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dissertation entitled

Study of Diffuse
Light in CD
Galaxy Clusters

presented by

Xania Scheick

has been accepted towards fulﬁllment
of the requirements for

Ph . D . degree in Physics

 

 

 

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MSU Is An Afﬁrmative Action/Equal Opportunity Institution

””1

_V__._.__-——-__..——

STUDY OF DIFFUSE LIGHT IN CD GALAXY CLUSTERS

By

Xania Scheick

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1993

ABSTRACT

STUDY OF DIFFUSE LIGHT IN CD GALAXY CLUSTERS

By

Xania Scheick

Conventionally, the gravitational potential of galaxy clusters has been mapped
using the galaxies themselves or X—rays as test particles. Using the intra-cluster
medium or diffuse light instead has the obvious advantage in sheer number of par-
ticles, i.e. better counting statistics. Analysis of diffuse light in two cD clusters
(A2670 and A2029) is described. Deep R—band CCD images of these clusters were
procurred at the KPNO 36” and 2.1m telescopes. On large scales, the diffuse light
is well ﬁt by a de Vaucouleurs’ proﬁle. This “smoothness” is suprising in light of
current cluster evolution theory which relies on violent interactions among cluster
members. Thus we are motivated to study the diffuse light on small scales, expect—
ing a priori to see clumpiness in the medium due to collisional or tidal stripping

mechanisms or the affects of dynamical friction.

Using a statistical approach, we have determined the source of the diffuse light
to be numerous low luminosity objects. The clumpiness of the diffuse light in
both clusters is described by autocorrelations of the residual images (after diffuse
light has been removed). From this analysis, we can determine a spatial scale of
the clumps and attempt to place some constraints on the faint end of the cluster
luminosity function. For A2670, we compute a differential luminosity function in

the cluster center that suggests real differences in the luminosity function within

the cluster center from a universal cluster luminosity function. We measure the V-R
color of the cD and cluster galaxies and the color gradient across the halo of A2670.
In A2029, we ﬁnd structures associated with ﬁve galaxies suggestive of wakes, i.e.
the gravitational response of the medium to galactic passage. The apparent lack
of signiﬁcant small-scale structure poses a curious problem for cluster evolution

models.

For those responsible: you know who you are.

iv

ACKNOWLEDGEMENTS

I would like to acknowledge and thank my advisor, Jeff Kuhn, for giving the
tools to complete this project. I would like to beg his forgiveness for leading a
separate life apart from physics; if I had devoted all my passion to science, I would
have saved him alot of money, headaches, etc, but would have gone insane. I should
also thank Juan Uson and Steve Boughn for help formulating the original thesis
and for many conversations afterwards. Many thanks to Debbie Benedict who was
always ready to hear my gossip when I couldn’t focus on the computer screen. I
can’t forget the perpetrators of my existence for brainwashing me to ”get educated” ,

my sibling who has just started his graduate program, and all my furry friends.

TABLE OF CONTENTS

LIST OF TABLES ........................................................ viii
LIST OF FIGURES ....................................................... ix
INTRODUCTION .......................................................... 1
1.1 Clusters of Galaxies .................................................... 1

1.2 CD Galaxies ........................................................... 2

1.3 Cluster Evolution Theories: Origin of Diffuse Light ..................... 6
1.3.1 Cooling Flows, Mergers, or a Primordial Origin ................... 6

1.3.2 Color, Velocity Dispersion, and CD Formation .................. 15

1.4 Previous Diffuse Light Measurements .................................. 19

1.5 This Investigation ..................................................... 21
OBSERVATIONS AND DATA REDUCTION .......................... 24
2.1 Observations .......................................................... 24
2.1.1 A2670 .......................................................... 24

2.1.2 A2029 .......................................................... 25

2.2 Data Reduction ....................................................... 26
2.2.1 Standard Processing ............................................ 26

2.2.2 Shifting and Tesselating ......................................... 27

2.2.3 General Photometry and PSF subtraction ....................... 30
ANALYSIS ................................................................. 32
3.1 A2670 ................................................................ 32

vi

3.1.1 Diffuse Light Proﬁle ............................................ 32

3.1.2 Number Density and Luminosity Function ...................... 43

3.1.3 Autocorrelation ................................................. 44

3.1.4 Color ........................................................... 53

3.1.5 Wakes .......................................................... 54

3.2 A2029 ................................................................ 57
3.2.1 Diffuse Light Proﬁle ............................................ 57

3.2.2 Autocorrelation ................................................. 60

3.2.3 Wakes .......................................................... 69
DISCUSSION .............................................................. 76
4.1 A2670 ................................................................ 76
4.2 A2029 ................................................................ 87
4.3 Concluding Remarks .................................................. 89
LIST OF REFERENCES ................................................. 90

vii

LIST OF TABLES

Table 1: Simple Wake Characteristics ......................................... 75

viii

LIST OF FIGURES

Figure 1: Gray—scale Image of the Central 10 arcrnjn2 of A2670 ................ 34
Figure 2: Contour Map of the Inner 1 arcmin2 of A2670 ...................... 35
Figure 3: Outer R-band Diffuse Light Proﬁle in A2670 ........................ 36
Figure 4a: De Vaucouleurs’ ﬁt to R-band Diffuse Light Proﬁle in A2670 ....... 38
Figure 4b: De Vaucouleurs’ ﬁt to V-band Diffuse Light Proﬁle in A2670 ....... 39
Figure 5: Total R-band Cluster Light & Diffuse Light in A2670 ............... 40

Figure 6: Square of the Variance per Radial Bin in A2670 Residual Image ..... 42

Figure 7: Object Number Density & Scaled Diffuse Light in A2670 ............ 45
Figure 8: Differential Luminosity Function for A2670 Inner Region ............ 46
Figure 9: R-band Autocorrelations of Inner & Outer Regions of A2670 ........ 48

Figure 10: V-band Autocorrelations of A2670 Data 8; Fit Subtracted Images ..49

Figure 11: Autocorrelations of 50 & 100 Masked Gaussian Objects ............ 51
Figure 12a: Histogram of V—R Color of Objects in A2670 ...................... 55
Figure 12b: Histogram of V-R Color of Objects in Background Frame ......... 55
Figure 13: V-R Color of the A2670 Diffuse Light .............................. 56
Figure 14: Gray-scale Image of the Central 4.5 arcmin2 of A2029 .............. 58
Figure 15: Contour Map of the Inner 1 arcmin2 of A2029 ..................... 59
Figure 16: Our and UBK’s R-band Diffuse Light Proﬁle of A2029 ............. 61
Figure 17: Autocorrelations of the Inner Region of A2029 ..................... 63
Figure 18: Autocorrelations of the Outer Region of A2029 .................... 64
Figure 19: Autocorrelations of the Inner Region of A2670 ..................... 67

ix

Figure 20: Autocorrelations of the Outer Region of A2670 .................... 68

Figure 21: Contour Maps of Candidate Wakes, 1. ............................. 70
Figure 21 (cont’d): Candidate 2. ............................................. 71
Figure 21 (cont’d): Candidate 3. ............................................. 72
Figure 21 (cont’d): Candidate 4. ............................................. 73
Figure 21 (cont’d): Candidate 5. ............................................. 74

Figure 22a: De Vaucouleurs’ Fit to Oemler’s A2670 Diffuse Light Measurement 78
Figure 22b: Oemler’s & de Vaucouleurs’ Fit to Our Diffuse Light Measurement 79

CHAPTER 1

INTRODUCTION

1.1 Clusters of Galaxies

Even though only ~ 5% of the galaxies are contained in groups and clusters
whose space density is larger than one galaxy per cubic megaparsec, clusters are
distinctly visible against the background of galaxies making up our present-epoch
universe. Abell (1958) catalogued the most dense of these during the original Palo-
mar survey. A typical Abell cluster contains 100 galaxies with a luminosity range

of two orders of magnitude over an extent of several megaparsecs.

Because of their high surface densities and large number of bright galaxies,
galaxy clusters are identiﬁed out to distances comparable to the horizon of the
universe making them a valuable tool for cosmology (Hubble 1936, Zwicky 1938).
Early research centered on the measurements of standard candles, such as luminosity
of the brightest cluster members (BCMs) or the characteristic luminosity L. in the
cluster luminosity function (LF), and standard metrics, such as radii of cluster
galaxies or that of the cluster as a whole. Research before the 19703 concerned
morphological description of sizes, shapes, and galaxy content of clusters and the

use of these parameters in cosmological investigations.

The next generation of research concerned galaxy evolution. Certain clusters
contain ”supergalaxies” like none seen amongst the ﬁeld galaxies. The general

population of galaxies in clusters is predominately (60%) elliptical and gas-free disk

systems (303), whereas the ﬁeld galaxies are mainly spirals (70%). The spirals
in clusters have ~ 0.2 mag larger B-V color than those in the ﬁeld. The cluster
environment also contains a pervasive, hot intergalactic gas observed by its X-ray
radiation. The research emphasis since the 19708 has been to determine how the
cluster galaxies evolve and affect the evolution of the cluster as a whole. Clusters of
galaxies are excellent laboratories for studying the dynamical evolution of galaxies,
for although the relative velocities are large (thus the timescales for interaction are
small), the galaxy densities are high, and therefore the probability for interaction

is substantially greater than in the ﬁeld.

1.2 CD Galaxies

W. W. Morgan called attention to the bright elliptical galaxies surrounded by an
extensive amorphous stellar envelope (Morgan 1958, Matthews et a1. 1964, Morgan
& Lesh 1965), which were called D galaxies, meaning ”dustless”. The largest and
thus most luminous of these, with an extent 3-4 times that of the largest 808 in the
cluster, was called a supergiant D galaxy or cD galaxy. The designation ”c” was

originally coined for stars with unusually narrow H lines which are now understood

to be superluminous (Tonry 1987).

The large size is only the primary characteristic of cD galaxies, but it is the one
used in classifying clusters (Struble & Rood 1982). Unfortunately there has never
been universal agreement on the proper use of the terms D and cD. Some observers,
including Morgan & Lesh, use secondary properties (like the cD is the BCM and is
centrally located in the cluster) to deﬁne cD-ness, but neither of these attributes is

necessary and sufﬁcient to identify a cD.

A brief description of these secondary characteristics is as follows: ch usually

reside in the cores of rich, regular clusters (Oemler 1974, 1976); however ch and
D8 are sometimes found in irregular clusters at local density enhancements. The
cD envelopes are often extremely large in extent, and the cD is frequently found
at the kinematical center of its cluster (Quintana & Lawrie 1982). They often are
very ”flat” galaxies and are aligned to a flattened distribution of cluster members
(Carter & Metcalfe 1980, Dressler 1981, Binggeli 1982); however as with other
giant ellipticals, their flattening is not primarily due to rotation (Faber et al. 1977,
Dressler 1979). Anywhere from 25—50% have multiple nuclei (Rood 85 Leir 1979,
Hoessel 1980, Schneider et al. 1983).

Velocity dispersion measurements of D and cD galaxies show ﬂat or rising pro-
ﬁles with increasing radius progressing well into the low surface brightness envelopes.
Carter et al. (1985) present rotation and velocity dispersion measurements in the
halos of one dumb-bell and two single nucleus ch out to roughly 35” or 24 R

2. The two ch show some indication that the velocity dispersion in-

mag/arcsec
creases for radii greater than 20” though there are large errors associated with the
outermost points. The increase is from about 300 km/s at the nucleus to 500 km/s
at their last data point. Dressler (1979) obtained spectra of the envelope of A2029
out to 100 kpc (roughly 45”). He reports that the velocity dispersion increases with
radii from roughly 370 to 510 km/s in this region. The proﬁle is smooth with the
exception of a ”bump” at 10 kpc which may be contamination from a nearby galaxy.
This behavior, flat or rising velocity dispersion proﬁles, is not seen in normal el-
lipticals. This result suggests that the outer envelopes’ dynamical states (i.e. the

dynamics of the cluster orbits instead of the kinematics of the underlying galaxy)

are inﬂuenced by the overall cluster potential.

Although not observed in all cD clusters, the following three characteristics are

thought by some researchers to indicate that the cD envelope is a separate entity
from the cD itself: the velocity dispersion increase, the apparent inﬂection in the cD
surface brightness proﬁle at ~ 24-25 mag/arcsecz, and the success of a two compo-
nent model (a normal elliptical with a ”cluster-ﬁlling” component) ﬁtting the latter
proﬁle. The break in the surface brightness proﬁle at ~ 25 mag/arcsec2 was ﬁrst re—
ported by Bahcall (1977) and Oemler (1976) as that point where the proﬁle changes
from or r‘2 to r'l'6 where r is radius from the cluster center. Schombert (1987)
works out cD proﬁle morphology criteria: ch all have properties of D galaxies (fol-
lowing 1.0.2.5 in the inner regions) with the addition of large extended envelopes, the
onset of which occur when there is a change of slope at around 24-25 mag/arcsecZ.

According to Schombert, there are many visually classiﬁed ch without extended

envelopes, as well as a few non-ﬁrst-ranked galaxies with cD envelopes.

Tremaine (1989) suggests the use of the term ”central galaxy” instead of cD
to denote a galaxy at the bottom of a cluster potential basin as measured by the
surface brightness of galaxies or X-ray surface brightness. Jones & F orman (1984)
show that in most cases the potential minimum as measured from the maximum
X-ray surface brightness coincides with the location of the brightest galaxy in the
cluster core. Beers & Geller (1983) ﬁnd that the potential minimum as marked by
the local maximum in galaxy surface density is often occupied by a bright galaxy.
Over 80% of the D and cD galaxies in the Beers & Geller sample are located at the
the surface density maxima, and over 80% are the brightest galaxies in the cluster
core. Faint D and cD galaxies are also located at the potential minimum, since
their root-mean-square (RMS) velocity with respect to the cluster mean is smaller
than that of typical galaxies in the cluster (Quintana & Lawrie 1982, Smith et

al. 1985). Following Tremaine’s deﬁnition, a central galaxy includes most galaxies

with extended envelopes or surface brightness proﬁles with relatively ﬂat logarithmic
slopes and those which are also usually brighter than typical galaxies and brighter
than any in the potential basin. Although, Malumuth (1983), Schombert (1984),
and others have pointed out that a galaxy looks distended because of the logarithmic
slope of the surface brightness proﬁle at the plate limit. This would then govern
whether or not a galaxy looks as though it has a halo. Their work suggests that

the cD core/ halo distinction is not a real physical one.

The interiors of cD galaxies have properties similar to normal ellipticals (Thuan
& Romanishin 1981), including velocity dispersion, mass—to-light ratios (M / L), op-
tical spectra and colors (therefore stellar populations), and densities (Faber et al.
1977, Dressler 1979, Malumuth & Kirshner 1981). Early aperture studies indicated
that ch have the colors of normal bright ellipticals (Lugger 1984 and references
therein). Valentijn (1983) showed the existence of blue cD envelopes for ﬁve out of
six ch from multicolor surface photometry. Color gradient studies of high luminos-
ity ellipticals are now quite extensive (e.g. Cohen 1986, Peletier et al. 1990, Mackie
et al. 1990). Mackie et al. (1990) found small color gradients over the inner 20
kpc for a sample of 11 central dominant galaxies. Mackie (1992) has obtained deep
g and r band CCD images of A2589, A2634, and A407 containing ch or objects
related to ch. He ﬁnds no evidence of a color change at the surface brightness
break that some think signiﬁes the start of the cD envelope, nor are the envelope
colors dramatically blue. In fact, for one object the colors become redder at larger
radii. Schombert (1988) used the Palomar 1.5m with reimaging optics and an RCA
CCD to obtain B-V proﬁles for three ch (NGC 6034, A1767 G1 and A1413 G1).
Errors in the colors at the envelopes are large (:l:0.25 mag), and the behavior of

the gradients especially in the envelope is difficult to judge, but Schombert suggests

both a lack of strong color gradient and blue envelope colors in all three ch. Up-
turns in color proﬁles (going redward with increasing radius) have been previously
seen in a small number of galaxies. Red gradients are seen in ~ 40% of McNamara
& O’Connell’s (1992) sample. A red envelope has been detected in a poor cluster
cD (Maccagni et al. 1988) although there is some concern over the care taken in

the analysis.

1.3 Cluster Evolution Theories: Origin of the Diffuse Light

1.3.1 Cooling Flows, Mergers, or a Primordial Origin

There are three current models of cluster evolution which may explain the origin
of the diffuse light. Cooling ﬂow theory introduces the idea that radiative cooling
of hot X-ray gas decreases its pressure and, then, this denser gas settles toward
the center of the potenial. If there is a galaxy at this location, the gas can collect
until sufﬁcient densities are obtained to start star formation (Fabian et al. 1984).
There are merger models (Ostriker & Tremaine 1975; Ostriker & Hausman 1977;
Hausman & Ostriker 1978; McGlynn & Ostriker 1980) in which a central dominant
galaxy is formed and continues to grow by galactic interactions and cannibalism.
The central mass distribution is also fed by material stripped from galactic halos
by galactic collisions and/or tidal stripping. In this model and the cooling ﬂow
scenario, clusters are currently evolving, and the variety of cluster properties we
observe now are characteristic of various stages of their evolution. The competing
model might be called ”primordial origin theory” (Merritt 1984a). Here the violent
processes that are occurring at the present time in the merger models are most
effective during the initial collapse of the cluster. The hypothesis is that all galaxies

originally had large halos, which were stripped by the tidal ﬁelds created in the

cluster collapse. The cD halo remains unaffected because of its position in the
cluster potential, except to receive the stripped material from the other galaxies.
In this model, the cluster ch are ﬁnished products—the timescales for mechanisms
like dynamical friction and collisional stripping to signiﬁcantly affect the cD being

longer than the Hubble time.

The cooling time for gas in some clusters may be short enough that ~ 1012 M@
of gas may accumulate at the cluster center over a Hubble time (anywhere from 10
to 1000 MG / yr are observed). Efﬁcient conversion of the gas into stars could create
a bright central galaxy. However, the colors of most central galaxies are inconsistent
with the substantial present star formation rate unless most of the stars are low-mass
and therefore undetectable. In this case, the M / L should be high, whereas in fact
central galaxies have the same M / L as normal ellipticals. Since the ch are so much
like normal ellipticals, one can conclude one of the following (Dressler 1984): i) the
accretion is taking place onto a pre—existing galaxy and has not signiﬁcantly altered
its structure; ii) the accretion is directed towards a center of dark matter binding
the cluster with core radius ~ 500 kpc, but dissipation in the gas causes it to form
a much more condensed structure; iii) a condensed structure in the dark matter,
such as a ”black pit” suggested by Blanford & Smarr (1984), forms a skeleton over

which the cD is built from inflowing gas.

Blanford & Smarr (1984) attempt to explain the large number of fast-moving
companion ellipticals found within ~ 10 kpc of many cD galaxies. They propose
that the dark binding material of the cluster actually has a much smaller radius (~
10 kpc) than the core radius, ~ 500 kpc, of the galaxy distribution. Binding these
companion galaxies with such high orbital velocities would make the time scale

for accretion by the cD quite long and would therefore explain why such multiple

systems are common. Observations of velocity dispersion proﬁles indicated that
some cD galaxies do not contain such black pits, since the velocity dispersion at 10
kpc would have to rise to ~ 700 km/s. Tonry’s (1984) observations also seem to
rule out black pits with core radii less than 12 kpc in A2199 (NGC 616) and A2634
(NGC 7720), which were the best candidates. Tonry’s (1986) numerical simulations
show that the orbits of galaxies remain highly elliptical as they are captured. Thus,
these simulations are able to reproduce the proper frequency of such companions

without an extremely concentrated distribution of dark matter.

A spectrophotometric study of cooling flow galaxies by McNamara & O’Connell
(1989) show small anomalies such as UV excesses. McNamara & O’Connell ( 1992)
present CCD imaging of 19 cooling ﬂow galaxies out to about 30 kpc which display
small color proﬁle anomalies, such as bluer central colors, with respect to a sam-
ple of non-cooling-ﬂow galaxies. While these results are interesting, interpretation
of the anomalies is difﬁcult due to the scatter in the correlations of cooling ﬂow
values, uncertainties in both metallicity levels and model predictions of mass drop-
out positions. Some galaxies with cooling rates expected to display large spectral
and photometric anomalies, e.g. IC 1101 in A2029 with 360 MG / yr, have normal
elliptical spectra. The formation of envelopes via cooling ﬂows would require pref-
erential drop-out at large radii. Similar results were found by Romanishin (1987)

for a smaller sample of cooling flow galaxies.

The strongest evidence for the dynamical evolution by mergers to date is the
study of Hoessel & Schneider (1985), which found up to 48% have multiple nuclei
(smaller galaxies seen projected on top of the luminosity proﬁle 10-20 kpc from the
center) and are assumed to be in the process of accretion. This level of multiplic-

ity in BCMs is nearly an order of magnitude larger than that expected for chance

line-of-sight superpositions of galaxies within the isothermal core of a rich cluster
(Tonry 1984). Schneider et al. (1983) show that multiplicity is peculiar to BCMs:
only 5% of second— and third-ranked ellipticals are observed to have multiple nu-
clei. They also show that even though the density varies an order of magnitude
for richness class 0 to 4 clusters, multiplicity is roughly independent of cluster rich-
ness. Considered naively, this result implies that evolution is more rapid in poorer
clusters, which is not unreasonable since the evolution rates are expected to be or
0,72 where 0., is cluster velocity dispersion (Merritt 1984a) which increases with
cluster richness (Bahcall 1981). While the interaction cross-section may increase
with the decrease in a”, the time between interactions also increases, and therefore
the number of interactions / time will decrease. Hence, evolution may not necessarily
be more rapid in poorer clusters, unless there are substantially more slow-moving

galaxies initially available to interact.

The constancy of the brightest center galaxy luminosity was thought to be the
result of homologous growth of the center galaxy, i.e. the galaxy maintains the
same shape with rescaled radius and mass. Within a ﬁxed aperture the luminosity
could stay constant with growth if the surface brightness of the galaxy decreased as
its scale size grew. The multiple-nuclei were viewed as the stripped cores of cluster
galaxies, driffting about within the halo of the cD. Sandage & Hardy (1973) found
an anti-correlation between the luminosity of the second brightest galaxy in a clus-
ter and the luminosity of the brightest. This was taken as evidence that there were
brighter galaxies in the cluster that had merged to form the cD, and the present
second brightest galaxy was originally lower ranked. The current observational evi-
dence shows no indication that the surface brightness decreases with size, however.

Schneider et al. (1983) and Schombert (1984) ﬁnd no anti-correlation between ﬁrst

10

and second brightest galaxy in the cluster.

Tonry (1986) observed a distance-limited sample of multiple nuclei from Hoessel
& Schneider ( 1985) and concludes that 65% of the nuclei have velocities in excess
of 300 km / s with respect to their central galaxies. Consequently only 1/ 3 of sample
nuclei could be interacting with the main galaxy. This indicates that many of these
nuclei are not in the process of merging but instead are on radial orbits passing
through the center of the cluster; i.e. they have velocities too large for circular
orbits expected by dynamical friction. Since the central dominant galaxies do have
normal M / L and there is no evidence for the ”black pits” , eccentric orbits are needed

to explain the high velocities.

Also, Merritt (1984b) demonstrates that the observed properties in multiple
nuclei systems can be predicted with models in which dynamical friction causes
galaxy orbits to decay. This evolution can produce a substantial increase in the
number of galaxies which pass near the center of the cluster without substantially
lowering their mean orbital velocity. Thus the multiple systems produced would
be transient phenomena having lifetimes ~ 107 yr. The distribution of galaxy
orbits ensures that an incoming nucleus would replace an outgoing one on a short

timescale.

Cowie & Hu (1986) observed the faint galaxies surrounding a sample of CBS,
and found that many of these galaxies were bound to the center of the cluster.
These galaxies may either be infalling to the cD, or they may be of such a low mass
that they are unaffected by dynamical friction. However, the dataset on which
Cowie & Hu based their conclusions is very inhomogenous as the spectra of galaxies
were obtained serendiptitously during a study of optical ﬁlaments in X-ray clusters.

Bower et al. (1988) have attempted to conﬁrm these results with a deep sample

11

about the cD in A2029. They ﬁnd no difference in the velocity dispersion of the
galaxies close to the cD and those drawn from the general cluster suggesting that
the fraction of galaxies bound to the cD is small. Unfortunately, this conclusion is
weakened by the presence of unexpected structure in the velocity ﬁeld which may
imply severe contamination of the inner sample by a sub-clump, or that the core
has not yet reached dynamical equilibrium. A detailed velocity investigation of
three cD clusters by Bothun & Schombert (1988) reveals that one cluster, A2589,
has a bound population with an inferred merger timescale of 3-4 Gyr. Gebhardt &
Beers (1991) investigated the existence of a population of galaxies with low velocity
dispersion in cores of rich clusters with a new statistical test. They claim that
there is no strong kinematical evidence for the existence of low dispersion ”bound”
populations in the vicinity of the D / cD galaxy for most clusters. Recent velocity
studies of multiple nuclei (Merriﬁeld & Kent 1991, Blakeslee & Tonry 1992) suggest
that at most 15% of these multiple nuclei are bound. A morphological analysis of
mulitple nuclei central dominant galaxies by Lauer (1988) shows that 50% of the
nuclei display morphological disturbances such as isophotal distortions, truncated
brightness proﬁles, and faint plumes. Many of these disturbances are explained by

high velocity encounters.

The LF for cluster galaxies does not differ signiﬁcantly from the ﬁeld (Schechter
1976, Tammann et al. 1979). However in many cases, the cD is much too luminous
to be a continuation of the cluster LF. Abell (1962) showed that there is remarkably
little variation of the shape of the LF and L. from cluster to cluster, consistent with a
”universal” function that he characterizes with two power laws. This means that the
processes that determined the luminosities of galaxies were either very insensitive to

local conditions such as density, temperature, and turbulence/ angular momentum

12

or that these conditions varied little from protocluster to protoﬁeld regions of space.
It also implies that the evolution of the distribution of luminosities has not been
substantial. Nevertheless merging, tidal stripping, and accretion are expected to
produce some evolution of the LF. The LP bright end is usually very steep in
clusters that have a luminous cD galaxy, i.e. there are few other bright galaxies.
This again could be interpretted as the result of dynamical evolution, where the

brightest have all merged to form the cD.

Tremaine (1989) contends that the resulting rate of accumulations of luminosity
at the cluster center appears to be too slow by more than a factor of two to produce
central galaxies with the luminosities observed, at least in virialized clusters seen
today. Lauer (1988) estimates the luminosity acquired from mergers over the cluster
lifetime to be ~ 2L... which implies that a central galaxy with 12L... cannot be formed
from merging processes alone. A related possibility is that central galaxies are
formed before the cluster virializes, during the early stages of hierarchical clustering
when the relative velocities of the galaxies are low enough that merging can occur
in pairwise galaxy encounters. However, so far there are no convincing numerical
models of hierarchical clustering in which the most massive stellar systems formed

resemble observed central galaxies.

A survey of cD galaxies in poor clusters was completed by Thuan & Romanishin
(1981). They found that the BCMs in poor clusters are missing the extended
envelopes despite their apparent cD-ness, but tend to be brighter and more diffuse
than giant ellipticals in rich clusters. They suggest that the lack of envelopes in
poor clusters implies that envelopes in rich clusters are a result of stripped matter
falling onto the centrally located cD. On the other hand, the merger rate of galaxies

in poor clusters should be higher than the rate in rich clusters because of the lower

l3

velocity dispersions. A higher merger rate could also be a reason why poor cluster

ch are more diffuse than typical giant ellipticals.

The cD envelope or diffuse light is thought to consist of either stars, unresolved
galaxies, or outer halos of resolved galaxies. There are two problems with the
common assumption that diffuse light consists of stars stripped from galaxies by
repeated close encounters with each other (Merritt 1984a). First a large fraction
(~ 1 / 3) of the cluster light is diffuse. This is equal to the luminosity contained in
all galaxies greater than the characteristic luminosity L... Collision stripping is not
that effective, and collisions cease to be important even before galaxies have lost all
their dark halos. Secondly, the observed radial proﬁle of the diffuse light is too large.
Matter stripped should move into orbits nearly coincident with those of their parent
galaxies. This implies that the density proﬁle should be more centrally concentrated
than that of the galaxies since the stripping timescale is a strong function of local
galaxy density. Very few collisions are going on far from the center. If the diffuse
light originated from galaxies, it was removed on a short timescale during the cluster
collapse. Any diffuse light component present would attain the same phase space
distribution as the galaxies which are undergoing violent relaxation at the same
time and remain approximately unchanged as the cluster potential relaxed. Merrit
contends that tidal stresses are more efficent than collisions at removing matter,

and stresses are probably greatest at collapse.

In order for any of these theories to be correct the cD galaxy must not only
be located at the center of the cluster but it must be at rest with respect to the
cluster; otherwise, it would not remain in the center. The initial observational re-
sults seemed to conﬁrm the cD galaxies special place. Quintana & Lawrie (1982)

examined the velocities of nine clusters and their ch. They found that the ch are

14

in the kinematic center of their cluster within the errors of the velocity measure-
ments. However, the errors were large partially due to the small number of galaxies
used to determine of the cluster mean velocity. More recent studies suggest that all
ch may not be at rest at the center of their cluster. Kinematic studies of clusters
of galaxies have shown that ch often have peculiar velocities of several hundred
kilometers/ second (Hill et al. 1988, Sharples et al. 1988). Closer examination of
the X-ray data shows that the peak of the X-ray emission may coincide with the cD
but the outer isophotes are not centered on the cD (Malumuth et al. 1989). Some
clusters show evidence for subsystems of galaxies which are not in virial equilibrium
with the rest of the galaxies (Fitchett 1988, Bower et al. 1988). Observations of
multiple nuclei BCMs suggest that ch may be evolving but not forming in the
present clusters (Lauer 1988, 1990). Several authors have suggested that cD galax-
ies are formed by mergers of smaller subsystems or a small subsystem with a larger
cluster (Merritt 1985, Fitchett 1988, Hill et al. 1988, Sharples et al. 1988). In
this case, the ch’ large peculiar velocity may be due not only to the uncertainty
in determining the cluster’s mean velocity but also to its recent introduction into
the cluster environment. The dynamical friction may not have had time to drag
the cD to the bottom of the potential well yet. Malumuth (1992), in order to test
whether cD galaxies with large peculiar velocities could be formed in clusters via
mergers, modiﬁed his original code, which takes into account two-body relaxation,
dynamical friction, galaxy-galaxy stripping collisions, and mergers, to follow galaxy
orbits in an N-body fashion. At the time of their formation the ch have a distri-
bution of peculiar velocities similiar to that of observed ch. However, by the end
of the simulation or 1010 yrs, the CBS have been dragged to the center by dynam-
ical friction, and the distribution of peculiar velocities is inconsistent with what is

observed. Their typical cD having nine mergers aquires a luminosity of 5L., which

15

compares to Morgan poor clusters with observed luminosity of 7L...

The cD not being at rest with respect to the cluster poses another interesting
problem concerning its envelope. Either the envelope is attached to the cD and
is moving with it, or the envelope is separate from the cD and the cD is moving
through it. If the envelope were moving and had traversed more than roughly a
tidal radius, Merritt’s tidal truncation scenario suggests that the envelope would
be ripped apart. If the cD were moving through the envelope, massive wakes due

to dynamical friction should be visible.
1.3.2 Color, Velocity Dispersion, and CD Formation

There is a well established relationship between integrated luminosity of early-
type galaxies and their color such that more luminous galaxies are redder (Sandage
& Visvanathan 1978). Similarly, concentric aperture photometry showed that galax-
ies are redder at smaller radii (Sandage 1972, Persson et al. 1979). These two
phenomena are thought to have common physical origin: higher metallicity of the
stellar population in more luminous galaxies and in the centers of individual galax-
ies. Hausmann & Ostriker (1978) suggested that the galactic environment may
produce systematic deviations from the mean color-magnitude relation. Their can-
nibalistic model predicts ﬁrst-ranked galaxies in early Bautz-Morgan type clusters
should be at least 0.1 mag bluer in U-B than their counterparts of the same mag-
nitude in later-type clusters. In their model, ch are the result of galaxy accretion.
Thus the color of the cD will eventually be dominated by the smaller bluer galaxies
it devours. The 0.1 mag increase is an order of magnitude estimate as this model is
based on a number of simplifying assumptions, such as quasi-homologous growth,
no galaxy color gradients, and mass, energy, and luminosity conservation at coeles-

cence. Lugger’s (1984) observations rule out a color difference as large as 0.1 mag

16

in U-B between cD and normal ﬁrst ranked galaxies to the 50 level.

Models of formation of galaxies involving the isolated collapse of a protogalactic
gas cloud have been shown to generate color gradients. Continuous color gradients
from nucleus to halo are thus considered evidence for galaxy formation via dissipa-
tional processes. Larson’s (1975) models are now known to rotate too rapidly and
have isochromes too ﬂat compared to observation. Larson derives extreme (10:1)
ﬂattening of isochromes due to angular momentum. However, these models may
not be consistent with results which suggest that giant ellipticals are ﬂattened by
anisotropic velocity dispersions. Carlberg (1984) did N-body simulations of the iso-
lated collapse of a gas cloud and included the effect of star formation sites. His
models rotate more slowly, have less ﬂattening of isochromes, and predict more lu—
minous galaxies have steeper gradients. Models treating collapse as dissipationless
(Gott & Thuan 1976, van Albada 1982) predict an accumulation of gas confined to

the inner regions, limiting the radius over which the color gradient could exist.

Up to now most studies have shown ch to have small or ﬂat color gradients.
The minimal nuclear color gradients support the scenario in which mergers diminish
or wash-out pre-existing gradients. White (1980) predicts a drop in the gradient
by ~ 20% for one merger event and ~ 50% from three binary mergers; however,
star formation triggered by these events was not taken into account. Red envelopes
(or a lack of blue envelopes) may imply that the source of the stripped material is
red galaxies rather than spirals. This is plausible because ch are only associated
with high density regions and these regions are rich in early-type galaxies. The lack
of blue envelope colors also contradicts the expectations of cooling ﬂow scenarios
which produce recent epoch star formation. Fabian et al. (1984) ran simulations

that produced red, low mass stars from cooling ﬂows and colors similiar to those

17

found in giant ellipticals. However, these processes should be conﬁned to the cores
of BCMs where the gas densities are high enough for star formation, which seems
unlikely in the extended envelopes. Sarazin’s (1988) metallicity estimates of the
hot intra—cluster gas range from 0.5 to 1.0 solar suggesting that the cluster gas is
not abundant enough to produce a metal-rich stellar population in the envelope.
Another possibility is that there exists a population of asymptotic giant branch
stars which are luminous, evolve rapidly, and dramatically inﬂuence red and infrared
colors (Chokshi & Wright 1987). Such short-lived populations may be present after
periods of high dynamical activity (stripping and merging). On the other hand,
the dust content in clusters is still up for debate. Hu (1992) derives an average
excess reddening of E B-V~O.19 above the foreground extinction for 10 cooling ﬂow
clusters. Hu contends the majority of the reddening may be associated with the

extended cluster component.

Rising velocity dispersions proﬁles have not been seen in normal elliptical galax-
ies. In most cases their dispersions fall with radius, although there are some that
apparently remain ﬂat. The velocity dispersion of the cD in evolutionary schemes
that rely on tidal stripping and mergers to form the cD / envelope should be repre-
sentative of the high-velocity dispersion, ~1000 km / s, of the cluster members. The
results of Dressler’s (1979) study conﬁrm an increase in velocity dispersion from
roughly 300 to 500 km/s which is a necessary but not sufficient condition for the
stripped debris hypothesis. It has been suggested that the difference in the velocity
dispersion of the nucleus and cluster indicates a different origin for the stripped
material comprising the cD and envelope. The fact that the stars are bound to the
system with this high velocity dispersion implies that the M / L increases signiﬁcant-

ly. The fate of these halos is quite different than those of galaxies in the ﬁeld. For

18

although ﬁeld galaxies should be able to hold onto their extensions, cluster galaxies

should be stripped, thus making that material the common property of the cluster.

The velocity dispersion increase can be interpretted as evidence for a component
of high M / L with a more extended mass distribution than that of the luminous mat-
ter. Dressler (1979) fashioned a model which accounted for all observed properties
of A2029 including the luminosity proﬁle of the cD, its dynamical structure, the high
velocity dispersion, and apparent mass discrepancy. A three-component King mod-
el composed of a normal elliptical galaxy, a high M / L cluster-ﬁlling and -binding
superstucture, and a component of intermediate M / L and velocity dispersion which
supplies the light of the extended halo. The high M / L component is tentatively
identiﬁed with stripped dark halos of cluster galaxies, and the intermediate M/ L
material is attributed to the dynamical friction process which disrupts massive lu-
minous galaxies as they encounter the cD envelope. Alternatively, Tonry (1983) has
suggested that these observations may be compatible with models in which the M / L
is assumed to be independent of radius. The rise in the velocity dispersion with
radius is then explained by invoking highly anisotropic velocity dispersions such
that the motions of stars in the halo are almost entirely tangential. Carter et al.
( 1985) data cannot distinguish unambigously between isotropic models with dark
matter and constant M / L models with large negative anisotropy. The ﬁrst model
has isotropic velocity dispersions and a two component mass distribution: a bright
component with a King density distribution and a dark, isothermal component with
a density distribution which is slightly more concentrated than that of the galaxies.
The second model has predominantly tangential motions in the galaxy halo and no
dark component. As is the case for most bright ellipticals, supergiant galaxies are

not ﬂattened by rotation. Rotation is more important in faint ellipticals (Davies et

19

al. 1983).

In support of a primordial origin of a non-extensive envelope are studies that
show ch ﬂattened and aligned to the overall distribution of cluster members on
scales up to 15/h Mpc (e.g. Sastry 1968, Carter & Metcalfe 1980, Binggeli 1982,
Struble 85 Peebles 1985, Rhee & Katgert 1987, Lambas et al. 1988). Similarly,
Struble (1987) has analyzed the distribution of 21 central dominant galaxies and
has found that both bright and faint isophotes are aligned with the cluster major
axis. There is also a tendency for the cD to be aligned with the nearest neighbor

cluster on scales less than 15/ h Mpc.

Rhee & Roos (1990) investigate this alignment property by addressing the fol-
lowing question: under what conditions will the initial large—scale anisotropy be
communicated to the innermost regions of the collapsed and virialized systems ?
They ﬁnd that during the collapse of prolate, initially homogeneous ellipsoids, in-
formation concerning the orientation is transmitted to the center of the particle
distribution. The way this is transferred is determined by the processes which oc-
cur during violent relaxation. Rhee & Roos ﬁnd that ch show a similar increase in
ellipticities of isophotes from the center as found in ﬁrst-ranked galaxies in a man-
ner that indicates that they are predominantly prolate (Porter 1988). Their results
suggest that ﬁrst-ranked galaxies are formed during the collapse of the cluster as
a whole and that they are generally, but not always, at rest at the cluster center.
The authors also note that their results do not depend sensitively on the amount

of substructure that exists during the collapse.

1.4 Previous Diffuse Light Measurements

A low surface brightness or diffuse component of the cluster light has been

20

measured in several D and cD clusters. The most relevant measurements for this
investigation are Oemler (1973) for A2670 and Uson et a1. (1991; hereafter UBK)
for A2029.

The earliest investigations to determine the fraction of diffuse light in clusters
yielded generally inconclusive results. De Vaucouleurs & de Vaucouleurs (1970)
estimated that in the Coma cluster, 40% of the light due to galaxies brighter than
19th magnitude is from intergalactic matter, but concluded that most or all of
this is due to the faint outer parts of the brightest cluster galaxies. Baum (1973)
photoelectrically intercompared the surface brightness of several vacant patches in
the ﬁelds of A1132 and A801 and found the excess light to be about 17% of the
galaxy light contained within a non-redshifted isophote of 26th magnitude. All of
this light could be accounted for by dwarf galaxies below the detection threshold
and the overlapping outer parts of bright galaxies. Similar conclusions for Coma
were reached by Melnick et al. (1977) with photoelectric drift scans and a sky
monitor telescope. They found an upper limit of 25% of the total cluster luminosity
comes from the intra-cluster medium (ICM). From an analysis of the isophotal
contours on the Palomar plates, Thuan & Kormendy (1977) found a value of 31%
for the diffuse component in Coma. Oemler (1973) measured the surface brightness
proﬁle of A2670 using a method of isophotometry on green photographic plates. He
reports that the cD has the structure of an elliptical galaxy out to 30 kpc and with
an enormous envelope traceable out to 1 Mpc which contains 35% of the cluster
light. Gudehus (1989) reports little if any diffuse light exists on the spatial scale
equal to that of the cD cluster in A1689 using a new method of surface photometry
applied to CCD exposures. He considers the diffuse light to be separate from the cD

and attempts to measure it after the cD proﬁle has been subtracted. Malumuth &

21

Richstone (1984), making use of the photometry of Malumuth 8: Kirshner (1981),
claim up to 60% diffuse light for richness class 3 clusters, with richer clusters having
more light. Their results also agree with computer simulations of tidal stripping.
There is some concern that their deﬁnition of excess light (as compared to a King

model) biases their estimates upward.

The results of the following investigators are discussed in more detail elsewhere
in this manuscript. In an effort to study color and the stellar content of cD galaxies,
Mackie et al. (1990) and Mackie (1992) did surface photometry of the innermost re-
gions of several D and cD galaxies. Schombert (1988) did single-band photographic
and CCD surface photometry to study the extended faint envelopes around 27 cD
galaxies. In his study, he only considers those envelopes which show a ”break” from
the surface brightness proﬁles of the parent galaxy. UBK use a statistical method
on a mosiac of CCD images to trace the surface brightness proﬁle of A2029 out
to 425/h kpc. They report that 23% of the total cluster light is emitted by the

cD / envelope.

1.5 This Investigation

This investigation describes some new techniques to study diffuse light in galaxy
clusters as is applied to two cD clusters A2670 (Scheick & Kuhn 1993) and A2029.
The approach is to measure the large- and small-scale anisotropy of the diffuse light
in order to address some questions concerning the origins of the diffuse light and

general cluster evolution.

In the case of A2029, the UBK measurement shows the extended halo following
a de Vaucouleurs’ proﬁle very closely out to 425 / h kpc. The smoothness of this
halo, as well as that for A2670 implies that the ICM is well-homogenized, which is

22

surprising in light of the violent galactic interactions that are thought to be present-
ly occurring in the cluster. Thus we are motivated to determine just how smooth
the proﬁle is. With deep CCD images, we measure the ﬂuctuations or small-scale
structure in the diffuse light. The structures that we might expect are clumpiness
from galactic stripping mechanisms of whose shape we do not have apriori knowl-
edge, or possibly over-densities or wakes as evidence of galactic passage, on the
spatial distribution of which there has been much theoretical work done (Weinberg
1989, Mulder 1983). Most studies on clusters of galaxies attempt to map the cluster
potential using the distribution of the galaxies themselves, or of the X-ray emitting
gas, which could in principle place strong constraints on the mass distribution (and
dark matter). We can turn the tables on this problem if we use the diffuse light
photons as the test particles, which have the obvious advantage over using galaxies
or X-rays in sheer number, and better “counting” statistics. From this approach,

we can ask direct questions of the cluster concerning the source of the diffuse light.

A2670 is the nearest (2 ~ 0.076) Abell cluster of richness class 3 with a su-
pergiant cD. Sharples et al. (1988) measured velocities for 220 cluster members
and obtained a cluster mean velocity of 22,843i64 km/ sec and a cD velocity of
23,282:l:100 km/ sec. They concluded that the hypothesis that the cD lies at the
dynamical center of the cluster can be rejected at more than the 99.9% conﬁdence
level. There is no evidence for signiﬁcant subclustering in A2670 (although see Bird
1993 for an alternative analysis of the Sharples et al. data). It is not a particularly
strong X-ray source (L, ~ 1044 ergs/sec, Jones & Forman 1984); a radial X-ray
proﬁle is shown in Sharples et al. (1988).

A2029 has been extensively studied (see Dressler 1981 and references therein;

see also Malumuth & Krishner 1985, Schombert 1987). Dressler’s estimate of the

23

LF shows the cluster to be one of the richest clusters in the sky with an estimated
richness 4.4 on Abell’s scale. It has a redshift of 0.0767. Its velocity dispersion is
1450(+185,-140) km/s determined from 47 galaxies (Bower et al. 1988). The cluster
is also a copious emitter of X-rays (McHardy 1978). Sarazin et al. (1992) report
X-ray emitting ﬁlaments from ROSAT images of the cD. There is some evidence
that indicates either the cluster center is contaminated by a foreground subclump

or the core is not in virial equilibrium (Bower et al. 1988).

The remainder of this thesis is outlined as follows: Chapter 2 describes the data,
and chapter 3 describes a multi-faceted analysis of these data. Chapter 4 provides
a discussion as to how these results compare to previous measurements and what

they tell us about cluster evolution.

CHAPTER 2

OBSERVATIONS AND DATA REDUCTION

2.1 Observations

2.1.1 A2670

We observed Abell 2670 with the 0.9m telescope at Kitt Peak National Observa-
tory (KPNO) on September 4-9, 1991. We used the NOAO STlK direct CCD chip
which has a relatively high full well capacity (4.0x105 e") and quantum efﬁciency
(66.3% at 700nm). The detector was mounted at the £7 .5 Cassegrain focus. The
pixels are 0.59”, adequate to the marginal seeing conditions of about 2.10” (full
width half maximum, FWHM, of the stellar radial proﬁle). We used Harris R and
V ﬁlters.

The 3 tesselated frames analyzed in this thesis were produced from data taken
over 3 separate nights. The exposure times were limited to 900 s to avoid overly _
saturating the stars in the ﬁeld. The pattern of observations of the cluster was
ﬁrst a center frame, then four frames offset 3’ in each direction, a center frame,
four frames offset 5’, and then repeat the whole sequence. On the most productive
nights, we obtained several hours integration time on the cluster center. However
after processing, we found that only 12 R frames (3 hours total) on the 3rd night, 6
V frames on the fourth night, and 5 R on the ﬁfth night were useful for this analysis.
We also made observations of ﬁelds approximately 30’ north and south of cluster

center, as representative of the background.

24

25

We observed a set of standard stars from Landolt’s UBVRI secondary calibra-
tion list (Landolt 1983). The secant law corrections were as large as 0.1 R magni-
tudes, while repeatibility of our standard star observations was approximately 0.05
R magnitudes. The light scattering properties of the telescope and detector optics
were measured with observations of the bright star Altair during 1 s exposures. The
point spread function (PSF) was constructed by matching the wings of Altair to
the proﬁle of an appropriately scaled bright Landolt star in our calibration frames.
Dark frames for all data frame exposure lengths were taken, as well as the standard
out-of-focus exposures of a white spot on the dome to produce domeﬂats, which

were used only in zeroth order processing.

2.1.2 A2029

We observed Abell 2029 on the KPNO 2.1m telescope on June 4-8, 1992. We
used the TIKA CCD chip which is characterized by a linearity limit of 2.5x105 e"
and good quantum efﬁciency (82% at 700nm). The CCD camera was mounted at
the RC focal plane (f7 .5). The pixels are 0.267” on a side. The seeing conditions

were roughly 1.5” over the observing run. We again used a Harris R ﬁlter.

The two tesselated frames analyzed here were produced from data taken on
two separate nights. The exposure times were 120 or 600 s on the two different
nights. With the shorter exposures, we were only using our observing time with
50% efﬁciency. We opted to increase the exposure time to 600 s regardless of
saturating the brighter galaxies in the frame. As we are interested in obtaining the
deepest exposure of the cluster center, we took observations offset anywhere from
5” to 90” from the center in one of the four directions. After processing, we found
35 R frames (120 s exposures) on the ﬁrst night and 23 R frames (600 s exposures)

on the third night were useful for this analysis.

26

We again observed a set of standard stars from Landolt’s UBVRI secondary
calibration list. Unfortunately, our 5 s exposures saturated all standard stars making
them useless for calibration purposes. This was not a problem as we were not
interested in correcting the diffuse light proﬁle for scattered light and could calibrate
with previous measurements of the diffuse light proﬁle. Again, dark frames for all

data frame exposure lengths and domeﬂats were taken.

2.2 Data Reduction
2.2.1 Standard Processing

For the A2670 data, the images were ﬁrst corrected for dark current by sub-
tacting an average dark frame of the appropriate exposure length. Calibration of
the pixel-to-pixel gain variations was accomplished by producing a median ﬂat with
8-16 frames from each night’s data. We can estimate how well we are ﬂat-ﬁelding
by computing the root-mean-square (RMS) variation per pixel in an image of the
ratio of two R ﬂats. The variation is 1.8 %, which is slightly less than the per pixel

shot noise we expected. The mean sky brightness was roughly 22.3 R mag/arsec”.

For the A2029 data, we relied on an algorithm developed for calibrating the
spatial nouniformity of the CCD array (Kuhn et al. 1991). This technique uses
the information in multiple, spatially displaced data images to determine the pixel
gain variations, even when the sources are extended. Input to this algorithm were
16 cluster data frames that had been dark subtracted, flattened with a domeﬂat,
and scaled to have the same mean intensities. After 20 iterations, a ﬂatﬁeld was
produced. The integrity of this ﬂatﬁeld was checked by comparing it to one produced
from a different subset of cluster data frames. The RMS variation per pixel of an

image of the ratio of two ﬂats is 0.4%, which is on the order of the per pixel shotnoise

27

expected if the sky brightness is roughly 60% of the full well capacity of the CCD
(we do not have a measure of the mean sky brightness due to the lack of calibration
stars) . It should be noted that the algorithm failed to produce a ﬂat for 13 frames
taken during the second night as there was as much as 0.2 mag difference in the
brightness of several galaxies over the course of the night due to high cirrus clouds.

Data from this night was not used in the analysis.

2.2.2 Shifting and Tesselating

As we are interested in measuring small-scale structure in the cD envelope, we
need the deepest observations possible. In order to do this with our exposure time
per image, we must ﬁrst shift the images to common coordinates and then tesselate
them. Sensitivity of our measurements to the inhomogeneity in the diffuse light, be
it wakes or other structure, requires that we determine the image shifts to sub-pixel
accuracy in order not to degrade our resolution. We devised a method which uses
information at all frequencies (instead of interpolation methods which smooth out

higher frequencies) to determine the fractional shift.

Letting D,(x) be the reference frame data, D,(x) be the data of the shifted
frame, and 6 be the offset of a shifted frame with respect to the reference frame, we

have

D3(x) = D,(x + 6)

If we take the Fourier transform (FT) of Dr and D3

D’,(k) = / D,(x)e”""dx

Df,(k) = / D,(x)e’k"‘dx

28

and then substitute the ﬁrst relation for D3 into the previous equation, we get
Df,(k) = / D,(x + 6)?”de
or with a change of integration variables to y = x + 6
D'.(k) = / D.(y)e“"<¥-5>dy = D'.(k)e-“‘".
We now minimize the following expression for 6:
(k - 5 — nag—in?

We can perform the shift in Fourier-space and transform the shifted image back to

real— space.

To solve the equation for 6 we used an amoeba algorithm (Press et al. 1992).
This algorithm implements the ”downhill simplex method” for multi-dimensional
minimization. A N-dimensional simplex is a geometric ﬁgure of N+1 vertices with
interconnecting line segments. To use this method, an initial simplex must be de—
ﬁned from the starting point P0. The remaining N points are given by P5=Po+z\;e.'
where e; are N unit vectors and A.- is a guess of the problem’s characteristic length.
The downhill simplex method takes a series of steps, most of which entail mov-
ing the point of the simplex where the function is highest through the opposite
face to a lower point, while maintaining the volume of the simplex. When it can,
the method expands the simplex to take larger steps. When it reaches a ”valley
ﬂoor”, the simplex tries to move along the valley. The simplex contracts itself in
all directions if it surrounds the lowest point. The algorithm terminates when the
decrease in the function value in the last step is fractionally smaller than some in-

put tolerance level. Generally speaking, a tolerance of 10'7 took approximately 40

29

iterations. The amoeba algorithm was able to reproduce a solution to the requested
tolerance level from any reasonable initial simplex, though it is not by any means
the fastest algorithm. It also failed to ﬁnd shifts when there were large positional
offsets between frames. For those images offset 3’ and 5’ from center, we approx-
imated the correct shift by a whole number of pixels and then used the amoeba
algorithm to ﬁnd the fractional shift. All k-space does not provide useful signal.
Images of DL/D’, revealed a distinct plane wave pattern for k less than roughly 100.
We took k = 128 for all shifts. Unfortunately, the amoeba routine does not readily
provide a standard error for the derived shift values. We checked its performance
by mapping the solution space to see that it had reached the true mininum (instead
of a local one). We also produced a histogram of the separations between the IRAF
APPHOT package (Davis 1989) coordinates of objects in a reference frame and a
frame that had been shifted using the Fourier algorithm. A Gaussian ﬁt to this
histogram yielded a mean of zero for the object position differences to within the

IRAF object position uncertainty, lending conﬁdence in our shift algorithm.

There is a drawback to using this method: the FT and inverse FT produce a
”Gibb’s ringing” at any point, line, or patch of discontinuity. Saturated stars and
hot columns transform back with associated spikes (alternating bright and dark
pixels) in the horizontal and vertical directions from the object. Fortunately, for
our purposes, this was not a problem. For the hot columns, we substituted the
image mean. The saturated stars’ proﬁles could still be measured and removed in
the PSF subtraction process. The ringing has a mean of the zero-point of the image
and therefore does not contaminate our measurement of the diffuse light. Also, as we
know how the ringing autocorrelates, we could distinguish it from any other signal.

Finally, since the ringing is only present near the image defects and discontinuities,

30

it cannot be responsible for any of our results which show a dependence on distance

from the cluster center.

After producing a set of shifted images per night, we averaged them per pixel.
The A2029 data was particularly contaminated with cosmic ray hits; we averaged
these frames robustly to remove them (i.e. computed a mean and standard deviation
per pixel and then computed a mean from those pixels whose intensity values lie
within the original mean :i: 2.5 standard deviations). Our A2670 dataset consists
of three frames: a tesselation of 12 in R, 5 in R, and 6 in V. For A2029, we have
two frames: a tesselation of 21 and 35 in R, the former having roughly 1.5 the
signal-to-noise (S / N ) of the latter. We also note that a comparison of radial proﬁles
of objects in a single frame and the ﬁnal tesselation did not reveal any systematic

degredation in the FWHM of the star-like objects.

2.2.3 General Photometry and PSF Subtraction

The following discussion of photometry and PSFs concerns the A2670 dataset.
The A2029 dataset was calibrated against the diffuse light measurement of UBK
by matching proﬁles in the radial range for which the ellipticity is roughly constant

and there is minimal contamination by scattered light.

Photometry was performed using IRAF’s PHOT routine assuming an uncrowd-
ed ﬁeld. All parameters were left at their standard defaults with the obvious excep-
tions of the detector characteristics, exposure time, and image dependent param-
eters. We used an aperture radius of 9 pixels or 5.3” (the FWHM for galaxy-like
objects being ~ 4-5 pixels).

In order to measure the diffuse light proﬁle cleanly at large radii, we must ﬁrst

correct for the contamination of scattered starlight by subtracting a scaled PSF

31

representing it. A PSF for both R and V bands was constructed using a bright
Landolt standard for the inner 6’ and a power law ﬁt to the wings of Altair for
larger radii. The scattered light for all objects brighter than 17 R magnitudes was
removed by the scaled PSF subtraction, excluding the cD itself. The 13 saturated
stars presented us a special case. As there were no magnitudes available, we relied
on ﬁtting a power law to the aureole. A survey of the surrounding Palomar plates

revealed no objects bright enough to affect our field.

CHAPTER 3

Analysis

3.1 A2670
3.1.1 Diffuse Light Proﬁle

Figure 1 is our deepest (3 hr) R-band tesselated image of the central 10’x9.7’ of
A2670. The faintest objects visible in this ﬁgure are roughly 23.9 R mag/arcsecz.

Figure 2 shows a contour map of the central 1 arcminz. The lowest contour is

0.1 A/ D units, and the contour interval is 0.7 A / D units. The tick marks in this
ﬁgure denote pixels. The isophotes that characterize the halo are circular about
a common center, which we take to be the spatial center of the cD. Using the
statistical method to determine the diffuse light described in UBK, the diffuse light
proﬁle can be measured out to ~ 3.5’ from the cluster center, at which point the
diffuse light signal slips into the background noise. This method basically involves
ﬁtting truncated Gaussian distributions to the histogram of pixel intensities found
within a radial bin, the distribution mean taken to be the diffuse light intensity for
that bin. As shown in UBK, the subtraction of the contaminating scattered light

from bright stars has a noticable effect on the diffuse light proﬁle.

The choice of the zero-point or background does have some effect on how far
out the diffuse light can be measured. Figure 3 shows the diffuse light as a func-
tion of radius of 1’ to 5’ from the cluster center. We take the zero-point to be

—0.00435:l:0.00020, the value at which the diffuse light signal is no longer decreas-

32

33

ing. We are conﬁdent we are measuring the true extent of the diffuse light as
we ﬁnd the same result from a super-tesselated frame formed with 17 individual
frames from our 2 separate nights of R-band data. Thus the diffuse light extends

to approximately 3.5’ or 230/ h kpc.

The RMS variation per pixel of the sky is about 2%. In our outermost bins, there
are on the order of 5000 pixels. Hence we are measuring a diffuse light signal that

is ~ 0.01% of the sky brightness. The conversion from A / D units to mag/arcsec2

is 23.19—2.5log(A/D units).

Figure 4 shows the best ﬁt de Vaucouleurs’ proﬁle (dashed line) for both the
R and V band data (points). This proﬁle has the following functional form (de
Vaucouleurs 1948):

[(1‘) : oe_aro.25

where I is the mean intensity in the radial bin whose central value is r and Io and
a are coefficients determined in the ﬁtting procedure. The ﬁt for R band has a
reduced x2 of 0.35, while that for V has 0.28. We should note that, although not
shown, the de Vaucouleurs’ proﬁle ﬁts poorly within a radius S 8” of the center;

this is also true of a King proﬁle and a power law.

What percentage of the total cluster light is the diffuse light ? Figure 5 shows
a log-log plot of the total R—band cluster light (solid line) and the diffuse light
(dashed line) versus radius. The total light follows a power law for all radii. For
smaller radii, the diffuse light follows the total light, as expected, considering the
sparsity of objects in this region, but falls away for radii greater than roughly
1’. We measure the total cluster light up to each radius in two ways: (i) simply

integrating the counts per radial bin directly from the image, (ii) integrating the

34

 

Figure 1: Gray-Scale Image of the Central 10 arcmin2 of A2670.

 

35

 

Figure 2: Contour Map of the Inner 1 arcmin2 of A2670.

J.
i

 

36

Aommohcv mSHUmu

00m 00m 0mm 00m 00H 00H 00H 0NH 00H 0m 00 ow

 

- -

 

 

 

 

 

000.0:
000.0:
N00.0|
0
N00.0
u000.0
000.0
000.0
H0.0
NH0.0

rICl pUEq-H

(snun CI/V)

Figure 3: Outer R-band Diffuse Light Proﬁle in A2670.

37

counts per radial bin converted from IRAF PHOT detected objects plus the diffuse
light proﬁle; We cannot directly remove the background galaxies as we do not have
precise differential photometry that is accurate from the cluster center out to the
“background” (a few degrees from cluster center). In addition, our offset frames (30’
from the cluster center) have a different object detection threshold. Without this
correction, the integrated total cluster light rises faster than the expected function.
We can estimate effects of our background uncertainty on the ratio by subtracting
a constant which forces the cluster light to go to zero for the outer 1’ of our image.
We note that the core radius as calculated by Dressler (1978b) is 0.31 Mpc for
an Ho = 50 km/s/Mpc (or 160/h kpc in our notation), implying that the outer
region considered could be only 3-4 core radii away, though this number may not be
relevant in this context as it is the point that the number density falls to half of its
central value, not the light distribution. The ratio of the diffuse light to the total
cluster light at a radius of ~ 3.5’ is roughly 0.30 when integrating total light from
the image directly, and roughly 0.37 when using the photometry list to compute
the contribution of the ﬂux per object to the total cluster light. Assuming a zero
background, the ratio is 0.29. The correct background is somewhere between these
numbers such that we can use their difference (0.08) as an estimate of the systematic

uncertainty in our measurement.

The remainder of the analyses was done using the residual image produced by
subtracting the diffuse light proﬁle. This was done in two ways: (i) subtracting the
actual statistical determination of the diffuse light per radial bin, (ii) subtracting
the de Vaucouleurs’ proﬁle ﬁt to that determination. The former is rougher within
a radius of 30” as the radial bin width has to increase to maintain a statistically

signiﬁcant number of pixels per bin. No diffuse light measurements were taken

38

 

 

 

 

 

 

 

 

 

\o
I r I l I 1 '
N
<11
r %‘ - °
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00
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N <11 to co 0 N <11 Lo 0
N N N N m m m m

(zvoesoxe/ﬁem) qq pueq—a

Figure 43.: De Vaucouleurs’ ﬁt to R—band Diffuse Light Proﬁle in A2670.

 

 

 

 

 

 

 

W
T I r I n I I I I ’
N
$7“ N
"' ‘ e" : ‘ '
F N
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<11 Ln \0 1\ co ox 0 H N m <11 0
N N N N N N m m m m m

(zvoesore/ﬁeui) rm pueq-A
Figure 4b: De Vaucouleurs’ ﬁt to V-band Diffuse Light Proﬁle in A2670.

40

¢.N N.N N

Aommoucv
m.H 0.H v.H N.H

mSHUcH 00H

H

0.0 0.0 0.0

 

H H

 

H

H

H

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Nm
Hm
0m
0N
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MN
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oesoxe/ﬁem)

(8..

Figure 5: Total R-

band Cluster Light & Diffuse Light in A2670.

41

within 8” due to the minimal number of pixels and the poor de Vaucouleurs’ ﬁt in

that region.

We used our measurements of the surface brightness ﬂuctuations to place limits
on the number and luminosity of objects that contribute to the diffuse light in each
pixel (analogous to Tonry & Schneider’s 1988 approach to measuring the distance
to galaxies from surface brightness measurements). Since our pixels may be smaller
than a typical contributing galaxy from the faint unresolved end of the galaxy LF,
we ﬁrst rebinned the data to a 2x2 pixel scale. If we now characterize the luminosity
of a faint contributor by 10, and if there are on average n(r) objects which contribute
to a pixel at a given projected radius r from the cluster center, then we expect a
mean surface brightness proﬁle of

105(1‘)
41rd2

 

S(r) =

for a cluster at distance d. The variance in the surface brightness in a ring of pixels

at distance r from the cluster center should be

 

02(r) = (2373;; + 03
as long as each pixel samples an independent line of sight, and where other sources
of measurement noise are contained in the 03 term. Since the sky background in our
data is much larger than the diffuse light signal, both photon and CCD read noise
contributions to 0(r) should be independent of the distance to the cluster center.
Thus we can determine a: by looking at 02(r) at large projected radii. Figure 6
shows a plot of 0(r)2 in A/ D unitsz. This data shows no evidence of the Poisson
noise due to diffuse light granularity. We can set a lower limit on n(r) by noting that
02(r)-a§(r) is less than 2x10‘5 at a radius of 16.8”. We have n(r) = Sz(r)/(02(r)

42

-a'3(r)) with S = 0.15 A/D units/pixel and 1 A/D units/pixel is equivalent to 22 R

magnitudes, and thus n(16.8”) _>_ 7.5x103. It follows that 10 is 5 3x103 Lg.

We stress here that we are only ﬁnding an upper limit on the ﬂuctuations in
the residual image, and therefore a lower limit on the number of objects. There is
a gradient in the residual image within roughly 12” of the center that artiﬁcially
inﬂates a, but beyond that the ﬂuctations show small variation about a constant.
Any errors introduced with our shift method or PSF subtraction will only degrade
this lower limit. We also note that for the unbinned data the 02 increases as expected

(i.e. by the number of pixels used in the binning) for the equivalent radius.

 

 

 

 

 

0.0003 . . . .

.1: 0.00025

(U)

f:

a 0.0002

:3

E 0 00015

:5 .

2" 0.0001

(I)

U

c:

.3 Se-OS

s...

to

> 1 l l l
0

5 10 15 20 25 30
radius (arcsec)

Figure 6: Square of the Variance per Radial Bin in A2670 Residual Image.

43

3.1.2 Number Density and Luminosity Function

Using the IRAF photometry data, we determined the number of objects per
radial bin. Figure 7 is a plot of the object number density (points) versus radius
along with a scaled version of the diffuse light proﬁle (dashed line). There is a
distinct difference in shape of the radial proﬁles of the diffuse light and the objects
in the ﬁeld for radii less than 150” even after accounting for the obvious uncertainty
in the number density background level. We do not conﬁrm the similiarity in number

density and diffuse light proﬁles claimed by Oemler ( 1973) or Schombert (1988).

Since the integration time and S / N of our background frames differs from our
data frames, we cannot remove contaminating background objects from a LF of our
cluster image by using the background images. However we can use the outer part
of our cluster image (i.e. outside the region we measure a signiﬁcant diffuse light
signal) for a background estimate. Figure 8 is just such a differential luminosity
function (DLF): the LF from the outer 150-300” has been subtracted from the inner
150”. Also, subtracting another outer annulus 240”Sr_<_300’ from the inner region
yields a similiar DLF, while subtracting two contiguous outer annuli (150” Sr3240”
and 240”_<_r§300”) yields a DLF consistent with zero. The DLF suggests that
there might be some excess objects for a R magnitude/ pixel brighter than 22., and
a deﬁcit for objects fainter. This deﬁcit is based on those points between 22. and
24.5 mag/ pixel, as we can not reliably measure fainter than 24.5 R mag/ pixel. We
make this cut-off based on a test performed to determine IRAF’s false detection rate
on an image of Guassian noise having the same mean as our data. The resulting LF
shows the peak of false detections to lie at 24.5 R mag/ pixel, and falls off similarly

to the data at fainter magnitudes.

If the LF were a separable function of radius and magnitude, then the expected

44

DLF should be a scaled version of, for example, the Schechter function. Clearly
our DLF indicates a departure from this behavior in the innermost regions of the

cluster.
3.1.3 Autocorrelation

Before we could perform an autocorrelation on our residual images, we had
to remove all objects. We did this by blanking out (assigning a large negative
number to) contiguous pixels (around all objects that were 2.5 standard deviations
above the image mean. Due to computing time constraints, we used 2562 pixel sub-
sections, one centered on the cD and four in the outermost corners of the original
10242 images. Because of the ”holes” in the image, the autocorrelation had to be

performed in real-space with the following equation:

I

A(<5) = 3,1}- £256”de
where A is the autocorrelation function of the separation 6 between pixels, N5 is
the number of measurements for each separation, and d;,- is the data or intensity
level at each pixel with position in the image i,j that has not been blanked out. We
note that typically pixels within a 20—30 pixel radius from the cluster center were
removed in the blanking procedure.

Figure 9 shows the autocorrelations for the 12 frame R-band tesselation cen-
ter (solid line) and 4 corners (dashed lines) for the residual image produced by
subtracting the diffuse light determination. Figure 10 shows the autocorrelations
for the center region in the 6 frame V-band tesselation for either residual images
in which the diffuse light determination (solid line) or a ﬁt to that determination

(dashed line) were subtracted. Though not shown, the autocorrelation of the 5

45

Aummonmv msHUmn

00m 00N 00N 00H

00H 00

0

 

 

I

l

N00.0:

N00.0
000.0
000.0
000.0
H0.0

NH0.0

 

 

0H0.0

Aqrsuep Jeqmnu a 10 PaIeos
Figure 7: Object Number Density & Scaled Diffuse Light in A2670.

46

meHm\mﬂduHQUME m

cm 0N 0N 0N NN 0N 0H 0H 0H
H q . . . H . Hocoocl

 

- W . moumm-
- - molmm-
. . melms-

.3888t. 1M¢.am&mw ﬁt ..... Emma. 14111;! o
. l A A. 02% 0 -i

- 1 00100
e

- - - melmm

   

- moumm-

 

 

 

 

 

. . _ c p . . mOlmm

 

{exrd/saaetqo go reqmnu
Figure 8: Differential Luminosity Function for A2670 Inner Region.

47

frame R—band tesselation center subsection has a similar shape and ﬁrst zero cross-
ing compared to the deeper R-band image. The autocorrelation amplitude for the
center subsection is also substantially larger than that for the corner subsections of
the 5 R-band frame tesselation. The diffuse light data subtracted and ﬁt subtracted
images yield autocorrelation curves that are similar in shape for any of our images.
The only processing done to these curves was to subtract an offset representative
of the value the autocorrelation approaches at large separations. We note here that
we can never know this offset exactly because the ﬁnite size of our picture does not
allow a large enough separation to be reached for the autocorrelation to truly go to

a constant. We can estimate this constant to be the square of the image mean.

If the diffuse light proﬁle were not spherically symmetric or the de Vaucouleurs’
ﬁt to proﬁle were not representative, the effect on the autocorrelation would be seen
at separations on the order of the entire frame. We tested this by subtracting the
de Vaucouleurs’ ﬁt from the image offset from the true center one pixel in both
perpendicular directions. The resulting autocorrelation has amplitude of roughly
that of the correct autocorrelation. For lags greater than 60 pixels, there is a distinct
difference in shape from the correct autocorrelation: instead of a signal oscilating
about the zero-point with ﬁrst crossing around lags of 60, the autocorrelation show
a roughly constant value above zero until lags of 180 and then drops to a fairly large
negative value at the largest lags. This test supports the signiﬁcance of the results
at small lags for the true autocorrelation. We do not expect any asymmetries in
the proﬁle to be as large as the one forced with this test, but, if they exist, they

would not substantially effect our result for small lags.

We devised several ways to test the autocorrelation algorithm and our data

reduction method. First, we autocorrelated an image of random numbers between

48

00H

00H .0NH 00H 00 00 00 . ON 0.

Aommoumv GoHumummmm HmHUmu

 

H H H H H H H

.1.
ll

14’.

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Col|| ‘o’n :0 a .Lnuohncg II
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Ya. ccccccccc 0,..-..cooooocnntu.o..uuﬁ}\l‘ nnnnnnnnnnn goes“! éigtad' ‘J .7 ".6“ l
3 4’ a I to I Y)‘ 0131“,..fpgli-L
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I \ ‘ o I “‘ of 0‘ II
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l" ‘ "l’l—I"-“‘\’\I”“u I 0

.II

1.
I.

l

p — — H n n —

 

 

 

 

 

001001

00|®N|

0010N

00100

00100

00100

mOImH

3V

(ZVSTFUH (II/V)
Figure 9: R-band Autocorrelations of Inner & Outer Regions of A2670.

49

A0000H00 GOH00H0Q00 HmHﬂmu
00H 00H 00H 0NH 00H

00 00

00

0N 0

 

H

 

4

. -‘U’
“““ ’

H

H H

q

 

H mOlmml
001001
001®NI

0010N
00100
00100
00100
0010H
0010N.H

 

 

00100.H

3V

(ZVSQIUH G/V)

Figure 10: V-band Autocorrelations of A2670 in Data 8: Fit Subtracted Images.

50

0 and 1, which resulted in a delta function at zero-lag with the proper constant
value of 0.52 for all other separations. A check on the reproducibility of our data
reduction method can be seen in the fact that the two separate nights’ R band
observations yielded strikingly similar autocorrelation functions when either the
diffuse light proﬁle or the de Vaucouleurs’ ﬁt to the proﬁle were subtracted. The
effect of blanking out pixels was investigated in three ways. First we checked the
effect of spatial ”holes” over a random noise distribution. We masked an image of
Gaussian noise with a pattern of holes produced for one of our cluster frames. The
resulting autocorrelation was the expected delta function at zero-lag with a value
equal to the mean squared for all other separations. We also changed the number
and size of the ”holes” by either lowering the threshold to blank pixels or by scaling
the radii of blanked regions found for a particular threshold. Both have the effect
of reducing the autocorrelation amplitude for small lags in the center region, but
not in the outer regions. Increasing the radii of blanked regions also has the effect
of reducing the amplitude at lags of roughly 30”-60”, which suggests that the larger
radius is required to assure our autocorrelation is not picking up scattered light

from objects whose PSF’s were not removed in this region.

How can we interpret this autocorrelation ? To begin to answer this question,

we made images of 50 and 100 Guassian galaxies of the form

_(1-10)2+§y‘9o)2

G=Ae 20

where x0 and ya are generated randomly, the amplitude A was 2, and dispersion 0‘
was 1, and the objects were superimposed on normally distributed noise with a zero
mean and a RMS variation of 0.0083 (comparable to the data frames). This image

was then masked with the ”hole” pattern that was used for real cluster data. The

51

resulting autocorrelation is plotted in Figure 11. For a hundred galaxies (dashed

line) the peak at a lag of 1 pixel is prOperly twice that for 50 galaxies (solid line).

An estimate of the FWHM of the autocorrelation peak is roughly three times a.

 

 

 

 

 

 

0.016 ‘ . . . . . . . .
0.014 -
0.012 . «
0.01 - 1

R?

< 0.008 - .

(D \

I.)

'2 0.006 ,

:3

O 0.004 .

\

:5
0.002 1

U

<12

0 J 1 1 1
1 2 3 4 5 6 7 8 9 10

radial separation (arcsec)
Figure 11: Autocorrelations of 50 & 100 Masked Gaussian Objects.

What does this simple model tell us about the origin of the spatial scale of the
cluster autocorrelation ? First of all, if we calibrate the autocorrelation at lags
of 1 pixel with the cD peak (11.07 ADU) value we ﬁnd that we are measuring an
effect that is less than 0.05% of the diffuse light, which is much smaller than the

variance statistic per pixel we described earlier. (Though at a radius of 16.8” where

52

the diffuse light is 0.15 ADU, the autocorrelation amplitude is ~ 2% of the diffuse
light.) We must be careful in interpreting the amplitude at small lags because the
signal we are measuring is affected by the number of pixels that are removed. The
autocorrelation signal is weighted toward the center of the cluster, as is apparent
from the comparison of autocorrelations of the central to the outer regions. As
more pixels are de-weighted from the center of the image (where most of the ”holes”
lie), the autocorrelation signal weakens. However, we may be able to compare the
amplitude of the autocorrelation to what is expected if the objects represent the
faint end of the LF. This calculation is done for both A2670 and A2029 in section
4.2.2.

At this low level, large scale (of order the CCD frame size) errors in our pho-
tometry (e.g. zodiacal light and extinction coefficients) could exist. Thus the mean
pixel value in a 2562 subarray may be biased, so that the large scale information in
the autocorrelation function is probably not reliable. Such errors appear as a zero-
point offset and spurious correlation amplitudes at large lags where there are also
signiﬁcantly fewer pixels at these separations. We are encouraged by the agreement
in the form of the V and R autocorrelation data at lags less than about 1’ (allowing

for a small offset error between the two colors).

While the autocorrelation function is noisy we can extract at least one piece of
information from these curves: a spatial scale. Our technique for removing objects
affects the amplitude of the autocorrelation at small lags. Scattered light from these
objects for which no PSF subtraction was performed affects the autocorrelation am-
plitude at lags of 30”-60”. Hence, an estimate of the FWHM of the autocorrelation
will be biased. Instead, we can safely characterize the ”clumpiness” of the material

causing the diffuse light ﬂuctuations with an exponential scale length of about 20-30

53

pixels (for lags less than 30”). This scale is independent of all the tests we have
performed with the data and corresponds to a clump size of 13—20/ h kpc. We em-
phasize this length must be interpreted as a size not a separation between objects.
The latter scale would be measurable as the distance between the zero-lag and a
secondary peak in the AC. Our half-length would describe a separation only if the

widths of the objects were larger than their separations, which does not seem likely.

3.1.4 Color

Next we investigated the color of the objects in our images, including the cD. By
matching photometry list coordinates of objects in the 5 frame tesselation in R and
the 6 frame tesselation in V, we generated a list of approximately 320 objects for
which we could produce a color (V-R) histogram (Figure 12a). We also produced
a similar histogram for single background frames located 30’ north of the cluster
(Figure 12b) for comparison. The color of sky is roughly 0.35 magnitudes. K
corrections at this color were approximated with the relation 6(V-R) ~ -z (Sandage
1972), where z is the redshift. We estimated a zero interstellar reddening from the
HI maps of Burnstein & Heiles (1982); A2670’s galactic latitude is approximately
68°. We measured the color of the cD to be 0.72 using the ﬂux within a radius of
18” about the cD in both R and V frames. As is apparent from Figure 12a, the cD

color lies near the peak of the histogram for the cluster.

We also measured the color gradient in the halo. We can compute the halo
color with the diffuse light measurements (Figure 13). There is roughly a drop of
0.6 magnitude over radius of 1.5’. When the error in the zero levels of the two
frames is included, the gradient ranges from 0.4 to 0.8 mag. We take the 0.6 (:l:0.2)

mag decrease in V-R over 1.5’ to be the gradient in the halo.

54

3.1.5 Wakes

By observing the wake of a massive galaxy, we could calibrate the gravitational
diffuse light response to learn about the transverse velocity and mass of the mov-
ing galaxy. Calculations of the shape and density enhancements of such wakes are
promising (Weinberg 1989, Mulder 1983). If the diffuse light has a velocity dis-
persion comparable to or less than the galactic dispersion, then local diffuse light
surface brightness enhancements of a few percent are expected. More speciﬁcal—
1y overdensities of 3-5% in the diffuse light should be measurable and distributed
approximately in a dipole pattern about the impinging galaxy. We attempted to
identify candidate galaxies by looking for a dipole-like distribution in their sur-
face brightness. Lauer (1988) reports possible wake detection around galaxies in
A2199, A1185, A779, and A1126. The appearance of his candidates is very similar
to theoretical predictions of Weinberg (1989). Using contour plots, we looked in
the residual image for any galaxies whose center was offset from the contour center
or had plume-like features associated with them. The 12 frame tesselation showed
that the outermost contour (indicative of the frame noise level) of the candidate
galaxies was just above the 5% level of the diffuse light at that radius. In an ef-
fort to increase the S / N, we added the 12 and 5 tesselation frames, measured and
subtracted the diffuse light proﬁle, and again looked for wakes. The S / N level in
this super-tesselated frame was at best 3%, which is barely sufﬁcient for a wake
detection. Out of the 4 candidates within 20”, we found none with a signiﬁcant
difference in central galaxy position with respect to the center of the surrounding

contours.

Frequency

Frequency

55

 

14 I I j I I

 

 

 

 

 

2 .-
/\
O \ . .

 

 

 

 

 

 

 

 

 

 

 

 

~0.5 0 0.5 l 1.5 2 2.
V-R color
Figure 12a: Histogram of V-R Color of Objects in A2670.
60 I I T I
50 r ﬂ
40 L
30 r
20 h
10 '
0 v . . ,.
-0.5 0 0.5 l 1.5 2 2.
V-R color

Figure 12b: Histogram of V-R Color of Objects in Background Frame.

56

A0000H00 mSHUMH

 

 

 

 

 

 

 

 

 

00 00 0b 00 00 00 om 0N 0H

 

 

0.01
0.01
0.01
N.01

Nr-lmkoq‘lN
OOOO

ruﬁem H-A

sepnq

Figure 13: V—R Color of the A2670 Diffuse Light.

57

3.2 A2029
3.2.1 Diffuse Light Proﬁle

Figure 14 shows our deepest (~ 2 hr) R-band tesselated image of the central
4.55’x4.50’ of A2029. The faintest objects visible in this ﬁgure are roughly 20.6 R
mag / arcsecz. Figure 15 is a contour map of roughly the inner 1 arcminz. The lowest
contour is about 0 A/ D units, and the contour interval is 400 A/ D units. The tick
marks in this ﬁgure denote pixels. We note that the isophotes have ellipticity which
varies from 0.85 for a long axis greater than 20” to roughly 1 (or circular) in the

center. UBK report a constant ellipticity of 0.90 at all radii.

The purpose of taking yet another data set on such a well studied cluster was
to search for and measure any anisotropy in the diffuse light proﬁle found by UBK
to be very smooth. We observed only the center of the cluster in order to maximize
the S / N; hence our frame covers only roughly the inner 4.5 arcmin2 or only 1/ 3 the
extent of the diffuse light proﬁle. We measured the diffuse light in two ways. First
we used UBK’s statistical method, described previously as applied to A2670, with
bins of a constant ellipticity 0.85 for long axes greater than 20”. We are able to
measure out to a long axis of about 150” before the number of pixels is insufﬁcient.
As shown in Figure 16, the resulting proﬁle (solid line) could be used to calibrate
our image against the UBK measurement (dashed line) for the range 20—100”, the
upper limit being the point at which scattered light contaminates the proﬁle. We
note that the lack of an estimate of background does not effect the calibration. The
residual image formed from the subtraction of this proﬁle was used to perform the

surface brightness ﬂuctuation analysis and to look for wakes.

Surface brightness ﬂuctuations were computed in the same manner as decribed

for A2670. The image was binned 4x4 in order to again consider a roughly 1 kpc2

58

 

Figure 14: Gray-Scale Image of the Central 4.5 arcmin2 of A2029.

 

59

 

Figure 15: Contour Map of the Inner 1 arcmin2 of A2029.

 

 

 

60

super pixel. In this binned image, we are only able to measure ﬂuctuations for a long
axis greater than 90 pixels. The diffuse light signal is roughly 45 A/ D units, and
the magnitude of the ﬂuctuations is less than 7; thus the number of objects must
be greater than 290. With our calibration per pixel (26.68—2.5log(A / D units)), the
luminosity per pixel is roughly 7.6x107 LG). Hence the luminosity per object must

be less than 3.2x105 L9.

The second method of determining the diffuse light was necessary for the au-
tocorrelation analysis. As the ellipticity is a function of radius and a PSF is not
available, we needed a way to remove the diffuse light and scattered light from bright
objects. The technique is simply to perform a variable radius aperture smoothing
on an image in which the seeing disk of objects excluding the cD itself are masked
(i.e. not included in the calculation). At each pixel, a robust average of pixels was
computed in a circle of the chosen radius. The aperture radii used were 3, 6, 9,
12, 15, 21, 27, 33, 39, and 45 pixels (the last of which is roughly 1/25 of the 2562
frame used in the autocorrelation). The resulting smoothed images were subtracted
from the original image, and the remaining ”seeing disks” were masked before the
autocorrelation was performed. The innermost regions of the resulting images were
less well represented by the larger aperture radii, but no large scale gradients were

apparent, and the regions for which this method had trouble were also masked.

3.2.2 Autocorrelation

Figure 17 shows autocorrelations when using the smoothing technique with
variable aperture radius for a 2562 pixels region about the center of the cD in
A2029. Figure 18 shows autocorrelations for a region furthest from the cD on the
same frame (the cD and center of this subsection are separated by 610 pixels).

The ten lines shown each ﬁgure correspond to the ten different radius apertures

61

0.N 0.N N.N

N

A00moumv mSHUMH 00H
0.HHMYIH 0.H N.H

H

0.0 0.0

 

 

.H

 

H

H

H

 

 

 

0m

00

Nm

0m

0N

0N

0N

NN

0N,

(zvoesore/ﬁem) qq pueq_H

Figure 16: Our and UBK’s R-band Diffuse Light Proﬁle of A2029.

62

used in the smoothing procedure. We note that the autocorrelation of the center
region maintains the same shape but increases amplitude with increasing aperture
radius until a radius of 45 pixels. For the outer regions, the amplitude and shape
remain roughly the same for all aperture radii. The autocorrelations for the inner
regions are somewhat dependent on the aperture radius, but they are not likely to
do be due to large scale gradients in the image because their overall shape does
not change. The effects of gradients may be becoming apparent at lags of 8-16” for
larger aperture radii. We can determine another exponential scale length: 17 pixels

or 4.5” which is roughly the same for all aperture radii choices less than 45 pixels.

For the sake of comparison, we performed this technique on our deepest A2670
tesselation. We again ﬁnd a distinct difference in the amplitude and shape of the
autocorrelation for inner and outer subsections (Figures 19 and 20, respectively).
Again there is an increase in amplitude with increasing aperture radius, but not
as pronounced as that for A2029. The amplitudes of the autocorrelation are not
easily comparable because of the difference in number of pixels that were removed
in the masking procedure. We can get a rough estimate for lags of 1 pixels by ”un-
normalizing” or multiplying the available number of pixels separated by 1. The
resulting numbers are the same order of magnitude. The expontential scale factor
determined from this method is only roughly 5.4 pixels or 3.2” , which is substantially

less than the 24 pixels or 14” obtained from the previous method.

We would like to compare the amplitude of the autocorrelation at small lags to
what we might expect from contributors representative of the faint end of the LF.
Assuming a single galaxy with constant surface brightness s and 11.0 pixels within
that galaxy separated by re, then the autocorrelation at r0 should be ~ n,osz/N,o,

where N", is the total number of pixels separated by re. For small objects nro

(A/D units"2)

AC

(A/D units“2)

AC

63.

 

 

 

 

 

 

0 2 4 6 8 10 12 14 16 18 20
radial separation (arcsec)

 

 

 

 

 

I I I I I I I I
d
H
d
.
.ﬂ
0‘
.. ‘ .......... I ........ .I “I ....... In \
n ’ I % v x \T‘ V
. ‘v"\. I
V'
-
-2 b d
- 3 - u
_4 l l L l J l l l l

 

 

O 2 4 6 8 10 12 14 16 18 20
radial separation (arcsec)

Figure 17: Autocorrelations of the Inner Region of A2029.

(A/D unitSAZ)

AC

(A/D unitSAZ)

AC

64

 

 

 

 

 

 

205 I I I '7 r I I ' '
‘I
\
2 P .
1
1'
1.5 r -
1 -
0.5 . j
l
f\ g} 1 .
”MA .. .\,-. Mw‘u, 1.3- x
O J F: . . 3. 5.41., ...... n aw ‘7,
—O 5 l I l l l l l L l

O 22 4 6 8

10 12

14 16 18 20

radial separation (arcsec)

 

I
N
U1

I

 

 

1-

l l l

 

l l

 

l l I

 

-3.5
O 2 4 6 8

10 12 14 16 18 20
radial separation (arcsec)

Figure 18: Autocorrelations of the Outer Region of A2029.

65

should go roughly as the area of the object. For N galaxies (separated by much
more than to) of varying surface brightness and area, we have to integrate from the
detection limit of our frame to zero brightness. Expressing the surface brightness

as the luminosity per area (L / A), we need to calculate the following integral:

thm 2

L
— L dL
/ A ¢( )
0
_ where ¢(L) is the number of objects at a given luminosity, i.e. the LF. We will

ignore for now the fact that our DLF for A2670 suggests a lack of faint objects, and

use a Schechter LF which has the following form:

¢(L) = $3"- ﬁfe—W
where No is normalization factor, L... is a characteristic luminosity of the cluster
and a has been determined empirically to be roughly -l.25 (although some studies
support -1.50) for almost all clusters. Dressler (1978a) has determined LF for both
A2670 and A2029 in the F band for a = -1.25. In order to convert from F to R
bands, we need a B—V color for our ch. The V-R color for A2670 is 0.72, and
from Mackie (1992), V-R for A496 is 0.70, and B-V is 1.15. Also Oemler (1974)
ﬁnds that galaxies with late-type spectra have a J-F = 1.1:l:0.10, which supports
our assumed B-V color of 1.15. We can convert Dressler’s characteristic F-band
absolute magnitude into a R-band L..: for A2670 it is 6.9x1010 LG), and A2029,
2.7x1010. We also need values for No. Dressler chooses them such that the observed
total number of galaxies in his sample is returned when he integrates his LF. Doing
this integration, we ﬁnd No for A2670 is 51, and for A2029, 142. For Ltim, we use
the brightness of the faintest detected object as found by IRAF: 29.2 R mag/arcsec2

66

for A2670 and 25.8 for A2029. Now we can compute the following integral with the
simplifying assumption that the area of the contributing galaxy is not function of
luminosity:

LlIm/L.

N t
if / xa+ze_zdr.

 

0

The integral can be done numerically with a Romberg integrator (Press et al. 1992).
Combining all these quantities, the expected autocorrelation at small lags should be
0.011 / A for A2670 and 7.8x105 / A for A2029 if that signal is due to the faint end of
the Schechter LF. The autocorrelations shown in the ﬁgures all have been normalized
by the number of pixels at each separation. For A2670, there are roughly 82,000
pixels separated by 1 pixel used in the autocorrelation with smoothing aperture
radius of 33. For A2029, there are roughly' 72,000 for an aperture radius of 39.
Multiplying these normalization factors by the average amplitude, we have 0.276
for A2670 and 1.87x106 for A2029.

We have yet to deal with the area of the contributing faint objects. The ex-
pontential scale factor is obviously too large; the faintest object IRAF detects has
a radius of roughly a few pixels. The important question is whether or not we can
estimate the number of pixels separated by lags of 1 as the area and then treat
the area as independent of luminosity. As the luminosity get smaller, the area gets
smaller, and the integral goes to zero, suggesting that the largest objects contribute
most to the integral. We can not have an area less than one as these calculation-
8 might imply when compared to what is observed. Unfortunately, the integral is
somewhat sensitive to detection limit: a change in the magnitude to 28. (from 29.2)
increases the result to 0.077/ A for A2670. We may have to be satisﬁed that this

simple calculation yields a ballpark ﬁgure comparable to the measured amplitude

(A/D units“2)

AC

AC (A/D unitSAZ)

67

4e-06

 

3.5e—O6
3e-O6
2.5e-O6
2e-O6
1.5e-O6
1e-O6
5e-07

 

-5e-O7

 

 

 

O 5 10 15 20 25 30 35
radial separation (arcsec)

 

3e-O6

2e-O6

1e-O6

-1e-O6 - \

-2e-06 .

 

 

 

 

 

_3e-06 l I l l l l l
O 5 10 15 20 25 30 35
radial separation (arcsec)

Figure 19: Autocorrelations of the Inner Region of A2670.

4O

(A/D unitSAZ)

AC

(A/D uniCSAZ)

AC

68

 

2.58-06 I f I j I I I

2e—O6

1223-;

1.5e—O6

f

 

le-O6 ﬂ

I

5e-O7

 

 

 

 

O 5 10 15 20 25 30 35
radial separation (arcsec)

4O

 

I
-1e-O6 In
-2e-O6 -
-3e-O6 -
-4e-O6 A

 

 

 

 

 

_5e_06 l l l l 1 l l
O 5 10 15 20 25 30 35
radial separation (arcsec)

Figure 20: Auto-correlations for the Outer Region of A2670.

4O

69

(especially considering the guestimates involved) until more sophisticated methods

can be performed (e.g. a Monte Carlo calculation).
3.2.3 Wakes

We report the possible detection of wakes in deepest image of A2029. Five
galaxies have plume-like features associated with them, similar to those reported
by Lauer (1988). These features are just visible in our second image of A2029
with its poorer S/ N. Figure 21 shows the outermost contours of the candidate
galaxies with the direction to the cD indicated with an arrow. We note the distinct
curvature of isophotes which is very similar to the simulations of Weinberg (1989).
With the exception of the third and ﬁfth candidates, the wakes are oriented with
a larger radial component than tangential with respect to the cluster center. The
lowest isophote in each of these contour plots is roughly 0, and the interval is 25
A / D units. These features range from 5 to 150% of the diffuse light level in their
vicinity. Table 1 lists the following simple wake characteristics for candidates 1
through 5: the distance from the cD (R), diffuse light value at the galaxy position
(DL), an estimate on the projected radius of the galaxy (r9), the length of the wake
(1",), the magnitude of the galaxy (mg), and that of the wake (mm). The wake
luminosity was computed be averaging those points above the mean galaxy proﬁle.
The brightest wake is only ~ 10’2"5 its parent galaxy. The galaxy proﬁles do not
show any evidence of being abnormal in any other way: for instance, less peaked,

as might be expected if signiﬁcant material were stripped away from the center.

There are velocity measurements for two of the candidates (Bower et al. 1988).
Candidate 3 has a small radial velocity above the CBS (390 km/s) as compared to
the cluster dispersion of ~ 1430 km/s, which could suggest that much of the motion

is tangential, and if the direction of the plume is any indication, then the motion is

70

 

 

 

 

 

Figure 21: Contour Maps of Candidate Wakes, Candidate 1.

 

 

I
T

 

 

 

 

Figure 21 (cont’d): Candidate 2.

72

 

 

 

 

 

Figure 21 (cont’d): Candidate 3.

 

 

 

 

 

Figure 21 (cont’d): Candidate 4.

74

 

 

 

 

 

Figure 21 (cont’d): Candidate 5.

75

around the cD in the plane of the sky. Candidate 4 has a radial velocity above the
CBS (970 km/s) closer to the velocity dispersion and a wake that is slightly fainter
in relation to the parent galaxy than candidate 3. It is possible that it is orbitting

with a smaller component in the plane of the sky.

What is really necessary in this analysis is color. A difference in color between
the wake and parent galaxy, i.e. a wake color on par with the local color in the
cD envelope and not a continuation of the color of the galaxy proﬁle, would pro-
vide strong support for the candidacy. We do not have data available in another
wavelength to do this analysis. Equally substantial but more difﬁcult would be
measurements of the wake‘and galaxy velocity dispersion as compared to the local

cD envelope dispersion. Without such analysis, these wakes remain only candidates.

Table 1: Simple Wake Characteristics

 

 

R(”) DL(A/D units) rg(”) lw(”) m9(mag/arcsec2) mw(mag/arcsec2)

1 61.9 13.0 2.9 2.9 15.29 25.21
2 13.5 335. .80 2.3 18.18 25.25
3 21.9 375. 2.7 2.7 15.87 24.54
4 54.2 48.1 2.7 2.0 16.89 24.87
5 159. 35.3 1.9 2.1 17.99 24.06

 

 

CHAPTER 4

DISCUSSION

4.1 A2670

The smoothness in the diffuse envelope in A2670 is evident in the fact that we
see no departure from the de Vaucouleurs’ proﬁle as far as we can trace it. Oemler
(1973) reports a measurement of the green surface brightness proﬁle out to 750 kpc
(Ho = 50 km / s / Mpc). Figure 22a shows a de Vaucouleurs’ ﬁt (solid line) to Oemler’s
data (points) taken from his Figure 4. Figure 22b shows Oemler’s data (crosses)
and a de Vaucouleurs’ ﬁt (dashed line) to our data (points). It is evident from
these ﬁgures that his measurements from photographic plates are contaminated by
scattered light. If this correction were made, his faintest measurement (roughly 29
green mag / arcsecz) of the diffuse light would have come at roughly 300 kpc, instead
of 750 kpc. We measure a scattered-light—corrected red proﬁle out to a radius of

460 kpc, which is a fair extension of Oemler’s measurement capabilities.

Another point for comparison is the percentage of the diffuse light to the total
cluster light. Our measurement yields approximately 30i8% , where the uncertainty
is mostly due to our uncertainty in background corrections. Oemler reports 35%,
though he considers the envelope to be separate from the elliptical core of the cD
galaxy. He arrived at this number by calculating the scale factor that will allow
his envelope to match his cluster proﬁle (see his ﬁgure 6, the scale factor being

roughly 0.27). By assuming that the diffuse light is a percentage of the cluster light

76

 

‘Fr

77

(i.e. 100'27diffuse light = cluster light), he computes the ratio of the diffuse light to
diffuse light plus cluster light to be 0.35. We do not conﬁrm this-the diffuse light
follows the total cluster light for approximately 1’ and then clearly declines more

rapidly with radius.

We must address the notion of the halo as separate from the cD. There has been
work done (Schombert 1988) in which clusters were identiﬁed to have diffuse light
by an apparent break in the cD’s surface brightness proﬁle. Before the break, the
proﬁle belongs to the parent galaxy, and after the break, it belongs to the envelope.
According to Schombert, this characteristic break in the proﬁle occurs around 24 V
mag/arcsecz. We see no such break in the proﬁle of A2670 in either R- or V-bands,
although the proﬁle is not well ﬁt by any common function for radii less than 8” , and

2

this is roughly the point the V-band proﬁle becomes brighter than 24. mag / arcsec .

We contend that the cD and its envelope or the diffuse light are one entity.

The smoothness of this halo implies that the ICM is well-homogenized, suggest-
ing that it was formed during the initial cluster collapse. Also (following Merritt’s
argument), matter stripped by galactic collisions should move in orbits coincident
with those of the colliding galaxies. This implies that the density proﬁle of the
stripped matter should be more centrally concentrated than that of the galaxies as
the time for stripping to occur depends strongly on the galaxy density. Though we
found that the diffuse light extends about a factor of two less than Oemler quotes,
it is still hard to invoke collisions as producing the smooth halo radii beyond 3 core

radii where the density has already fallen by a factor of 2.

What is the source of the intra—cluster light or cD halo ? Our limits on the
variance-to-mean diffuse light ratio suggest the number of sources per pixel is large

(2 7.5x103). The luminosity of each source is less than 3.0x103 L9, which is about a

 

78

 

1.6 1.8 2 2.2 2.4 2.6
(arcsec)

.1.4
log radius

 

1.2

 

 

 

23
24
25
26
27
28
29
30
31
32

(zvsesole/ﬁem) qq ueexﬁ

Figure 22a: De Vaucouleurs’ Fit to Oemler’s A2670 Diffuse Light Measurement.

79

 

 

 

l l H l l I l m
+
‘1' 0Q
+ ”(3%

+ '6' g m

1- + g,“ "' ’

+ 3?. ' N

21'"
+ 088'
+ 6
.6 -

I- + 0° N
:0 A
+ .9 U
* 9 0
+ U)
9 m U
P- + 9.0 H o H

0 H
+ ,0 g

+
+ ° u)
+ .2
.- + _, H U
+ 16
+ H
+
0
.1.
+ 0
L l l l L I l O

 

18
20
22
24
26
28
30
32
34

(zvoesore/bem) qq uaexﬁ a a

Figure 22b: Oemler’s & De Vaucouleurs’ Fit to Our Diffuse Light Measurement.

 

80

factor of a hundred smaller than the luminosity of the faintest dwarf galaxies. This

suggests that the source of the diffuse light is stars, not faint unresolved galaxies.

Dressler (1978a) determined the LF of A2670 from photographic plates. Unfor-
tunately a direct comparison is impossible as we do not have sufﬁciently accurate
background measurements. Our DLF does suggest that there is a shortage of faint
objects (or overabundance of bright ones) within the extent of the halo. Our number
density of objects does not resemble the diffuse light proﬁle. The diffuse light signal
is not large enough for the statistical noise level near the cluster center to selectively
obscure faint objects in the central region. We also do not see a signiﬁcant increase
in the number density of bright objects in the center so as to attribute the lack of
faint galaxies to obscuration. A deﬁcit of faint galaxies might be caused by two
things. As the cluster tidal ﬁeld is larger in the center, the fainter galaxies might
have been tidally stripped. If mergers are more prevalent in the center (because the
density is higher) then more bright galaxies could be expected to live there, though
the current number density distribution (that we measure at this epoch) does not
reﬂect a great central enhancement. Alternatively, the apparent excess of bright
objects may be simply due to mass segregation, that is, brighter heavier objects

falling to the center due to dynamical friction.

One interesting question we can ask of the apparent deﬁcit is whether or not
there are enough missing objects to account for the diffuse light. If we integrate the
DLF, i.e. the number of objects per pixel weighted by the luminosity, we ﬁnd that
the faint objects fail to account for the diffuse light by about 2 orders of magnitude.
Surprisingly, the excess light from the bright objects is approximately the same

order of magnitude as the diffuse light.

The color gradient of the halo is a potentially very interesting diagnostic. It

81

could tell us how well the cluster is mixing material stripped from galaxies. It
could give information on the age of the central versus outer regions of the ICM, as
well as indicate possible regions of star formation. We can compare our estimate
of the halo color gradient with the range of values found by Mackie et al. (1990)
for the innermost regions of 14 central dominant galaxies. Considering only the cD
morphological type, the change in V-R color per kpc ranges between -0.002 to 0.013.
For BM class 1, they ﬁnd the average V-R gradient to be 0.000:l:0.002 mag/kpc.
These gradients were derived out to a maximum radius of 20 kpc (h = 1 / 2). In
these units, our gradient is —0.003(:t:0.001)/kpc, which we measure over roughly
210 kpc. Another comparison may be drawn with Mackie’s (1992) g—r measurements
of cD envelopes extending out to roughly 1’. For the 3 cD’s studied (A2589, A2634,
and A407), the author reports no evidence of excessive blue colors in the envelope,
while for A2589, the envelope becomes 0.2 mag redder than the nucleus at large
radii. Also, Schombert (1988) measured the B-V color of 3 cD galaxies (NGC 6034,
A1767-G1, and A1414-G1) and reported no evidence of strong color gradients or
blue envelopes. However, blueward gradients have been found in 5 out of 6 of the
ch studied by Valentijn (1983). For A496, he ﬁnds roughly a 0.6 mag drop in the
B-V color over 2’ along the semi-major axis. This is the same rough drop we see in

V-R for A2670.

The interpretation of color gradients by means of analysis of stellar populations
implies the sorting of various age and composition sub—populations. The lack of
a priori knowledge about the ages of the star populations in cD galaxies and the
metallicity abundances makes analysis of the color gradients difﬁcult. Blue halos
are expected in models in which the cD halos are formed from remnant material of

tidal interactions on the spiral galaxies in clusters (Ostriker 1977). This scenario

 

82

does not explain the observed very red nuclei of ch (Valentijn 1983, Mackie 1992
and references therein). Metal abundances are thought to inﬂuence the observed
colors of star populations in two ways. First when the metallicity of a given star
on the giant branch is increased, the effective temperature of the star is decreased
leaving its bolometric luminosity unchanged (Rood 1972). Tinsley (1978) estimated
the B-V color increases by 0.25 when the metallicity is increased from 0.01 to 0.04,
while Mould (1991) estimated the V-I color increases by 0.28. This color variation
is not enough to explain the color gradient reported here or by Valentijn. Secondly,
the appearance of hot horizontal branch stars in old metal poor populations affects
the color. However this phase is relatively short in a star’s evolution (O’Connnell
1982), and therefore the fractional contribution of the horizontal branch light in
a normal old metal population is small and never dominates in R- and V-bands
(Rabin 1980, Iben & Renzini 1983). The color-spectral index relation (Faber 1977,
Sandage and Visvanathan 1978, McClure et al. 1980) indicates that less luminous
galaxies are bluer and have lower metal indices and has often been interpreted as
the effect of metallicities on color. However, on the basis of an inverse correlation in
the line strength between the Balmer lines and the metallic lines in galactic nuclei,
Heckman (1980) has shown that the less luminous galaxies are bluer because of the

presence of a young stellar populations.

It seems plausible that the color gradient in the ch indicate ongoing star for-
mation as a consequence of gas-acretion processes. In this interpretation, the radial
color distribution should reﬂect the different rates of star formation and / or radial
dependence of the intial mass function of star formation. The detected light in the
cD halos should be a mixture of young and old stars. The young stars will dominate

the B—V, hence it is feasible to interpret the B-V gradients in terms of the properties

83

of a young population. The V-R color may represent more of a mixture. It might
be interesting to pursue observations of the halo color in the infrared with the hope

of learning more about the distribution of the older halo star population.

The focus of this study was to measure any departures of the diffuse light proﬁle
from the smooth de Vaucouleurs’ proﬁle. The autocorrelation has proven to be our
most sensitive probe. It has also allowed us to extract a potentially useful spatial
scale. Unfortunately, our two different methods of removing the diffuse light in
A2670 have not yielded comparable numbers (3” or 14”), though we are conﬁdent
we are measuring a signal not found in the outermost regions of the cluster. This
number describes a characteristic size of the clumpiness of the material giving rise
to diffuse light ﬂuctuations. These clumpings may well be unresolved galaxies in
the center of the cluster, although as we described earlier the diffuse light is much

too smooth to be composed entirely of unresolved galaxies.

If the autocorrelation gives a measure of the physical extent of the inhomogeni-
eties in the diffuse light, can these clumpings give us an estimate on the age of the
cluster ? That is, can we determine the timescale for an initial inhomogeneity to
evolve to the scale we measure ? If we have a clump in the density distribution we
can describe its motion with the continuity equation. Here we imagine the diffuse
light to be a relaxed group of background orphan stars which are on approximately
random trajectories such that they have a null group velocity, and the clump has a
group velocity resembling that of the galaxy it was stripped from. It is not difﬁcult
to show that the lifetime of the inhomogeneity goes as the time to orbit the cluster.
This once again suggests that the diffuse light is not currently being formed as it

takes far too long for inhomogenieties to smooth out.

On the other hand, these clumpings may represent the LF below our detection

84

limit. Our rough calculation of this contribution to the autocorrelation yields results
that are on the same order as what is observed (ignoring the unknown size of the
contributing objects). However, there is evidence that the LF function in the center
of A2670 is abnormal; i.e. there is a lack of faint objects from what is expected for a
Schecter LF. Our rough calculation certainly rules out an large upturn in the faint
end of the LF, implying that a Schecter LF is not that poor of a representation for
this region of the LF. A more sophisticated analysis, one in which the characteristics
of contributing faint galaxies are considered, will be necessary to validate the results

of our rough calculation. We might then be able to place tighter constraints on the

form of the LF.

Until recently, studies of clusters of galaxies with dominant ch have found
them at the kinematical center of the cluster (Malumuth et al. 1992 and references
therein). With the now larger sample of galaxies, several of the clusters have a
cD with a peculiar velocity of several hundred kilometers / second. For A2670, the
peculiar velocity is 439:1:119 km/s. The fact that A2670 and 16 other clusters
(although for an alternative perspective see Gebhardt & Beers 1991) with dominant
cD’s have signiﬁcant peculiar velocities poses a problem for current models of cluster
evolution which require the cluster be not only located at the center of the cluster,
but at rest with respect to the cluster as well. Merritt’s tidal truncation scenario
would make fast work of any large elliptical that spent a signiﬁcant time away from
the center. Another problem arises in how the diffuse light can remain smooth if
it is either attached to and moving with the cD at the peculiar velocity or if it is

somehow ﬁxed and the cD is moving through it.

We did a simple calculation of the damping time for a cD in a external potential.

The cD is bouncing back and forth within a tidal radius with an initial velocity of

85

the peculiar velocity. We chose two forms for density distribution of the ICM: either

homogeneous with a density

__ 902
p0 _ 41rGr3

where a is the velocity dispersion, G the gravitational constant, and r0 is the radius
at which the density falls to half its central value (taken as the cluster core radius),
or a King density proﬁle

Po
(1 +r2/r313/2'

 

W) =

A constant density gives rise to a harmonic oscillator force density, —41eror/ 3,
while the King density yields a more complicated expression for the force density,
but roughly equivalent results. We solve the following equation using a ﬁfth order
Runga Kutta method (Press et al. 1992):

dv M
dt

 

 

_ _ 2 L ”M _ 3'21 2:311
_ 47rln(A)G M012" [erf(\/§a) 1r 0' c ]+a(r).

The ﬁrst term is Chandrasehkar’s dynamical friction formula (Binney & Tremaine
1987) where v M is the velocity of mass M, ln A is the coulomb logarithm, and erf
is the error function. The second term is either expression for the external force
density. The constants were chosen to be a = 880 km / s, r0 = 160 kpc, M = 1013 M9,
and p0 = 5.0x106 MQ/kpc3. We make the following note on the choice of mass: the
M/ L of ~ 3 for galaxies and an absolute V magnitude of -25.2 for the cD (Oemler
1973) yields a lower cD mass bound of M = 3x1012 M0. Alternatively, Oemler
quotes a total mass for the cluster of 1.12x1015 to 1.89x1015 MG from velocity
dispersion measurements and a cluster M / L of 150 to 255 MG). Given the diffuse
light-to-total light ratio, it appears that 1013 M9 is a reasonable lower limit to the

cD mass. For the coulomb logarithm, we use our cD mass choice (the mass of an

 

86

ICM constituent being negligible), a maximum impact parameter of a core radius,
and a velocity far from the impact of the cluster velocity dispersion. With these

values, ln A is about 1.

We want to estimate the damping time for the cD. Is this the same as the cluster
age ? We are assuming that the cD has somehow already formed and has become
caught in the tidal ﬁeld. In this scenario, its peculiar velocity is either left over from
the formation process or it resulted from some impulsive interaction with another
body. If it is the former case, the damping time must be roughly the age of the
cluster for us to observe an anomolous velocity; if it is the latter, the interaction
had to happen long enough ago such that the halo could re-homogenize. As we
showed before, that timescale is roughly the orbital time of a test particle within
the cluster, which is ~ 109 yrs. For a range of initial distance from the cluster

center Sro and velocity 30, the damping time was consistently 2x109 to 3x109 yrs.

Malumuth (1992) has run more sophisticated N-body simulations in order to
understand the distribution of cD galaxy peculiar velocities. He also found that
cD’s form in poor clusters (100 galaxies) from the general population (after roughly
9 mergers) and relax to the center in about 3x109 yrs. The modeled distribution of
peculiar velocities viewed at a cluster age of 1010 yrs differs signiﬁcantly from the
observed distribution: it is hard to make enough cD’s with high peculiar velocities

due to the efﬁciency of dynamical friction and two-body relaxation.

What about the possibility of sub-clustering in A2670 ? As discussed by
Sharples et al. (1988), A2670 may be contaminated by a foreground sub-cluster.
They model this possibility with a primary cluster having the systematic velocity
of the cD and a secondary lower velocity component. With the entire sample of 220

galaxies, they can rule out this hybrid model with any choice of component sizes

87

to a conﬁdence interval of 2 95% level using the Kolmogorov-Smirnov test, except
when the components are equal. They also consider and rule out the possibility
of a clump of galaxies centered on the cD itself. (Although using mixture mod-
elling techniques, Bird 1993 reports a four-group split as the ”statistically preferred
model.” Three of the four groups have position centroids consistent with each other
within the 10' interval implying that a merging event may be occuring along the
line-of-sight to the system.) The picture favoured by us (and Sharples et al. 1988)
is one in which the cD galaxy formed relatively early in the cluster’s evolution; the
presence of a substantial peculiar velocity for the cD indicates the mixing process
is not yet complete. If there really is sub-clustering in A2670, we will then have an
even harder task to explain the smoothness of the diffuse light in the presence of

interacting sub-clumps.

4.2 A2029

UBK showed that the diffuse light proﬁle followed a de Vaucouleurs’ proﬁle out
to 425 / h kpc. Although we do not go out as far and do not correct for scattered light,
we conﬁrm the smoothness in the diffuse light proﬁle. UBK also report that the
isophotes have a constant ellipticity 0.90 at all radii. With slightly better resolution

data, it is apparent that the ellipiticity increases to 1. for radii less than 20”.

According to Schombert’s (1988) classiﬁcations, A2029 is technically not cD
because it does not have a diffuse light envelope as characterized by the inﬂection
in the surface brightness proﬁle. The velocity dispersion measurements as function
of radius (Dressler 1979) also show no inﬂection. Both suggest that the cD and

diffuse light are one entity.

Dressler (1979) also found no evidence of rotation within 30 kpc of the center

88

of the cD, but reports tenative results of rotational velocity of 100-200 km/s in
the outermost regions. Even if this rotation is real, comparison with the velocity
dispersion indicates that the cD is not supported primarily by rotation, as is the
case in elliptical galaxies. However, work by Bower et al. (1988) suggests there is
structure in the velocity ﬁeld; i.e. there exists a segregation of galaxies with slightly
positive velocities from those with slightly negative velocities. The authors suggest
two possible explanations. First, there may exist a sub-clump superimposed on
the core of A2029, which is not unlikely given the nature of hierarchical clustering.
Second, the entire system is rotating. This is contrary to the ”classical” picture of
cluster structure as the high velocity dispersion implies that the cluster core is not
in virial equilibrium. However, this effect may occur if the cluster has formed by

the decay of the a binary cluster.

The surface brightness ﬂuctuation measurements also indicate that the source
of the diffuse light is numerous (2300) low luminosity (S 3x105 Lg) objects. The
autocorrelation results indicate again that there is some clumpiness of material with
spatial scale ~ 17” more prevalent near the center of the cluster. What is new for
this cluster is 5 wake candidates. Extremely deep optical images were necessary
for the detection; the features were just visible on our data frame with 1.5 times
less S / N. Without color or velocity data, we have no conﬁrming evidence that these
features are really the wakes formed by the parent galaxy passing through the
diffuse light. Until those measurements are made, numerical simulations can be run
to calibrate the response of the diffuse light. This would allow a determination of
the mass of the impinging galaxy. We could check this mass determination against
that obtained with measurements of the parent galaxies’ luminosity and assuming

a standard M / L for cluster galaxies.

89

4.3 Concluding Remarks

We argue that the cD envelope is old (greater than 1010 yrs) as indicated by its
smoothness, but the cD velocity with respect to the cluster center (or the presence
of sub-clumps) is evidence for clusters youth (less than 1010 yrs). This is a curi-
ous problem for cluster evolution models. It will be interesting to perform similar
measurements for other cD’s with high peculiar velocities to see if they too appear
to be falling through the cluster potential, not disturbing its halo as it does so. If
all of these clusters also have large cooling ﬂows, indicating that the luminosity is
generated on short timescales, the halo velocity would then be decoupled from the
cD. Further, more sensitive, measurements of the diffuse light anisotropy may reveal
evidence for motion of the cD through the halo or multiple-nuclei interactions. If
these measurements show as little inhomogeneity as we report here, the currently

favored cluster evolution theories will have to be reconciled with overall smoothness

of the diffuse light.

Also of great interest would be further measurements of the velocity dispersion
of the diffuse light as function of position in the cluster. This would allow as study
of the dynamical anisotropy of the cluster. A continuous velocity dispersion proﬁle
(well past the 24-25 mag/arcsec2 reported inﬂection point in the surface brightness
proﬁle) would aid our understanding of the origin of the diffuse light, i.e. if the

inner and outer regions really have a different origin.

Finally, questions concerning the X-ray diffuse light should be addressed in a
manner similiar to what is discussed here. One might imagine that inhomogeni-
eties (e.g. Ha ﬁlaments, the ”evidence” for cooling ﬂows) in this proﬁle would be

correlated with those in the other wavelengths.

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