesima. Ti procesi uglavnom su rezultat specifičnosti
galaksija u kojem se zbivaju, poput njihovog oblika, oblika gravitacijskog potencijala
(odnosno oblika haloa tamne tvari), količine plina ili interakcije sa susjednim manjim galaksijma. Nastanak spiralnih struktura, zvijezdanih prečki, prestenova plina i
mladih zvijezda tipične su posljedice spore unutarnje evolucije galaksija. Slika 1 Uvoda
u ovu disertaciju shematski prikazuju osnovne procese koji djeluju u galaksijama.
Opažanje galaksija ranog-tipa
Astronomija je opažalačka znanost koja se od ostalih znanosti razlikuje po tome što ne
možemo proizvoljno prilagodavati galaksije (ili ostale objekte) našim eksperimentima,
kao niti promijeniti naš položaj u odnosu na njih. Na sreću, galaksija u Svemiru ima
gotovo neizmjerno mnogo, a i opažanjem udaljenih objekata, promatra se u prošlost,
u mladi Svemir, tako da je proučavanjem većeg broja galaksija moguće dokučiti njihov
nastanak i evolucijski razvoj. Ipak, da bi dobili što potpuniji uvid u trodimenzionalnu strukturu i dinamiku galaksija, nužno je sakupiti podatke iz što raznovrsnijeg i
većeg broja izvora. Za proučavanje strukture i dinamike eliptičnih galaksija, na primjer, potrebni su podaci o raspodjeli, kinematici i vrsti zvijezda, te o količini i raspodjeli
plina i prašine. U ovoj je disertaciji, iz tog razloga, predstavljen širok opseg opa žanja:
s površine Zemlje i iz Svemira, od radio do optičkih valnih duljina.
Raspodjela zvijezda utvrduje se slikanjem galaksija. Krajem 19. stoljeća fotografski aparat je revolucionirao astronomiju, a pojava digitalnih detektora, tzv, CCDa,
sedamdesetih godina dvadesetog stoljeća, omogućila je gotovo neslućeni napredak u
proučavanju detalja svemirskih objekata. Ipak, pravi korak naprijed u istraživanju detalja galaksija bilo je lansiranje Hubblovog svemirskog teleskopa (HST) u orbitu 1990.
godine. Slika 3 prikazuje HST u orbiti. Svjetlost koju sakuplja zrcalo na HSTu ne prolazi kroz atmosferu, koja djeluje poput filtera odstranjujći i zagladujući informacije
koje donose fotoni iz udaljenih svemirskih objekata. Zaista, opažanja HSTom promijenila su naše poimanje “jednostavnih” eliptičnih galaksija, koje su pokazale komplicirane strukture odvojenih komponenti i malenih diskova prašine i zvijezda u svojim
središtima.
Kinematiku i vrstu zvijezda u galaksiji moguće je istraživati snimanjem njihovih
spektara. Svijetlost galaksije, koju teleskopi skupljaju i koja, prolazeći kroz prizmu,
biva razložena po valnim duljinama, stvaraju zvijezde. Medutim, osim u najbližim
149
Slika 3 — Lijeva slika - Hubblov svemirski teleskop (HST) u orbiti. Instrumenti s HSTa korišteni su
u studijama predstavljenim u drugom i trećem poglavlju. Desna slika - SAURON, dvodimenzionalni
spektrograf, namješten na fokus 4.2m William Herschel teleskopa na La Palmi. Opa žanja SAURONom
korištena su u četvrtom i petom poglavlju ove disertacije. Otisnuto sa dopuštenjem NASAe i SAURON
tima.
galaksijama (udaljenih do otprilike 3 milijuna svjetlosnih godina2 ), nije moguće opažati
spektre pojedinih zvijezda, već snimljeni spektri nose integriranu informaciju o mnoštvu zvijezda koje se nalaze na našoj liniji gledanja. Tako proučavajući spektre galaksija mi ustvari istražujemo prosječne karakteristike mnoštva zvijezda. Ipak, potrebno
je znati i od kuda iz galaksije, koja se vidi kao dvodimenzionalna projekcija na nebu,
dolazi snimljeni spektar. Suvremena je tehnologija omogućila izradu posebnih dvodimenzionalnih spektrografa, koji dijele svjetlost po valjnim duljinama, istovremeno bilježeći informaciju odakle je svjetlost došla s neba. Na taj način, krajnji rezultat je trodimenzionalni skup podataka s informacijom o položaju na nebu i valnoj duljini (x, y, λ).
SAURON, prikazan desno na Slici 3, je upravo takav instrument. Nalazi se na William
Herschel teleskopu na kanarskom otoku La Palmi i izgraden je za proučavanje strukture i kinematike galaksija ranog tipa, kao i vrsta zvijezda koje se nalaze u njima.
Vodič kroz disertaciju
Teorija nastanka i evolucije galaksija je složena i sastoji se od mnogo dijelova koje treba
dobro razumijeti i uklopiti u sukladnu sliku. Svako poglavlje ove disertacije posvećeno
je jednoj strani teorije o nastanku i evoluciji galaksija. Istraživanja predstavljena u disertaciji usredotočena su na aktivnost, strukturu, kinematiku i dinamiku bliskih3 galaksija ranog-tipa.
Aktivne galaksije
Središnji dijelovi mnogih galaksija ranog-tipa odašilju zračenje koje nije zvjezdanog
porijekla. Takva središta galaksija se nazivaju aktivnim galaktičnim jezgrama - AGJ. Trenutno shvaćanje aktivnosti u jezgrama galaksija se bazira na paradigmi da se u središtu
2
Jedna svjetlosna godina je udaljenost koju svjetlost prode u godinu dana i iznosi otprilike deset tisuća
milijardi kilometara. Astronomi često koriste i jedinicu parsek, gdje je 1pc ∼ 3.3 svjetlosne godine.
3
Blisko je vrlo relativan termin u astronomiji. Andromeda, galaksija slična našoj, nalazi se na optprilike 3 milijuna svjetlosnih godina. Galaksije u ovoj disertaciji, koje se smatra blikim, nalaze se na
udaljenostima od oko 20 do 100 milijuna svjetlosnih godina, a astronomi će koristiti ovaj termin i na
objekte koji su do 10 puta udaljeniji. Nakon toga počinje udaljeni Svemir.
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Hrvatski sažetak
svake aktivne galaksije nalazi masivni objekt, nazvan crna rupa, koji ima toliku masu
da ništa, čak ni svjetlost, ne može uteći njegovom gravitacijskom djelovanju. Materija privučena gravitacijom crne rupe, pada na nju i tokom tog procesa snažno zrači u
okolni prostor. U dalekom Svemiru postoje snažni AGJ-ovi; kvazari i radio galaksije
su dva primjera. Medutim, jezgre bliskih galaksija, iako pokazuju odredenu aktivnost,
puno su slabije. Uoliko se uzme u obzir da su “tihe” bliske galaksije svojevrsni potomci “bučnih” dalekih galaksija, sve one moraju imati crne rupe u svojim jezgrama 4 .
Jedan od mogućih razloga neaktivnosti u bliskim galaksijama je nepostojanje materijala (goriva), koji pada na crne rupe (strojeve) i prouzrokuje aktivnost u jezgrama.
Aktivnost u bliskim galaksijama je proučavana u drugom poglavlju disertacije.
Skup galaksija, opažan s Very Large Array radio interferometrom i sa HSTom, je bio
podijeljen na dva dijela: galaksije sa i bez prašine. Opažanja su pokazala da iako galaksije s prašinom češće pokazuju aktivnost u svojim jezgrama, galaksije bez prašine isto
posjeduju aktivne jezgre. To znači da postojanje prašine vidljive sa HSTom nije nu žan
uvjet za postojanje AGJ u bliskim galaksijama.
Nuklearni zvjezdani diskovi
Opažanja Hubblovim svemirskim teleskopom otkrila su postojanje malenih (< 1 00 ) zvjezdanih diskova u jezgrama bliskih galaksija ranog tipa. Ovi diskovi su vrlo tanki (30
pc u usporedbi s 300 pc tankog diska u našoj galaksiji), i često na neki način povezani s
velikim diskovima koji postoje u nekim galaksijama. Zvjezdani diskovi su vrlo zanimljive strukture, koje se mogu iskoristiti za proučavanje centralnog gravitacijskog
potencijala galaksija (npr. mjerenje centralnih gustoća i masa crnih rupa), ali i za istraživanje evolucije galaksija.
Dva su vjerojatna scenarija nastajanja nukelarnih zvjezdanih diskova. Jedan je
vezan uz scenarijo interakcije galaksija, kada se veća galaksija spaja s manjom. Tada
uhvaćeni plin tone do dna gravitacionog potencijala, do jezgre galaksije, i pri povoljnim uvijetima stvara disk. U interakciji sa crnom rupm u središtu, disk se dinamički stabilizira i stvara zvijezde. Po drugom scenariju, mali zvjezdani disk mo že
nastati i pod utjecajem nekog od sporih procesa, na primjer, kao posljedica transporta
materijala iz vanjskog dijela galaksije prema centru uzrokovanog nestabilnošću velikog galaktičkg diska. Moguće je da i kombinacije procesa djeluju u nastajanju nuklearnih zvjezdanih diskova. U svakom slučaju, ukoliko su diskovi imali drugačiji
evolucijski put od ostatka galaksije, za očekivati je da će se to odraziti na razlikama
u kemijskoj strukturi i starosti zvijezda.
U trećem poglavlju disertacije prikazana su opažanja četiri bliske galaksije s poznatim nuklearnim diskovima (NGC 4128, NGC 4570, NGC 4621 i NGC 5308). Galaksije
su opažane s dva instrumenta na HSTu, rezultirajući sa spektrima i slikama trenutno
4
Crne rupe su indirektno otkrivene u središtu 30tak bliskih galaksija na osnovu njihovog gravitacijskog utjecaja na kretanje plina i zvijezda u neposrednoj blizini. Njihove mase su, izgleda, povezane sa
veličinom galaksije u kojoj se nalaze, a dosada otkrivene se kreću u rasponu od milijun do nekoliko milijardi sunčevih masa. U Svemiru postoje i manje, zvjezdane, crne rupe sa masom nekoliko puta većom
od mase Sunca, za koje se vjeruje da nastaju u eksplozijama zvijezda. Porijeklo velikih crnih rupa u
središtima galaksija nije poznato.
151
najviše moguće razolucije (0.00 05, odnosno 0.00 0455)5 . Opažanja su otkrila raznovrsne i
pomalo neočekivane strukture u jezgrama, ne nužno povezane sa zvjezdanim diskovima. Zvijezde u proučavanim galaksijama su uglavnom stare, ali imaju različit kemijski
sastav. Vjerojatno je da zvjezdani diskovi nastaju kombinacijom različitih brzih i sporih
procesa. Na slikama galaksije NGC 4128 otkriven je i tranzijent, koji bi mogao biti prva
zabilježena supernova u NGC 4128 galaskiji, ali čije stvarno porijeklo ostaje nepoznanica.
Dvodimenzionalne kinematičke mape
Ukoliko nema svemirskih objekata ispred i iza opažane galaksije, spektroskopskim
opažanjima moguće je odrediti njezina kinematička svojstva. Brzinu gibanja jedne zvijezde moguće je odrediti analizom njezinog spektra, ali opažani spektri galaksije se
sastoje od spektara mnogih zvijezda koje se nalaze na liniji gledanja. Te zvijezde imaju
različite brzine, i posljedica toga je da su spektralne linije puno šire nego u spektru
jedne zvijezde. Iz tog razloga, zajednički spektar donosi informaciju o raspodjeli brzina zvijezda u galaksiji duž linije gledanja.
Dvodimenzionalne kinematičke mape produkti su opažanja sa dvodimanzionalnim spektrografima. One prikazuju kako se kinematički parametar, poput brzine, mijenja ovisno o položaju u galaksiji projeciranoj na nebo. Mape su vizualno vrlo zahvalne, medutim potrebno ih je i pažljivo proučiti. U četvrtom poglavlju ove disertacije opisana je metoda kojom se mape mogu opisati i u detalje proučavati. Metoda
se bazira na harmoničkoj analizi mapa, i slična je metodama korištenim u istraživanju
površinskog sjaja galaksija (fotometrija) i analizi mapa brzina od radio opažanja. Iz tog
razlog nazvana je kinemetrija. Metoda je prezentirana, testirana i upotrebljena na modelima kinematičkih mapa, kao i mapama opažanja sa SAURONom. Iznenadujući preliminarni rezultat je da su dvodimnzionalne mape brzina opažanih eliptičnih galaksija
vrlo slične mapama brzina zvijezda koje se gibaju po kružnim putanjama u diskovima,
iako se zvijezde u eliptičnim galaksijama uglavnom ne nalaze u diskovima.
Dinamički modeli
Potpuno razumijevanje intrinsičnih oblika i struktura galaksija moguće je samo detaljnim dinamičkim modeliranjem. Stvaranje takvih modela je teoretski pothvat koje
se osniva na zakonima fizike, a uključuje ideje i pretpostavke o istraživanim objektima (ili procesima). Ipak, samo modeli koji mogu reproducirati opažanja se smatraju
fizikalnim. Teoretske konstrukcije su ograničene tek maštom ljudi, ali svijet oko nas je
jedinstven. Da bi ga objasnila, teorija se mora slagati s opažanjima.
Peto poglavlje ove disertacije sadrži detaljnu dinamičku studiju zvjezdane i plinovite komponente eliptične galaksije NGC 2974. Opažanja se sastoje od opažanja sa zemaljskim i svemirskim teleskopima i dvodimenzionalnim spektrografom SAURONom,
te su korištena u konstrukciji i provjeri teoretskih modela. NGC 2974 je neobična
eliptična galaksija jer sadrži veliku količinu plina, koji je ioniziran zračenjem zvijezda.
Dinamički modeli plinovite komponente galaksije su bazirani na pretpostavci da se
5
Rukometna lopta na vrhu zagrebačke katedrale, gledana iz barke u Leidenu, bila bi velika otprilike
(lučne sekunde).
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Hrvatski sažetak
plin giba u tankom disku koji je nagnut pod odredenim kutem prema našem pravcu
gledanja. S obzirom da se plin giba u istom gravitacijskom polju kao i zvijezde, rezultati se mogu usporediti s rezultatima modeliranja zvijezdane komponente.
Opažanja zvijezda u galaksiji NGC 2974 upućuju da njihova raspodjela čini trodimenzionalnu strukturu sa osnom simetrijom. Prema tome potrebno je napraviti modele galaksije koji imaju istu simetriju. Elegantna metoda konstrukcije galaksija je Schwarzschildova metoda superpozicije zvjezdanih orbita. Metoda se bazira na ideji da
su galaksije dinamički objekti koji se bolje mogu opisati kao nakupine neovisnih orbita nego kao nakupine zvijezda koje medudjeluju svojom gravitacijom. Pojedine orbite tada ne predstavljaju zvijezde, već skupine zvijezda i umjesto 10 11 neovisnih zvijezda moguće je konstruirati galaksiju sa 104 neovisnih orbita. Koristeći kinematička
opažanja galaksije NGC 2974 napravljeni su Schwarzschildovi modeli njezine zvjezdane komponente. Rezultati zvjezdanih modela se slažu sa rezultatima modela plina,
iako je otkriveno da korišteni modeli ne mogu precizno odrediti nagib galaksije.
Ova studija je iskorištena i za detaljno testiranje Schwarzschildove metode konstrukcije osno simetričnih galaksija. Testovi su obavljeni na teoretskoj galaksiji, dakle,
modelu kojem se znaju sve osobine. Metoda se pokazala uspješnom, jer je odredila sve
parametre korištenog modela galaksije, kao i njezinu unutarnju strukturu i raspodjelu
zvjezdanih orbita. Ipak, testovi su potvrdili da se nagib galaksije, koristeći raspoloživa
opažanja, ne može odrediti sa sigurnošću.
Pogled u budućnost
Osnovni koncepti nastanka i evolucije galaksija, kao i kozmološka pozadina procesa
koji djeluju, se smatraju poznatim i oblikovani su u paradigmu moderne astronomije.
Mnogo je, ipak, neriješenih pitanja koja nas izazivaju i očekaju naš odgovor.
Istraživanja predstavljena u ovoj disertacij postavila su temelje budućem radu sa
dvodimenzionalnim kinematičkim mapama galaksija ranog-tipa. Sljedeći korak je primijeniti kinemetriju i dinamičke modele na većem broju galaksija te analizirati njihovu
strukturu, kao i simetrije i svojstva koja se odražavaju na opažanim mapama i posljedica su procesa koji su oblikovali galaksije. Takoder, opažanja nuklearnih zvjezdanih
diskova iskoristiti će se za mjerenje masa crnih rupa u tim galaksijama.
Općenito, napretci su mogući u opažanjima, ali i u konstrukciji teoretskih modela.
Modeli galaksija za sada uzimaju u obzir poziciju i kinematiku, ali ne i vrste zvijezda.
Galaksije su sastavljene od zvijezda različite starosti i kemijskog sastava, i ta se informacija takoder treba uvrstiti u modele da bi oni mogli u potpunosti opisati galaksiju,
kao i njezinu prošlost. S druge strane modele treba generalizirati tako da mogu opisivati i galaksije koje imaju triaksialnu simetriju. Članovi SAURON tima započeli su već
rad na ovim idejama.
S opažalačke strane, pojava teleskopa s 8 - 10 metarskim zrcalima opremljenim
tehnologijom adaptivne optike, koja ispravlja utjecaj atmosfere, te široka upotreba
dvodimenzionalnih spektrografa otvaraju nove opažalačke mogućnosti. One će otvoriti
novi prozor u strukturu, kinematiku i vrste zvijezda bliskih galaksija, kao i uvid u svojstva udaljenih kozmoloških objekata od kojih galaksije nastaju.
Curriculum vitae
I
saw the first light on June 10, 1975 in Zagreb, Croatia, where I also spent the next
twenty five years. My parents encouraged me in all my interests, and astronomy
did not play a major role in my adolescent years. In the winter of 1996, I was fortunate enough to have the opportunity to go on a working visit to Višnjan Observatory.
The vastness of the night sky that my eyes then saw, enticed me to investigate the
processes that turn the darkness into light. On November 12, 1999 I graduated from
the Faculty of Mathematics and Natural Sciences of the University of Zagreb, with a
study of “Ultra-high energy cosmic rays and Greisen-Zatsepin-Kuzmin cutoff”, under
the supervision of Dr. Mladen Martinis.
After a period of work at the Institute Ruder Bošković, in the group of Dr. Martinis, I moved to Leiden to work on a PhD project “Nuclei of nearby early-type galaxies” under supervision of Dr. Walter Jaffe and Prof. Tim de Zeeuw. The goal of this
project was to study in detail the structure, kinematics and dynamics of nearby galaxies using observations from the Hubble Space Telescope and by the new integral-field
spectrograph, SAURON, at the William Herschel Telescope. During this project, I joined
numerous observing runs at the William Herschel Telescope on La Palma, the CanadaFrance-Hawaii Telescope on Mauna Kea, and the MDM telescope on Kitt Peak. I participated in a NOVA fall school in Dwingeloo (2000), in conferences on La Palma (2001)
and in Ringberg (2002), in the IAU Symposium in Sydney (2003) and the Lorentz Center meeting with the Nukers (2004). During the last four years I have taken part in
all meetings of the SAURON team, of which I become a full member in 2003. I enjoyed
organising the seasons of the observatory football team, as well as helping and participating in Science and Open day activities. I learned a great deal by assisting in the
course of Active Galactic Nuclei given by Prof. Tim de Zeeuw.
My investigations of light in the Universe will continue at Oxford University where
I will join the group of Prof. Roger Davies.
153
Nawoord / Acknowledgments
F
years ago I started on a journey, with two suitcases and a back-pack. How lonely I
felt on that September day! The journey is about to come to its end, and I feel everything
but alone. During the last four years I carried old friendships along, but I also met so many
interesting people on the way. The last four years were not only spent on the work presented
in this thesis, and you all made them pass too quickly.
I am greatly indebted to Michele Cappellari, who was always available and had ready
advice that helped in the making of this thesis. I am also grateful to Richard, Glenn, Ellen
and Jesus for numerous discussions and patiently letting me use their computers. My sincere
thanks go to the members of the SAURON team, who offered so much inspiration necessary for
finishing this thesis. I am proud to be a member of this team. I am very grateful to Anne-Marie
Weijmans for correcting and adding many a beauty mark to “my Dutch” in the Nederlandse
samenvatting. I am greatly indebted to the secretarial support of Marja Zaal, Kirsten Groen and
Jeanne Drost. The members of the Leiden computer group deserve all the praise, for readily answering all my questions and often working after-hours to make the system reliable. I am also
grateful to Prof. Pavlovski for telling me The Netherlands is the place to be, and to Dr. Martinis
for encouraging and helping me to go. I have enjoyed the hospitality of the Johns Hopkins
University in Baltimore, where a part of this thesis research was conducted. I thank het Leids
Kerkhoven Bosscha Fonds for financial support. I would also like to thank M.E.J. van den Bos
- van Sambeek and the workers at IPA/ECM for helping an “allochtoon” to feel at home.
Dragi moji roditelji, bez vaše dobrote, podrške i pouzdanja u mene, a ponajviše bez vas
samih, sigurno ne bih pisao ove redove i zato ovu knjigu posvećujem vama. Brate moj, ti i
tvoja obitelj ste bili uvijek spremni pomoći i razveseliti me. MariaRosa, you melted most of the
stress and helped along the way so much!
There are many people at the Sterrewacht that made the past four years unforgettable. The
friendship with Wouter and Kirsten started over combined cooking and Dutch lessons, and it
went on to many relaxing activities, trips and outings. Gijs, thanks for the hint to put a lot
of onion on a herring. Garrelt, I enjoyed our cycling trips. Kirsten and Richard, I will never
forget all the tasty meals you cooked for me, as well as your support, friendship, books and,
of course, the name of the best whiskey ever. Pedro and Ivo, our outings, movies and Friday
evening discussions kept me sane in the last year. Mariska, Erik-Jan, Kristen, Nadine, spelers
van de Forza voetbal team, Zan, Ammerentie, Carlo, Jaap, Robb en de andere schermers van
de LUSV, hartelijk bedankt voor alles. Joško, Bojan, Robi, Fanči, Hrčo, Ico, Bo žo, Šime, Hrvoje
i Tomo - naši razgovori, susreti, bordanja, ronjenja, morski i zagrebački provodi, nezaboravni
su trenutci koji su smanjivali udaljenost od domovine.
At the end I would like to thank all the good people of Leiden, who made my stay so
enjoyable and made me feel at home here. The hardest part of the PhD project comes now: to
leave you all.
OUR
154
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