Lieder PhDT

Lieder PhDT
submitted to the
Combined Faculties of the Natural Sciences and Mathematics
of the Ruperto-Carola-University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
Put forward by
Stefan Lieder
born in: Torgau, Germany
Oral examination: May 26, 2014
stefan lieder
Priv.-Doz. Dr. Thorsten Lisker
Prof. Dr. Volker Springel
Prof. Dr. Klaus Meisenheimer
Prof. Dr. Ulrich Uwer
March 2014
Stefan Lieder: Fossil Groups in the Course of Galaxy Evolution © March 2014
Fossil groups are X-ray bright galaxy groups characterized by a central elliptical galaxy that
dominates the total light of the group in the optical. We present here a photometric analysis of
the nearest fossil group NGC 6482 down to Mr ' −10.5 mag — to our knowledge the deepest
fossil group study yet, which can probe its faint satellite system in a meaningful way. We find
signatures that the brightest group galaxy must have undergone a gas-rich merger in the past,
favoring the cannibalism scenario for NGC 6482, i.e., the brightest galaxies in the group center
have merged to form the dominant central elliptical. We find the faint-end slope of the luminosity function to be within the range of values typically found in ordinary cluster environments.
We thus conclude that the NGC 6482 fossil group shows photometric properties consistent with
those of regular galaxy clusters and groups, including a normal abundance of faint satellites.
We additionally investigate fossil groups in a state-of-the-art semi-analytical model. From a
sample of 59 fossil groups with masses comparable to NGC 6482 we find that their properties
are similar to non-fossil systems. Both reside in similarly dense environments and have similar
number density distributions of dwarf galaxies. We do not find a "missing satellite problem" in
the semi-analytical model. The faint-end slopes of the luminosity functions cover a range that
is covered by observations. In particular, the faint-end slope of NGC 6482 is in good agreement
with the slopes determined in the 59 fossil groups of the model. Specifically, we confirm the picture of a transient fossil phase as both fossil and non-fossil systems spent similar time periods
in the fossil phase. Therefore, this suggests that fossil and non-fossil groups are representations
of the same evolutionary track of ordinary galaxy groups, supporting the cannibalism scenario.
From the perspective of galaxy evolution there is no difference between fossil and non-fossil
Fossile Gruppen sind Galaxiengruppen, die im Röntgenlicht hell erscheinen und sich durch
eine zentrale elliptische Galaxie auszeichnen, deren optisches Licht das der gesamten Gruppe
dominiert. Wir präsentieren hier eine photometrische Analyse der nächsten Fossilen Gruppe
NGC 6482 bis zu aboluten Helligkeiten von Mr ' −10.5 mag — nach unserem Kenntnisstand
ist das die tiefste Studie einer Fossilen Gruppe, die es ermöglicht, deren System lichtschwacher
Galaxien aussagekräftig zu erforschen. Wir finden Anzeichen, dass die hellste Gruppengalaxie
einen gasreichen Verschmelzungsprozess hinter sich hat, was für das Kannibalismus Szenario
für NGC 6482 spricht, d.h., die dominante, zentrale Galaxie ist aus einer Verschmelzung der
hellsten Gruppengalaxien entstanden. Wir finden eine Steigung des lichtschwachen Endes der
Leuchtkraftfunktion, die in Einklang mit publizierten Werten normaler Galaxienhaufen ist.
Wir folgern daher, dass die Fossile Gruppe NGC 6482 photometrische Eigenschaften normaler
Galaxienhaufen und -gruppen besitzt, einschließlich eines normalen Reichtums lichtschwacher
Satellitengalaxien. Darüberhinaus untersuchen wir Fossile Gruppen in einem der neuesten
semi-analytischen Modelle. In einer Auswahl von 59 Fossilen Gruppen, mit Massen vergleichbar zu NGC 6482, finden wir heraus, dass diese Eigenschaften haben ähnlich derer nichtfossiler Systeme. Beide Typen befinden sich in ähnlich dichten Umgebungen und haben einen
ähnlichen Reichtum an Zwerggalaxien. Wir finden kein "missing satellite"-Problem im semianalytischen Model. Insbesondere bestätigen wir das Bild einer vergänglichen fossilen Phase,
da sowohl fossile als auch nicht-fossile Systeme ähnliche Zeiträume in der fossilen Phase
verbringen. Daher folgern wir, dass fossile und nicht-fossile Gruppen Repäsentationen ein
und derselben Entwicklung von gewöhnlichen Galaxiengruppen sind, was das Kannibalismus
Szenario unterstützt. Aus der Sicht der Galaxienentwicklung bestehen keine Unterschiede zwischen Fossilen Gruppen und deren nicht-fossilen Pendants.
1. Lieder et al. 2013, A&A 559, A67:
A normal abundance of faint satellites in the fossil group NGC 6482
refereed publication that is not part of this thesis
2. Lieder, Lisker et al. 2012, A&A 538, A69:
A deep view on the Virgo cluster core
This thesis contains no material that has been accepted for the award of any other degree or
Heidelberg, March 2014
Stefan Lieder
1.1 Cosmology
1.2 Structure formation
1.3 Galaxy classification and properties
1.4 Galaxy evolution and environmental effects
1.5 Fossil Groups
1.6 Thesis outline
ii observations
2 data
2.1 NGC 6482
2.2 Observations
2.3 Data reduction
2.4 Calibration
3 methods
3.1 SExtractor
3.2 Ellipse fitting
4 sample selection and photometric procedures
4.1 SExtractor and morphological classification
4.2 Color-magnitude diagram
4.2.1 Photometric procedure for magnitude and colour measurement
4.2.2 Fiducial sample definition via color-magnitude selection
4.3 Surface brightness profiles measurements
5 results
5.1 Spatial distribution
5.2 Photometric scaling relations
5.3 Luminosity function
5.4 The Brightest Group Galaxy NGC 6482
5.5 A disrupted galaxy around MRK 895
6 discussion and conclusions
6.1 Brightest group galaxy
6.2 Photometric scaling relations
6.3 Luminosity function
iii simulations
7 data
7.1 The Millennium-II Simulation
7.2 The semi-analytic model of Guo et al. (2011)
7.3 Selection of clusters and groups
8 definition and literature evaluation of fossil systems
8.1 The X-ray luminosity criterion
8.2 The magnitude gap
8.3 Finding elliptical galaxies
8.3.1 Ellipticals as passive galaxies
8.3.2 Ellipticals as bulge-dominated systems
8.4 Fossil groups as relaxed systems
8.5 Summary of selection criteria
9 history and properties of fossil systems
9.1 Fossil clusters
9.1.1 Properties
9.1.2 The fossil phase
9.1.3 Progenitor halos
9.2 Fossil groups
9.2.1 Properties
9.2.2 The fossil phase
9.2.3 The faint satellite system
10 discussion and conclusions
10.1 Fossil clusters
10.2 Fossil groups
v appendix
a data reduction
a.1 Bias correction
a.2 Flatfielding
a.3 Astrometric calibration 100
a.4 Background subtraction 100
a.5 Coadding images
b tables
Part I
About a hundred years ago, Einstein (1916) presented a set of equations to describe gravitational processes comprehensively. His theory, commonly known as General Theory of Relativity, treated gravitation as a geometrical property of space and time and gave physicists a tool
to answer fundamental questions about the Universe. In the 1920’s and 1930’s several scientists
developed a homogeneous and isotropic class of universe models based on a curved spacetime
that is the foundation of the cosmological standard model (Friedmann 1922; Lemaître 1927;
Robertson 1929; Walker 1935). Its application to Einstein’s field equations revealed that space
has an expanding nature. Independently, Lemaître (1927) and Hubble (1929) concluded that
an expanding universe causes the observed increasing recessional velocity1 of galaxies with
increasing distance from Earth. It was the first convincing cosmological evidence that the Universe is actually expanding. In return, Lemaître (1931) concluded that – if going back in time
– all energy must have been packed in a "unique quantum". The Universe began as a very hot
and very dense spot and is expanding since. This model of a hot Big Bang became the standard
model of cosmology (see the monumental Weinberg 1972 for a review).
In the 1960’s first doubts arose concerning the Big Bang model. In the Friedmann-LemaîtreRobertson-Walker (FLRW) models the Universe was nearly flat in the beginning and its curvature evolves away from flatness if the Universe is dominated by either matter or radiation. That
we seem to live in a flat universe today (Hinshaw et al. 2013) is a very special case and known as
the flatness problem (Dicke & Peebles 1979). On large scales, the Universe is homogeneous (Maddox et al. 1990). If this is a result of physical processes occurring shortly after the Big Bang, the
question arises how different regions right after the Big Bang can be causally connected since
information can propagate only with speed of light. In conclusion, the large-scale homogeneity
must be an initial condition. This striking problem is called horizon problem (Rindler 1956 for a
general discussion, McCrea 1968 and Misner 1969 for the first awareness of the problem, and
the celebrated Dicke & Peebles 1979 for a review). Another problem is given by the structure of
the present universe. Stars, galaxies and galaxy clusters have grown by gravitational instability.
There must have been a seed for this growth. A causing perturbation must also be considered
as initial condition for the Big Bang – known as structure problem. Guth (1981) and Linde (1982,
1983) proposed a phase of accelerated expansion in the very early universe – called inflation –
in order to solve all the three mentioned problems. The phase is characterized by a domination
of vacuum energy – which Einstein called cosmological parameter Λ in his equations – that
drives the Universe naturally flat. It suggests that our universe even today is practically flat.
This is supported by observations as indicated in Fig. 1.
Inflation also solves the horizon problem since the region in causal contact becomes arbitrarily large between the Big Bang in the inflationary phase. According to the theory by Guth and
Linde, at temperatures greater than 1027 K (Grand Unification) matter was in a state known in
1 Hubble took spectra of galaxies and observed that they were redshifted. He supposed that the redshift origins from
a Doppler shift, i.e., the galaxy is moving away from us – it recedes. The farther away a galaxy the longer it took the
light to reach us but also the higher its redshift as Hubble observed. Therefore, redshift describes the same fact (in
a first approximation) as lookback time and distance do. In astronomy, those three expressions are often arbitrarily
replaced by each other.
quantum field theory as vacuum. In this vacuum, quantum fluctuations can occur, i.e., temporary changes of the amount of energy in a point in space as predicted by Heisenberg’s uncertainty principle. For a virtual time ∆t a particle-antiparticle pair with the energy ∆E is created.
During inflation the scale length of quantum fluctuations grow faster than the horizon expands
so that initially causally connected quantum fluctuations become suddenly supra-horizon (curvature) perturbations. After inflation, the horizon continues to expand and the perturbations
cross the horizon again and become true density perturbations (see Lyth & Riotto 1999 for a
review on physical models of inflation). These density perturbations will cause gravitational
Summarizing, quantum fluctuations are proposed to cause density perturbations which are
the seeds of the structures of the Universe we observe today. Thus inflation predicts structure growth (see Sect. 1.2). Guth (1981) also mentions that all initial inhomogeneities and
anisotropies are smoothed and inflation naturally results in a "huge region of space which
is homogeneous and isotropic". Inflation is thought to end in a transition phase when "inflating" matter is converted to ordinary matter (including dark matter, see below) and radiation.
But in this picture the Big Bang is not looking like an expanding fireball anymore (Linde et al.
1994). Instead, we are now considering a huge amount of inflating balls (Guth calls it "bubbles")
producing new balls, producing new balls, etc. And although inflation solves many problems
and plays a major role in cosmology, it should kept in mind that it is only a hypothesis and not
supported by any other field of physics.
Following inflation, the Universe was very hot and radiation-dominated. Photons can create
spontaneously matter–antimatter pairs which again "immediately" annihilate. A macroscopic
separation of matter from antimatter therefore should be excluded. One the other hand, today we observe a matter-dominated universe. It was pointed out first by Sakharov (1967) that
baryon number violation (essentially needed to form a baryon excess), CP and C violation as
well as interaction without being in thermal equilibrium (both to maintain the baryon excess)
are conditions that can form a matter-dominated universe. The interested reader is referred to
Dine & Kusenko (2003) for a review of baryogenesis – how the baryon excess is formed. As a
result of this asymmetric process we can assume that once the temperature of the Universe has
dropped below ∼ 1012 K, approximately 10−4 s after the Big Bang, its constituents are all known
(and unknown) matter particles like photons, electrons, neutrinos, protons and neutrons, and
maybe a species of dark matter (see Sect.1.2). As the Universe continues to expand, particles
drift out of thermal equilibrium. About 1s after the Big Bang at temperatures around 1010 K
weak interactions, that had kept neutron/proton ratio in equilibrium, were not possible anymore so that this ratio was frozen at 0.25 (Beringer et al. 2012). But long before the remaining
free neutrons decayed, nucleosynthesis began.
Today we know that the abundance of 4 He as compared to hydrogen in stellar atmospheres
is in the range of 0.2 6 Y 6 0.3 in mass units (see e.g., Caloi & D’Antona 2007; Tremblay
& Bergeron 2008). Even in the 1940’s it was known, that the He/H ratio was much higher
(Unsöld 1944; Schwarzschild 1946) than hydrogen burning in stars can account for (simple
calculations show that Y ' 0.05, Bartelmann 2010). Thus, the observed abundance of 4 He is
unlikely produced in stars and we need to consider that 4 He was in place already before stars
have been formed. In the 1940’s nuclear physicists began to work out how nuclear fusion may
have proceeded in the early universe. Gamow (1946) gave the important note that in the Big
Bang model "the conditions necessary for rapid nuclear reactions were existing only for a very
short time (∼ 102 s), so that it may be quite dangerous to speak about an equilibrium state" like
the process of hydrogen burning in stars. The important step in 4 He fusion is the fusion of
deuterium because it is more efficiently able to fuse to 4 He than pure hydrogen.
1.1 cosmology
Figure 1: Parameter space for cosmological FLRW models in which the current radiation density is negligible. The
solutions are parametrized by the current matter density ΩM and vacuum/dark energy density ΩΛ , both relative
to the critical density. A flat universe as expected from inflation corresponds to ΩM + ΩΛ = 1. Shaded regions
belong to 1σ, 2σ and 3σ confidence regions and are constrained by independent measurements of the CMB
fluctuations (CMB), baryon acoustic oscillation (BAO) and the Supernova Cosmology Project (SNe), respectively.
The measurements indicate that we are living in a flat universe dominated by dark energy, i.e., the expansion
of the Universe is accelerating. Figure taken from Amanullah & the Supernova Cosmology Project (2010), their
Fig. 10.
Alpher et al. (1953) reason the early period of the standard model of nucleosynthesis. By
that time it was clear that no other stable nuclei with mass numbers between 5 and 8 exist
(but traces of D, 3 He and 7 Li which are used to end up in 4 He, see Tytler et al. 2000; Beringer
et al. 2012 for a review). The conditions needed for nucleosynthesis (temperatures around 109 K)
were in place about 100s after the Big Bang. While the Universe expands, its temperature drops,
being unable to produce heavier stable elements so that after 100s more the Universe was too
cold and nucleosynthesis was essentially completed. Thus, cosmological nucleosynthesis can
only generate light elements (H, D, 3 He and 4 He) and heavier elements are the result of further
processing in stars. Beringer et al. (2012) estimates a 4 He mass abundance of Y ' 0.25, i.e., the
Big Bang model predicts that 25% of mass has been produced in primordial Helium, strongly
in agreement with observations.
Based on temperature estimates at nucleosynthesis, Gamow (1948) showed that the energy
budget in the early universe must have been dominated by radiation. He introduced the concept to put the radiation to the epoch when matter and radiation energy densities had the same
amplitude – about 60.000 years after the Big Bang. At this time, matter was still fully ionized
(T ' 3.000K) and the plasma was locked to the photons by Thomson scattering. As the Universe continues to expand, ∼ 400.000 years after the Big Bang electrons and protons combined
to form neutral atomic hydrogen. After this recombination, photons could move relative to the
baryonic matter so that the Universe became transparent and the photons kept their properties
from their last scattering – a black body spectrum.
Based on temperature estimations from nucleosythesis, Alpher & Herman (1948) predicted
a radiation corresponding to a present time temperature of the order of 5 K. It was an antenna
"temperature excess" of 3.5 ± 1 K, accidentally found by Penzias & Wilson (1965), that Dicke
et al. (1965) identified as the cosmic microwave background (CMB) radiation – a relic of the
Big Bang. The Cosmic Background Explorer (COBE) satellite (Mather et al. 1990) has shown
that the CMB radiation occurs as an almost ideal black body radiation with a temperature of
2.725 K (Fixsen 2009). This is a strong evidence for the Big Bang theory since photons can be
thermalized in less than a Hubble time (see below) only from a hot, dense initial state (Binney
& Tremaine 2008).
In 1970, Peebles & Yu and Sunyaev & Zeldovich, independently, investigated density perturbations (see above) which lead to the formation of structure in the Universe, i.e., to formation
of galaxies (see Sect. 1.2). They predicted that these perturbations should excite sound waves
in the relativistic plasma which cause spatial fluctuations in the CMB radiation with an amplitude of the order of 10−4 which subsequently were not found. Already thirty years earlier
Zwicky (1933) and Oort (1940) found by the analysis of velocity distributions in galaxy clusters and galaxies that most of the containing matter is non-luminous – Zwicky called it dark
matter. Peebles (1982) came up with a solution of the seemingly non-existing CMB fluctuations
if connecting it to the dark matter. Given that dark matter consists of "very massive, weakly
interacting particles and that the primeval fluctuations were adiabatic2 ", the fluctuations in the
CMB may be of an order of magnitude lower than originally predicted.
In simulations by Davis et al. (1985) it turned out that the cosmological structure formation
can be only explained if the dark matter was cold already in the early universe, i.e., its thermal velocity was negligible as compared to the Hubble flow3 (Blumenthal et al. 1984; Bond &
Efstathiou 1984). Finally, COBE discovered the predicted CMB anisotropy at the expected amplitude (Smoot et al. 1992) and dark matter became "confirmed" part of our universe. Follow-up
missions WMAP (Spergel et al. 2003; Hinshaw et al. 2013) and Planck (Planck Collaboration
2013) increased the spatial resolution of the temperature anisotropies significantly and put narrow constraints not only on the dark matter content of the Universe (see Hu & Dodelson 2002
for the effects of cosmological parameters on the CMB anisotropies).
There have been tremendous efforts to determine precisely the key cosmological parameters
describing our universe using different approaches, like:
• type 1a supernovae luminosities and light curves at different distances (Riess et al. 1998;
Perlmutter & Supernova Cosmology Project 1999; Suzuki et al. 2012),
• Cepheids and type 1a supernovae using the Hubble Space Telescope (HST, Freedman
et al. 2001; Riess et al. 2009),
• the anisotropies of the CMB by Wilkinson Microwave Anisotropy Probe (WMAP, see
also Sec. 1.2, Spergel et al. 2003; Hinshaw et al. 2013) and Planck (Planck Collaboration
2 Also known as curvature perturbations because they induce inhomogeneities in the spatial curvature. Adiabatic
perturbations correspond to fluctuations in the energy density of a system.
3 The Hubble flow is the motion of galaxies due to the expansion of the Universe.
1.2 structure formation
• and the baryon acoustic oscillation (BAO), an imprint of the plasma sound waves on
large scale galaxy structures (Eisenstein et al. 2005; Blake et al. 2011; Beutler et al. 2011;
Anderson et al. 2012).
The expansion of the Universe can be expressed by the Hubble parameter which varies with
time. Of cause, it can be taken as a constant at present time – commonly termed Hubble constant
H0 – and represents the proportionality of recession velocity and distance found by Lemaître
(1927) and Hubble (1929) as mentioned above. Those measurements which focussed on the
Hubble constant revealed values in the range 67.3 6 H0 6 74.2 km s−1 Mpc−1 . The inverse of
the Hubble constant has the dimension of time and is called Hubble time. Under the assumption
of a uniform expansion, it would correspond to the age of the Universe. But as a consequence
of the FLRW metric the expansion depends on the ratio of mass to dark energy. Since this
ratio can vary with time, the Universe may either accelerate or decelerate and the age of the
Universe needs to be corrected. Using a Hubble constant of 69.7 km s−1 Mpc−1 , the Hubble
time is ' 14.0 Gyr which gives an age of the Universe as t0 ' 13.76 Gyr (Hinshaw et al. 2013).
Hence, the expansion in past was almost uniform and the Hubble time can be used as proxy
for the age of the Universe.
Two more points are worth mentioning regarding the cosmological measurements. First,
the baryon content of the Universe makes up 4.6% whereas the dark matter comprises 23.6%
(Hinshaw et al. 2013; Planck Collaboration 2013). Hence, the dominant matter component in
the Universe interacts only gravitationally (and maybe through weak interaction). It is pointed
out above (and in Sect. 1.2) that it has to be "cold", therefore it is dubbed cold dark matter.
Second, since measurements of the cosmological parameters are determined independently,
they constrain the model of the Universe using FLRW metric without any assumptions. The
anisotropies of the CMB as well as the BAO and the Supernova measurements in union yield a
universe with almost perfectly flat geometry that requires a significant amount of dark energy
at present time (∼ 71.8%, Hinshaw et al. 2013; Planck Collaboration 2013). That means, the
expansion is accelerating or in other words, the Universe has entered a second phase of inflation
(see Fig.1).
Summarizing, the inflationary Big Bang theory is strongly supported by observations but
it needs an invisible matter component (CDM) and an unknown (dark) energy component –
corresponding to Einstein’s cosmological constant Λ. This thesis is based on the ideas of this
ΛCDM universe and in particular use measurements of its cosmological parameters.
structure formation
The primary process for formation of large-scale structures in the Universe is gravitational instability. But the detailed growth depends on the nature of the initial fluctuation. Jeans (1902)
discovered that gas pressure prevents gravitational collapse on small spatial scales and can
cause acoustic oscillations in the mass density as pressure and gravitation balance. On large
scales gravitation dominates and mass density inhomogeneities grow exponentially with time.
The growth of structure by gravitational instability is accurately described by linear perturbation theory but the growth of small density and velocity perturbations must take into account
expansion. Lifshitz (1946) put structure formation on a relativistic perturbation foundation as
he worked out how density perturbations grow outside the horizon (during inflation). In luminous galaxies the density is many orders of magnitudes larger than the critical density. Galaxy
formation therefore needs highly non-linear density fluctuations. Zel’dovich (1970) gave an approximate solution for the growth of large density perturbations. Although his approximation
breaks down as the non-linear evolution proceeds, it allows the computation of gravitationally
collapsing matter and arrives at the conclusion that the collapse must be anisotropic. This leads
to disk-like structures which will appear as filaments and sheets (Doroshkevich 1970; see below). Moreover, it provides an explanation for the origin of the angular momentum of cosmic
structures. The whole formalism of non-linear perturbation and its application to cosmology is
reviewed by Bernardeau et al. (2002).
When radiation decouples from matter during recombination, the Jeans analysis of a gas mix
of hydrogen an helium at a temperature of T ' 4000K shows that baryonic clouds with masses
larger than 106 M (solar masses) collapse gravitationally (Doroshkevich et al. 1967; Peebles
& Dicke 1968), i.e., stars with masses we see today should not be formed from these clouds.
Silk (1968) showed that the photon-baryon fluid becomes less perfect during the expansion.
While photons are still coupled to the baryons the mean free path increases. Viscosity and
conductivity are large, leading to a damping of fluctuations smaller than the horizon. This
Silk damping essentially eliminates all fluctuations on scales smaller than 10 Mpc or 1014 M ,
respectively. Hence, galaxy sized perturbations are washed out.
As pointed out in the previous section, dark matter (DM) is the key to explain the fluctuations
in the CMB radiation, i.e., for galaxy formation (Peebles & Yu 1970; Peebles 1982). DM particles
are considered to be collisionless and not interacting electromagnetically (as well as strongly)
so that photon pressure does not affect them. The motion of relativistic DM particles will wash
out any perturbation because the particles can freely propagate from overdense to underdense
regions (free streaming). Once the particles cool down, i.e., they have non-relativistic thermal
velocity, free streaming is not important anymore and the particles can clump (Blumenthal
et al. 1984). According to the epoch when DM particle become non-relativistic, DM is called
cold (very early), warm (early) or hot (late)4 . Basically, the more massive the DM particle is,
the earlier it will cool down and become non-relativistic. Free streaming is the reason, why the
only known DM candidate, the neutrino, is not viable for DM because it is hot (Shandarin et al.
1983; White et al. 1984).
It has been shown by Davis et al. (1985) that cold DM is able to reproduce large scale structures of the Universe and can explain the CMB anisotropies the best. Such weakly interacting
massive particles (WIMPs) that lack strong and electromagnetic interaction have not been discovered yet and are only predicted if the standard model of particle physics is extended5 .
Since small-scale fluctuations in the CDM are not subject to Silk damping, after recombination
baryons can fall into potential wells already generated by CDM clumps. Baryon density fluctuations can then grow faster in those and the gas clouds will fragment (Hoyle 1953) and collapse
gravitationally, igniting star formation (Abel et al. 2002). During the collapse, gas dissipates
energy, which along with angular momentum conversation leads to the formation of protogalaxies containing disk structures as shown by Larson (1976) and Fall & Efstathiou (1980).
As outlined in Sect. 1.1, baryons have decoupled at redshift z ' 1100, 4 × 105 years after the
big bang6 , and could form neutral hydrogen and helium (Spergel et al. 2003). Additionally, the
photon pressure lowered and the atoms have fallen into the potential wells of the preexisting
DM overdensities. Hydrogen and helium atoms will settle down and undergo violent relaxations as they can collide (see below). Therefore, they will be heated an get exited, resulting
4 The reference to "early" and "late" is given by the epoch and the corresponding radiation temperature when the
largest galaxy-sized perturbations (M ' 1013 M ) enter the horizon (Blumenthal et al. 1984).
5 There a many WIMP candidates with masses > 1GeV available in Supersymmetry. The thermal motion of such a
particle would become non-relativistic at temperatures of ∼ 1013 K corresponding to a cooling time of 10−6 s after the
Big Bang – long before recombination. See Jungman et al. (1996) for a review on supersymmetric WIMP candidates.
6 As pointed out in footnote 1, age of the Universe t (likewise the lookback time) and the spectroscopic redshift z of
galaxies are cosmologically correlated as t(z) ∝ (1 + z)2/3 .
1.2 structure formation
in emission of photons and free electrons. These electrons then can be used to form molecular
hydrogen, radiating at lower temperatures. Thus, by radiation the atoms and molecules loose
energy enabling them to cool. Due to that dissipational process baryons cool faster than the collisionless DM particles. This is probably the reason why we observe more baryonic mass than
DM in the centers of galaxies (Cappellari et al. 2006). The gas will sink down to the bottom of
the DM potential wells and condense into clouds which eventually collapse gravitationally so
that stars can be formed. These first stars were not polluted by metals7 , but we do not know
how they looked like and we do not know their typical mass.
However, the CMB provides evidence8 for a great ionizing radiation at z ' 10 (Hinshaw
et al. 2013). In the framework of the described picture, this suggests that during this period,
400 million years after the big bang, first stars must have ionized the surrounding gas. Since
temperatures > 104 K are needed to ionize hydrogen (for helium it is even more), the first stars
must have been very massive (∼ 100 M , see Abel et al. 2002). With the growing number of
those stars, the fraction of ionized gas increased and until z ' 6 the Universe was completely
filled with ionized intergalactic medium9 (Kashikawa et al. 2006). The whole process is called
reionization because the Universe has entered a second epoch of ionization after decoupling (see
Chap. 6 of Barkana & Loeb 2001 for a review of reionization).
Let us continue with the collapse of DM halos, which one can think of the "top hat" model
of a sphere (Padmanabhan 1993). In a homogeneous universe the matter outside this sphere
will not exert any forces on the particles within it. Basically, the larger the density within
this sphere the faster the particles within it will collapse. In practice, density fluctuations are
neither spherically symmetric nor isolated and as the sphere collapses the particles within it
will undergo violent relaxation10 and settle into virial equilibrium11 . This configuration is called
a halo and the whole process is often referred to as virialization. During the collapse the density
of the halo inceases and its radius shrinks. The oldest halos have had the most time to collapse,
being able to form the highest densities. That is indirectly seen in Fig. 2. Lacey & Cole (1993,
see their Appendix A) calculate a lower limit for the radius within a galaxy cluster is in virial
equilibrium – the virial radius. They estimate the density within this sphere with ' 178 times
the critical density of the Universe (that is needed for a region to collapse). At larger radii, i.e.,
in regions with lower density, the sphere can not be relaxed and in virial equilibrium. In galaxy
clusters, the region denser than 200 times the critical density often is considered to be in virial
equilibrium. The virial radius then is labeled r200 or rvir and the mass enclosed by that radius
is called the virial mass (M200 or Mvir ), often considered to be the cluster mass. However, even
the relaxed core of a galaxy cluster will be disturbed if new galaxies fall in and join the cluster.
Critical to any theory of structure formation is the prediction of the abundance of halos, i.e.,
the number density of halos as a function of mass. From that prediction constraints can be
drawn towards the abundance of galaxies in the Universe. A successful analytical model to
gain understanding of the physics of structure growth was developed by Press & Schechter
(1974). The so-called Press-Schechter theory is based on the ideas of density perturbations, linear
7 In astronomy, all elements heavier then He are termed metal, basically all elements which were formed in stars.
8 The CMB appears to be polarized. The degree of polarization depends on the probability that a CMB photon has
been Thompson-scattered since recombination. From the degree of polarization the redshift of reionization can be
estimated from the optical depth with respect to Thompson scattering (Haiman & Holder 2003).
9 This is known from the most distant galaxies, quasars, that show inhomogeneous distributions of neutral hydrogen
and helium in their spectra.
10 Relaxation is produced by collective gravitational effects. As a result, Lynden-Bell (1967) showed that relaxation
occurs "violently", i.e., the energy of a particle is changed significantly on very short time scales.
11 A state with, on average, balanced kinetic and potential energy. See e.g. Binney & Tremaine (2008) for a derivation
of the virial theorem for a gravitational potential
gravitational growth, and spherical collapse. While this theory considers only one particular
characteristic volume from which the halo distribution is calculated, Bond et al. (1991) extended
this picture by including the effects of other volumes, i.e., they incorporated accretion and
mergers. Basically, the outcome of the model is a mass function that grows exponentially on
the low-mass side. Above a characteristic halo mass, the number density declines rapidly, i.e.,
for massive halos. The exact behavior of the low-mass end depends on the shape of the initial
power spectrum of the perturbation. Based on these ideas, Schechter (1976) proposed an analytic approximation for the luminosity function (LF) of galaxies which has the same form, but
it relates the luminosity of galaxies to the number density distribution. For a sufficient large
volume, such as galaxy clusters, the Schechter function is a good representation of the LF as
illustrated in Fig. 4b, and is generally in use (Croton et al. 2005; Faber et al. 2007). In particular,
the logarithmic faint-end slope is of interest when observational studies are compared to each
other as well as to simulations (Bell et al. 2003; Li & White 2009).
Gravitational N-Body simulations which follow the way that gravity enhances the small
initial ripples in the ΛCDM universe show that small DM halos evolve from the initial DM
fluctuations (Springel et al. 2005b; Boylan-Kolchin et al. 2009). Galaxies would be build from
successive merger of smaller DM (sub)halos containing the first stars. This picture is called
bottom up or hierarchical scenario because galaxies form early and then fall together to form
clusters and larger structures (Searle & Zinn 1978). Massive galaxies are therefore built up of
smaller fragments, i.e., their progenitors, or building blocks, can be considered dwarf galaxies
(Read et al. 2006; see also Sect. 1.3). All these halos will evolve in a sense that they grow and
merge with time to form the filamentary cosmic web that we observe today (see Fig. 2, but also
Colless et al. 2001).
Based on the inhomogeinities of the CMB (from WMAP), Sánchez et al. (2006) calculated
how DM particles must have been distributed at recombination and how the halos became
denser while they accreted baryonic matter. They then compared the obtained matter power
spectrum (based on ΛCDM cosmology) with the results of the spatial distribution of galaxies
from the 2dF Galaxy Survey (Colless et al. 2001). They found that both power spectra agree
in the region where they overlap, i.e., on these scales the distribution of luminous galaxies is
identical with the expected DM halo distribution as indicated in Fig. 2. This strongly supports
the above described picture of galaxy formation, based on ΛCDM.
Although the great success of the ΛCDM cosmology is to explain the homogeneous and
isotropic CMB and its anisotropies connecting it with the distribution of galaxies as we observe
it today, it suffers from some difficulties. On the one hand, there is the so called missing satellite
problem. As computer capabilities increased and simulations were able to mimic less massive
halos, it turned out that the simulations based CDM overpredict the abundance of faint satellite galaxies both in galaxy groups12 and Milky Way sized systems by roughly an order of
magnitude (Moore et al. 1999; Klypin et al. 1999). One possible explanation for this problem is
the suppression of star formation in low mass halos by supernova feedback, yielding literally
"dark" halos which we can not observe (Kauffmann et al. 1993, see Sect. 1.4). Moreover, different
environmental effects may cause the lack of substructure as indicated by Simon & Geha (2007).
Recent investigations show that the missing satellite problem can be solved if DM is warm,
comprising of massive particles of ∼ 1 keV (Smith & Markovic 2011; Lovell et al. 2012)
Another difficulty arises from cosmological N-Body simulations. Navarro et al. (1996) found
that, regardless the applied cosmology and power spectrum, DM halos settle down to an universal mass density profile (NFW profile). It is a two-power law, i.e., a power law at both largest
12 The difference between a galaxy group and a galaxy cluster is basically defined by the number of members. While
a group consists of some dozens to some hundred galaxies, a cluster of galaxies has some thousand members.
1.2 structure formation
(a) Sloan Digital Sky Survey (Blanton 2008)
(b) Millenium Simulation (Springel et al. 2005b)
Figure 2: (a) Galaxy distribution of the nearby universe as observed by SDSS. Galaxies are color-coded according
to the age of their stars. The redder, more strongly clustered points show galaxies made of older stars. The
outer circle is at a distance of ∼ 800 Mpc, which is approximately the side length of the box in figure (b). The
lower slice is thinner than the upper slice, so it contains fewer galaxies. (b) Dark matter density field at present
time as calculated by the Millenium Simulation. Halos are color-coded by density and local dark matter velocity
dispersion. The simulated universe is homogeneous and isotropic on large scale but on small scales structure
becomes prominent. Due to its appearance these filaments (in interplay with the less dense voids) are called the
cosmic web. The comparison of both images shows that the structures of the densest regions (filaments) in the
simulations can be identified with the filaments of the oldest galaxies.
and smallest radii with a smooth transition. While the profiles are steep in the center, they are
shallow near the virial radius. At smallest resolved radii, those central cusps have been found
in both galaxies and galaxy clusters using different techniques (Hayashi et al. 2004; Sand et al.
2004). The conflict arises from the apparently non-existing cusp in low surface brightness and
dwarf galaxies (McGaugh et al. 2003; Spekkens et al. 2005). Those cored halos may be also indicated by the non-detection of WIMP annihilation gamma-ray signals in 25 dwarf galaxies,
provided a cuspy DM profile (Strigari et al. 2008b; Fermi-LAT Collaboration 2013). But the lack
of annihilation signals can also indicate that WIMPS, i.e., CDM is not suitable for our universe.
On the other side, Macciò et al. (2012) show that warm DM is not viable either. A possible
solution to the problem is provided by other studies (Navarro et al. 2004; Merritt et al. 2005,
2006) which indicate that density profiles of DM halos have an approximate universal form
that is better described by an Einasto (1965) profile. It is a single power law and has the same
mathematical form as a model which is used to describe surface-brightness profiles of galaxies
(Sérsic profile, see Sect. 1.3) but it is fitted to the space density, without any cusp. In either
case, one has to keep in mind that both the NFW and the Einasto profiles generally try to fit a
spherically symmetric model to the approximate triaxial ellipsoids of DM halos, and yield an
accuracy of the order of 5% (Navarro et al. 2010). Both are thus good approximations for the
density distribution in DM halos.
There is another point to mention regarding the DM profile in halos. In galaxies it is often
assumed that their gas is in hydrostatic equilibrium13 . This condition allows a direct determination of the galaxy’s total mass because we know how much gravity is needed to prevent the
13 i.e., the systematic and turbulent hot gas velocities are subsonic
gas to escape (Mathews & Brighenti 2003). From the thermal X-ray spectrum of the hot gas
temperature profiles can be gained in order to estimate the virial mass of the galaxy (stars and
DM) using a NFW profile for the DM. Thus, it can be used to constrain the DM content of
the galaxy (see e.g., Humphrey et al. 2006). The same technique can be applied to the brightest
cluster galaxy (sitting in the center of a galaxy cluster) to measure the dark matter distribution
of a whole galaxy cluster (Pointecouteau et al. 2005; Vikhlinin et al. 2006).
As computer technology advances, large N-Body simulations are able to produce DM structures in great detail (see Fig. 22; Springel et al. 2005b; Boylan-Kolchin et al. 2009; Klypin et al.
2011). They predict overdensities and underdensities, manifested as sheets, filaments and voids
– observed large-scale structures14 described by (Geller & Huchra 1989) and (Gott et al. 2005).
However, all these simulations lack an important ingredient – baryons. They deal with DM only,
because the calculations for billions of particles are time consuming, even when considering
only one kind of interaction (gravitation). The physics of real galaxies is much more complicated. Here, so-called semi-analytic models (SAM) come into play, originally proposed by White
& Frenk (1991). These incorporate, e.g., feedback from supernovae, gas cooling, star formation
or the effects of galaxy mergers (see e.g., Kauffmann et al. 1993; Lacey & Cole 1993; Cole et al.
1994; Somerville & Primack 1999, but also Sect. 1.4). These processes are usually based on theoretical models but include observationally based assumptions, like the Tully-Fisher relation
of spiral galaxies (see Sect. 1.3). That is, the model is tuned to fit observations in order to investigate how galaxies may have evolved. Today, these models are advanced and predict many
properties of galaxies and galaxy clusters (see, e.g., Bower et al. 2006; de Lucia & Blaizot 2007;
Guo et al. 2011). In particular, the galaxy catalogs of SAMs are a valuable tool to constrain the
expected distribution of galaxies along the line of sight. However, these catalogs still have some
short comings since certain properties of semi-analytic galaxies are not yet in perfect agreement
with observations (Guo et al. 2011, 2013).
This thesis will make use of the concepts introduced in this section. In particular it will make
use of the semi-analytic model by Guo et al. (2011) that is tuned to fit the low-redshift galaxy
population and is based on the Millenium-II Simulation by Boylan-Kolchin et al. (2009). On
of the goals is to figure out if the missing satellite problem still present (by means of the LF’s
faint-end slope), even though baryonic processes have been taken into account.
galaxy classification and properties
There is a variety of galaxies across the sky. The intuitive approach to classify those is to order
them by morphology. Based on earlier studies, Hubble (1926) introduced a scheme that divided
galaxies into diskless (ellipticals, E) and disk galaxies (spirals, S). While elliptical galaxies were
subdivided according to their elongation/ellipticity (E1 through E7), spirals were differentiated by the size of the nuclear region, how tightly spiral arms are wound and the degree of
condensation in the arms (Sa through Sc). Both types of galaxies merge into each other as ellipticals occur with ellipticities larger than 0.7 but without spiral structure. These galaxies usually
exhibit a disk and are called lenticulars or S0. Within the spiral sequence, Hubble called the
galaxies early through late regarding their structural complexity15 , but disregarding the "temporal connotation" of the adjectives. Although the connotation was originally meant to define
14 Even a filament of DM only was observed by weak gravitational lensing (Dietrich et al. 2012).
15 "This sequence of structural forms ... exhibits a smooth progression in nuclear luminosity, surface brightness, degree
of flattening, major diameters, resolution, and complexity." (Hubble 1926)
1.3 galaxy classification and properties
Figure 3: The Hubble Tuning Fork, a galaxy classification scheme by Hubble (1926). Spiral and elliptical galaxies merge in lenticular S0 galaxies. Since spiral galaxies can exhibit bars, they form two distinct branches.
The diagram reads early-type (elliptical) galaxies through late-type (spiral) galaxies. Image taken from:∼imamura/123/lecture-3/lecture-3.html
spiral galaxies, in the 1940’s and 1950’s astronomers began to term ellipticals as early-type galaxies and spirals were referred to as late-type galaxies, still being in use16 .
Furthermore, Hubble (1926) introduced the SB class for spiral galaxies exhibiting a bar and
the irregular galaxy type (Irr) for galaxies which could not be assigned to E or S type. Hubble’s
classification scheme of nearby galaxies can be summarized in a diagram as illustrated in Fig. 3,
usually referred to as the Hubble Tuning Fork or the Hubble Sequence. Commonly in literature, a
galaxy is morphologically described by means of its Hubble type.
It was recognized later that Hubble’s Sc class spans a wide range in the degree of resolution
so that Shapley (1951) introduced another Sd class to account for the more irregular galaxies.
de Vaucouleurs (1959) added the Sdm, Sm and Im type for very late-type systems that resemble
the Magellanic clouds.
Almost all galaxy types listed by Hubble are of high intrinsic luminosity because they were
chosen from a list of the apparently brightest galaxies on the sky. With the discovery of the
fainter galaxies in the Local Group17 (Shapley 1938) the enormous range of luminosity within
the group of E galaxies was recognized so that the dwarf elliptical (dE) class18,19 for the fainter
ones was introduced by Baade (1944) when he found two other faint systems in the Local
Group. In the context of their Virgo cluster study, Sandage & Binggeli (1984) tried to separate
between dEs and Es by adopting a surface brightness rather than a total galaxy luminosity
criterion. They described two new classes of dwarf galaxies. The dEs containing a disk feature
are termed dS0, quite similar to E and S0 galaxies. Blue dwarf galaxies with very compact
appearance were dubbed blue compact dwarfs (BCD). Additionally, dEs were now separated
from dE,N through the existence of a nucleus – a central luminosity excess. As sensitivity
16 This thesis will use these expressions as they are defined here, including S0s to the early-types.
17 The Local Group is the galaxy group, the Milky Way is part of.
18 Kormendy et al. (2009) criticized that the name dwarf elliptical is confusing, because it implies that dEs are small
scaled versions of giant E galaxies, which is maybe not the case. Therefore, they prefer the term spheroidal.
19 There is a range of galaxy brightnesses to divide between dwarf and giant galaxies. The total magnitudes reach
from MB ' −18 mag (Boselli et al. 2008) to MB ' −16 mag (Ferguson & Binggeli 1994). The large range (almost an
order of magnitude) in luminosity shows that the transition is smooth.
increased in the era of charge-coupled devices (CCD), new features have been revealed in dEs.
Spiral arms were discovered as well as very faint disk signatures (Jerjen et al. 2000; Lisker et al.
2006). Late-type dwarf spirals, however, are generally not found but the link between dwarf
irregular galaxies (dIrr) and spiral galaxies is discussed in Matthews & Gallagher (1997). Then,
there are the diffuse dwarf spheroidal galaxies (dSph), structureless faint20 dEs (Grebel 2001). In
addition, new early-type dwarf galaxies have been discovered, like tidal dwarfs, ultra-compact
dwarf galaxies and ultra-faint dwarf galaxies (Duc & Mirabel 1998; Hilker et al. 1999; Simon &
Geha 2007).
In short, the zoo of dwarf galaxies is far from being homogeneous and its "taxonomy ... typically opens a Pandora’s box" (Tolstoy et al. 2009, for a review). But giant galaxies are not free of
confusion either. Kormendy & Bender (2012) link dwarf "spheroidals" to a whole sequence of S0
galaxies originally proposed by van den Bergh (1976). Moreover, Emsellem et al. (2007) ordered
early-type galaxies by their kinematics rather than morphology, with slow rotators tending to
be brighter and more massive galaxies. Not to mention, the complexity of late-type galaxies
with their bunch of classification types. Generally spoken, the deeper the observations and the
better its resolution the more different early-type systems became. It is beyond the scope of
this thesis to address this topic. For simplification, we will stick to the scheme published by
Sandage & Binggeli (1984) but summarize all late-type dwarf galaxies as dwarf irregulars (dIrr).
In the following, properties of the main galaxy types in the nearby universe shall be discussed.
Properties of dwarf galaxies are nicely summarized by Grebel (2001).
Elliptical galaxies. These smooth, featureless stellar systems cover several orders of magnitude
in luminosity, including the brightest cD galaxies in the Universe, sitting in the center of galaxy
clusters. These brightest cluster galaxies (BCGs) contain an elliptical core surrounded by a diffuse envelope on scales of hundreds of kpc. While BCGs have luminosities up to 100 times that
of the Milky Way, normal, giant ellipticals are a few times more luminous. Ellipticals contain little or no cool interstellar gas or dust and little or no disk structure. The stars in most ellipticals
are very old and have ages comparable to the age of the Universe (Thomas et al. 2005). Because
there is no gas to generate new, young blue stars, those galaxies appear red, i.e., the major part
of their light is emitted on longer optical wavelengths. Typically, ellipticals are overabundant
in dense centers of galaxy clusters, but only few are found in the field21 .
In ellipticals, the isophotes – surfaces of constant surface-brightness – have an elliptical shape.
While only the projection of a galaxy’s brightness distribution is observed, indirect measurements strongly suggest that two types of shapes, triaxial and axissymmetric, exist (Binney 1978;
Lisker et al. 2007). The brightness of E galaxies decreases smoothly with radius so that an edge
is hardly to determine. In order to obtain a meaningful quantity for a galaxy’s size, the effective radius Re is defined as containing half of the galaxy’s luminosity. In many galaxies,
the isophotes vary with radius, but generally, a correlation between Re and the luminosity is
found (see Chap. ii). A powerful formula to describe the surface-brightness profile of elliptical
galaxies is the Sérsic law (Sérsic 1963)
" #
R 1/n
I(R) = Ie exp −bn
where I(R) is the surface-intensity at radius R, Ie is the effective intensity at the effective radius
Re and n is the Sérsic index. This index describes the curvature of the profile, i.e., the concentra20 Grebel (2001) characterizes dSphs by MV > −14 mag.
21 Commonly, astronomers refer to the field as low density regions in the Universe, in contrast to high density regions
like galaxy clusters.
1.3 galaxy classification and properties
tion of light, and is correlated with the luminosity of the elliptical galaxy. While giant ellipticals
are found to have n ' 4, defining the de Vaucouleurs or R1/4 law (de Vaucouleurs 1948), dEs
typically show Sérsic indices of between n ' 1 and n ' 2, and dSphs exhibit exponential
profiles with n ' 1 or shallower (see e.g., Lieder et al. 2012). That is, from a relative point of
view, giant ellipticals have much more light concentrated in the center than dEs, which in turn
appear more diffuse. A detailed review of the Sérsic model is provided by Graham & Driver
It appears that E galaxies follow a number of relations. Faber & Jackson (1976) discovered
first, that luminosity scales with velocity dispersion22 of stars in E galaxies (L ∝ σ4 ). Later, it
became clear that the Faber-Jackson relation is a projection of a thin plane – the fundamental
plane –, spanned by three global observables: Re , Ie and σ (Djorgovski & Davis 1987; Dressler
et al. 1987). After Jorgensen et al. (1996) showed that the FP is not in agreement with the commonly assumed virial equilibrium (see Sect. 1.2), only one reasonable explanation remained,
already realized by Faber & Jackson (1976). The ratio of mass and luminosity in E galaxies is
not a constant, but varies with luminosity.
To measure the DM content of ellipticals is more complicated than in spiral galaxies since
there is no ordered rotation of stars to infer from. Beside tracing their hot gas through X-Ray
emission as pointed out in Sect. 1.2, a different approach has been successfully applied. Côté
et al. (2003) used hundreds of globular clusters in the Virgo cluster to show that their radial
velocities need a dark halo assuming the velocities to be random. Similarly, but based on stellar
kinematics of nearby ellipticals, Cappellari et al. (2006) find evidence for dark matter, but its
contribution to the mass inside Re is 6 30%. Furthermore, their careful dynamical analysis
show that the most luminous galaxies have (dynamical) mass-to-light ratios M/L ∼ 6, while
"normal" ellipticals show M/L ∼ 1. On the other hand, the ultra-faint galaxies of the Milky Way
have M/L > 100 (Strigari et al. 2007). That implies a minimum in M/L, commonly applied in
simulations by means of the stellar-to-halo mass (e.g., Hopkins et al. 2013).
Spiral galaxies. This galaxy type, to which the Milky Way belongs, is composed of a disk and
a bulge – a central bright extended spheroidal region of tightly packed stars. There are two
types of bulges. A classical bulge looks like an elliptical galaxy, being red due to its composition
of population II stars23 and exhibiting a de Vaucouleurs profile. In pseudobulges or disky bulges
star formation is still ongoing and they contain stars that orbit in an ordered fashion in a
plane that is defined by the outer disk. However, the origin of bulges is not well understood
(see Kormendy & Kennicutt 2004 for the formation of pseudobulges and Gadotti 2009 for a
summary on bulges).
As already suggested by the name, the disks of these galaxies contains spiral arms, filaments
of star forming regions dominated by O and B stars. Those young and luminous stars dominate
the light of the galaxy, so that it appears blue in optical wavelengths. The disk has typically an
exponential light profile and contains also a lot of dust which can extinct the light of the stars,
in particular the short wavelengths. That is, such a galaxy, when observed edge-on can appear
rather red as we will see in Sect. 4.2.2. Not only the dust, but also molecular gas and old stellar
populations, dominating the mass of the disk, are arranged in the spiral pattern (Calzetti et al.
2005; Regan et al. 2001). The bulge-to-disk ratio in terms of luminosity is decreasing from Sa to
22 The velocity dispersion is the statistical dispersion of velocities about the mean velocity from a group of objects,
such as a galaxy cluster.
23 Population II stars are metal poor. Thus, they are thought to have formed early, when only little metals were
Sd galaxies as well as their total luminosity does, whereas in Sds the knots of stars and HII
regions are the brightest.
A bar – an elongated smooth structure composed of stars in the central region – is very
common in spirals, about two thirds have one (Eskridge et al. 2000). Spiral (and irregular)
galaxies are very abundant in the field (about 80%), but in dense regions their fraction drops
to 10% (Dressler 1980), hinting to environmental influences on the evolution of spiral galaxies
(see Sect. 1.4).
The rotation curves of spirals are easy to measure since the gas in the disk is a good tracers.
One only has to account for the orientation of the galaxy and can utilize the Doppler effect. Like
the Milky Way, spirals rotate considerably faster in their outer region than it is expected from
Kepler’s law and the light distribution. In fact, the dark matter density in spirals is derived
from rotation curves (van Albada et al. 1985). The shape of the rotation curves in spiral galaxies
is very similar to each other. In particular, in the outer regions they level out at a maximum
velocity vmax , i.e., they become flat (Rubin et al. 1978). Similar to the Faber-Jackson relation in
2.5 – called the
ellipticals, it exists a relation between a spiral’s vmax and its luminosity: L ∝ vmax
Tully-Fisher relation (Tully & Fisher 1977). There is a significant scatter in the relation, partly due
to the varying M/L ratio in spirals, resulting in different slopes quoted in literature. Derived
(dynamical) M/L ratios are of the order of 1 6 M/L 6 10 in the optical B-band (van Albada
et al. 1985; Persic & Salucci 1988). The Tully-Fisher relation is the same for all spirals but it is a
function of wavelength (Sakai et al. 2000).
Lenticular galaxies. The transition from ellipticals to spirals is smooth, so that S0 galaxies may
be accidentally classified as Sa or E7 galaxy (Sandage & Bedke 1994). Like spirals, they exhibit
a rotating disk and a bulge but their bulge-to-disk ratios are systematically larger than those
of spirals (Dressler 1980). Like ellipticals, they lack spiral arms or extensive dust lanes. Cool
gas and dust is only little abundant or absent. As a consequence of the missing gas, stars are
not forming, qualifying those galaxies as early-type. Similar to ellipticals, lenticulars account
for almost the half of all bright galaxies in the central regions of galaxy clusters but are very
rare in the field or low density regions, respectively (Dressler 1980). Those correlations and the
finding that the Tully-Fisher relation of S0s lies systematically below that of nearby spirals lead
to the conclusion that S0s were "spiral galaxies that have faded since ceasing star formation"
(Bedregal et al. 2006).
Irregular galaxies. These galaxies lack commonly any organized structure. Basically, they are the
extension of the spiral sequence, becoming less luminous (e.g., Roberts 1969; Garnett 2002). The
low-luminosity ones are the dIrrs. Like spirals, irregular galaxies are gas-rich. They contain a
lot of dust and HII regions24 with many star forming regions embedded (Hunter et al. 2006).
In parts, they appear irregular because of dust extinction but also due to the young luminous
stars that dominate the emission of Irrs so that they appear blue (see e.g., Lieder et al. 2012).
It is possible that once the galaxies have used up or lost their gas reservoir, they transform
into the red spheroidals (Kormendy & Bender 2012). Irregulars are very common in the local
neighborhood (' 30%) but less present in galaxy clusters, in particular in their cores.
In the following chapters, we will make intensive use of the galaxy classification (and notation), introduced here.
24 In contrast to HI regions containing neutral hydrogen, HII regions are clouds of ionized hydrogen. They are typical
sites for star formation. The radiation of the new born stars ionizes the surrounding gas.
1.4 galaxy evolution and environmental effects
galaxy evolution and environmental effects
As sketched in Sect. 1.2, after recombination gas clouds can grow and gravitational instabilities
lead to the formation of disk-like protogalaxies. These galaxies will accrete gas from the surroundings due to its gravitational attraction. At high redshifts, the accretion will occur in so
called cold streams along the filaments of the cosmic web of large-scale structure25 . These gas
flows are too dense to be shock-heated, in particular they cool faster than pressure can be developed to support a shock (Kereš et al. 2005; Dekel & Birnboim 2006). In cold streams stars form
in clumps and merger of these clumps take place, which are essentially indistinguishable from
minor mergers of gas-rich dwarfs (Dekel et al. 2009). However, the rotational disk configuration
of a galaxy tends to be preserved while mergers of the clumps form a central spheroid. Unless, there is no other galaxy nearby, the galaxy will evolve through internal processes. When
a molecular cloud has cooled down to less than 20 K, a starburst converts only a small fraction
of it into stars and blows the remainder away into the interstellar medium (ISM). The process of
blowing gas away is called feedback. Two types of feedback in the course of galaxy evolution
are semi-analytically well studied.
Supernova feedback. Due to supernova explosions the ISM is heated up to 107 K. This enables gas
to escape from low-mass galaxies, with speeds of some hundreds of km/s. These galactic winds
of the first stars, have presumably led to the presence of low-surface brightness dwarf galaxies
(Larson 1974; Dekel & Silk 1986). After the first star formation period until reionization, these
galaxies were not able to retain their gas for subsequent star formation. This leads to the idea
that if at reionization a galaxy has not had formed stars yet, it may "evolve" into a "dark-dark
halo", because subsequent star formation is not possible (Dekel & Woo 2003). Moreover, (Governato et al. 2010) have shown that strong outflows from supernovae can inhibit formation of
bulges, explaining the diffuse appearance of dwarf galaxies.
AGN feedback. An active galactic nucleus (AGN) is a compact region in the center of a galaxy that
is much more luminous than normal centers of galaxies (possibly over the whole spectrum).
The energy output of an AGN is believed to be driven by an accretion disk of a supermassive
black hole26 (Lynden-Bell 1969; Kormendy & Gebhardt 2001). In the nearby universe, AGNs
are found to "reside almost exclusively in massive galaxies" (with stellar masses larger than
∼ 1010 M ) that resemble ordinary early-type galaxies (Kauffmann et al. 2003). These galaxies
are massive enough to prevent the supernova-ejected gas from escaping so that it is trapped
in the potential well of the galaxy. That has been proven by the detection of thermal X-ray
emission of these hot gas spheres in early-type galaxies (e.g., Böhringer et al. 2000). The gas
can dissipate by radiation, resulting in so-called cooling flows onto the center of the galaxy. The
black hole at the center accretes the gas and a significant fraction of energy emerges as a collimated outflow. This outflow – called jet – heats the surrounding gas, counterbalancing the
cooling flow (Omma et al. 2004). The remarkably similar X-ray morphologies of these systems
hint that they have reached a kind of steady-state, not growing anymore (Donahue et al. 2006).
Since the supermassive black hole in the center prevents the gas from falling onto the center,
it effectively quenches star formation, making the galaxy red and passive. More interestingly,
the galaxy can not create more luminosity, resulting in the exponential cut-off (see Fig. 4b) of
the luminosity function at the bright end (White & Rees 1978; Benson et al. 2003; Springel et al.
25 Such a gas filament from the early universe has recently been observed for the first time (Cantalupo et al. 2014).
26 A supermassive black hole is at least as massive as 106 M . Correlations of galaxy luminosity and velocity dispersion suggest that every massive galaxy harbors a supermassive black hole (Ferrarese & Merritt 2000; Häring & Rix
(a) Morphology-density relation, taken from Dressler (1980)
(b) Luminosity function in different environments, taken from Binggeli et al. (1988)
Figure 4: The morphology-density relation. (a) The fraction of galaxy-types vs. logarithmic projected density in
Mpc−2 . In the densest regions of galaxy cluster, early-type galaxies (E, S0) dominate, while late-type galaxies
(S+Irr) are the majority in the field (leftmost datapoints). (b) Another representation of the morphology-density
relation by means of the luminosity function of field galaxies (top) and the Virgo cluster (bottom), the logarithmic
number density log ϕ(M) (with arbitrary zeropoint) vs. total magnitude in B band (MBT ). The classes dS0 and
"dE or Im" are not illustrated but included in the total LF over all types. The luminosity function in the field is
dominated by late-type galaxies while particularly at the faint end, the LF in the Virgo cluster is dominated by
early-type galaxies. In both cases, there is an exponential cut-off at high luminosities as well as an exponential
faint end. The faint-end slope in the underdense environment is shallower than in the dense environment of the
cluster, i.e., there is no universal LF.
2005a; Sijacki et al. 2007).
As pointed out in the previous section, there are more early-type galaxies in dense regions
while low-density regions are dominated by late-type galaxies (Dressler 1980), illustrated in
Fig. 4a. This correlation is known as the morphology-density relation and suggests that external
processes, triggered by the environment of a galaxy, also influence its evolution. Here, we shall
introduce the main mechanisms that will have influence on this work.
Galaxy mergers (see Fig. 5, panels 4,5,10). In the context of a hierarchically emerging universe,
interaction and mergers between galaxies are an essential process in galaxy formation and evolution. Stars which have been formed by such an event are unlikely to stay on circular obits,
possibly forming a bulge. During a merger, the central black holes of the participants will be
fed by surrounding gas that easily can fall onto the black hole, because the gravitational field
is highly distorted. Thus, black hole growth is expected when galaxies merge (Hopkins et al.
In the early universe merger were more frequent due to the higher galaxy density. Today,
galaxy-galaxy interactions become more likely in the environment of galaxy groups where
gravitational attraction has a higher impact since galaxies move slowly relative to each other
1.4 galaxy evolution and environmental effects
(Zabludoff & Mulchaey 1998), in contrast to clusters where high internal velocities hinder
galaxy encounters. There are many classification of galaxy mergers. Major mergers are interactions of galaxies of comparable mass, while minor mergers are classified as interactions between
dwarf and giant galaxies. If one of the participating galaxies is a late-type galaxy, the merger is
called gas-rich or wet. The gas in the disks of the galaxies will be violently shocked when two
halos merge. In the overdensities of the shocking wave star formation will be ignited, i.e., the
merger of gas-rich galaxies gives rise to produce a starburst that heats the galaxy (Kennicutt
1998). Also, aside from star formation, simulations show often disc components, well after the
merger event (Springel & Hernquist 2005; Cox et al. 2006; Lotz et al. 2008; Hopkins et al. 2009).
However, already in the 1970’s the idea grew that red, elliptical galaxies can be produced by
a merger of spiral galaxies (Toomre & Toomre 1972; Toomre 1977). But the properties of the
remaining elliptical depend on mass ratio, morphological type, gas fractions and orbital parameters of the progenitors (Barnes 1988; Hernquist 1992). The brightest elliptical galaxies can
only be formed from dry mergers, i.e., by galaxies with little or no gas (e.g, van Dokkum 2005;
Bell et al. 2006; Hopkins et al. 2007). Minor mergers on the other hand, can form spheroids,
merger-built (pseudo)bulges that could can evolve into the dEs we observe today (Kormendy
& Kennicutt 2004; Naab et al. 2009)
Depending on the morphological criteria, resolution or projection, timescales for major mergers range from 0.1 Gyr to 1.9 Gyr for wet mergers, while morphological signatures of dry mergers disappear after 0.2 Gyr (Springel & Hernquist 2005; Bell et al. 2006; Lotz et al. 2008).
Another interesting finding is the imprint of galaxy mergers on the isophotes of the remnant.
Hopkins et al. (2009) found in wet mergers the surface-brightness profile to be different from a
de Vaucouleurs profile, with Sérsic indices of n ∼ 3. Moreover, the deviation of the isophotes
from perfect ellipses towards a disky structure (see Sect. 3.2) suggests that bright elliptical galaxies could have undergone wet a merger, even if no morphological merger signature remains
visible (Khochfar & Burkert 2005; Cox et al. 2006; Kormendy et al. 2009). Boxy elliptical galaxies,
in contrast, could be the remnants of dry mergers (Naab et al. 2006). Furthermore, Emsellem
et al. (2007) found kinematically decoupled cores of kpc scale in bright elliptical galaxies. Additionally, Huang et al. (2013) find on the same scale subcomponents in the surface-brightness
profiles of massive E galaxies. They argue in favor of the two-phase formation scenario (Oser
et al. 2010). The inner component may be the outcome of the initial dissipational phase at high
redshift (first galaxies formed by cold streams), while the outer component is added by material of dry minor mergers during the second dissipationless phase. But they admit, major
mergers do not fit in this picture. Oser et al. (2012) additionally find that the properties of earlytype galaxies are predominantly determined by frequent minor mergers because they are more
likely compared to major mergers.
In the core of galaxy clusters, where galaxies have typical velocities of ∼ 2000 km/s, galaxy
mergers are unlikely to occur because the interactions are too fast for dynamical friction27 and
the collision will the participants not slow down enough (Binney & Tremaine 2008). Hence,
encounters will have a stronger effect in the environment of galaxy groups with lower speeds.
That gives rise that the cluster galaxies in the center of clusters have been "preprocessed" by
mergers in groups that eventually merge to form clusters (Dubinski 1998).
In summary, galaxy mergers produce very likely elliptical galaxies. In the course of the cosmological evolution, in the current epoch, mergers will occur in dense environments like galaxy
groups (and clusters), contributing an important piece to the morphology-density relation.
27 Kinetic energy of the motion of the galaxies is transferred to the motion of stars within the galaxies. This leads to a
deceleration of the galaxies. The whole process is called dynamical friction and was proposed in a series of papers
by Chandrasekhar (1943).
Tidal stripping and galaxy harassment (see Fig. 5, panels 6,7,9,11,12). If the encountering galaxies
contain gas, it will compressed by the tidal forces, triggering star formation. Since the galaxies
move with different velocities as compared to the colliding gas, these star forming regions are
manifested by blue tidal tails (e.g., Jarrett et al. 2006). That material can rearrange itself and form
so-called tidal dwarf galaxies (Duc et al. 2000).
Spiral galaxies in clusters will pass by many other galaxies and experience only weak encounters which will not produce tidal tails (in the above described fashion), but they are not
unaffected either. As mentioned above, if the encounter between two galaxies is too fast, dynamical friction is not working properly. Crossing times are of some tens Myrs only, so that the
interaction can be treated by impulse approximation. That is, the encounter results in a change
of velocities of stars only, rather than a redistribution Binney & Tremaine (2008). Many of those
encounters will alter the shape of the galaxy and eventually strip off the outer part the galaxy28 .
This process is called galaxy harassment, and due to the tidal truncation it can transform spiral
and disky galaxies into dEs and dSphs, as shown by Moore et al. (1996, 1998). This scenario
in combination with merging processes may lead to the domination of elliptical galaxies in
cluster centers – explaining the morphology-density relation. Moreover, the model predicts an
abundance of floating stars in the centers of galaxy clusters, unattached to any galaxy. Deep
observations of the Virgo cluster find "tidal streamers" and diffuse light around the massive
elliptical galaxies, confirming the harassment picture (Mihos et al. 2005; Ferrarese et al. 2012).
Ram-pressure stripping (see Fig 5, panels 1-3). In a galaxy cluster, hot gas becomes more concentrated towards the center due to the lower potential well, typically observed in the X-Ray
(e.g., Böhringer et al. 2000; Sanderson et al. 2003). As outlined before, the gas may origin in
either supernova or AGN outflows, or has been released by the shocks of previous mergers.
Typically, galaxies move through the cluster with velocities of ∼ 1000km/s, and the impact of
this intergalactic gas produces ram pressure, sweeping away the (cold) galactic gas (Gunn &
Gott 1972). In practice, the sweep will shock the galactic gas, which gives rise to star formation,
so that supernova-driven winds and ram-pressure stripping go hand in hand (Gavazzi et al.
1995). If the galaxy is massive enough and the inclination angle between the disk of the galaxy
and the orbital plane is favorable, the expelled gas can fall back onto the galaxy (Vollmer et al.
2001; Roediger & Hensler 2005). Ram-pressure stripping in the group and cluster environment
can be relevant at large distances from the center. Bahé et al. (2013) show that the depletion of
hot and cold gas begins at 5rvir , quenching star formation as the galaxy falls into the dense
environment. Also the hot gas halo of (early-type) galaxies can be stripped sufficiently at that
Based on their model, Gunn & Gott (1972) presumed, that ram-pressure stripping "expects
no spiral in central region of clusters like Coma". Dressler (1980) argues in parts against rampressure stripping as a complete model for the morphology-density relation because most of
the S0 – which might be stripped spirals – are found outside rich clusters even though they
are more prevalent in rich clusters. On the other hand, simulations show, that this mechanism
"naturally accounts for the morphology of S0 galaxies" (Quilis et al. 2000), yielding a complete
gas loss of disk galaxies (Roediger & Hensler 2005). In addition, Lin & Faber (1983) make
ram-pressure stripping the primarily responsible process to turn dwarf irregulars into passive
dwarf spheroidals because they will become completely gas-stripped after only one crossing
28 Within the central regions of galaxy clusters (∼ rvir ), a galaxy’s DM halos will be stripped first, though not completely. The formerly extended DM halo will be truncated and the DM particles are smoothly distributed within the
cluster center. This enables the stripping of the baryonic component. Due to the many encounters, the kinetic energy
of the stars is increased and they can become unbound. The morphology of the galaxies involved is asymmetric
and disturbed.
1.4 galaxy evolution and environmental effects
Figure 5: "Virgo cluster as a laboratory for studying the effects of interactions and environment on galaxy evolution.
The different panels show likely examples of various evolutionary processes at work. (1)-(3) a ram-pressurestripping sequence, illustrating gas stripping before, during and after its peak intensity (as inferred from HI
observations). (4) a remnant of a gas-poor merger. (5) a gas-rich dwarf being accreted by M49 and an example of a
"wet" accretion event. (6) an S0 galaxy with an extended star-forming ring, perhaps triggered by tidal interactions.
(7) an interacting pair with tidally triggered star formation. (8) a possible post major merger Sa galaxy. (9) a
candidate tidal dwarf system. (10) a possible binary dwarf system. (11) a close companion of M49 that has
likely undergone severe tidal stripping. (12) a faint dwarf elliptical galaxy that shows faint spiral arms, possible
evidence for the transformation by the tidal forces acting in the cluster environment. All images are in the g band;
the scale is as shown in each panel (100" corresponds to ∼ 8 kpc at the distance of the Virgo cluster)." Figure taken
from: Ferrarese et al. (2012)
through the cluster (Mayer et al. 2006; Boselli et al. 2008). However, Weinmann et al. (2011)
showed that ram-pressure stripping in the group environment is too strong for dwarf galaxies
when comparing the Guo et al. (2011) SAM to observations. Similarly, a dynamical analysis of
spiral galaxies in the Virgo cluster indicates that ram-pressure stripping is stronger when it is
derived from the ICM density only (Vollmer 2009).
We have seen that many mechanisms exist to account for the morphology-density relation
observed by Dressler (1980). There are intrinsic processes as well as external ones that influence
the evolution of galaxies. Much progress has been achieved by incorporating those mechanisms
in cosmological simulation to search for explanations of galaxy properties. The observational
part of this thesis will make statements using arguments which are based on the findings
sketched in this section. On the other side, the SAM we will make use of in the second part of
this thesis incorporates not only those mechanisms presented here.
Section taken
from Lieder
et al. (2013)
fossil groups
The study of so-called fossil groups (FGs) began about two decades ago. Ponman et al. (1994)
found the first of these systems: X-ray luminous galaxy groups characterized by their dominant
bright central elliptical galaxy resulting in high mass-to-light ratios. The formal definition by
Jones et al. (2003), generally adopted by the community, is the following:
1. Ensure that there is a dominant galaxy in the group by adopting an R-band magnitude
gap ∆m12 of at least two magnitudes between the two most luminous galaxies. They
restrict that criterion to galaxies within half of the group’s projected virial radius rvir
to ensure that L∗ galaxies have had enough time to merge owing to dynamical friction,
since the merging timescale within 0.5rvir for these systems is shorter than a Hubble time
(Zabludoff & Mulchaey 1998).
2. Exclude "normal" elliptical galaxies that are not located in the center of the group by
finding a hot gas halo that surrounds the galaxy (typical of central galaxies). This is
achieved by a minimum X-ray luminosity of LX,bol = 1042 h−2
50 erg/s.
Ponman et al. (1994) interpreted their observations as witnessing the final stage in a group’s evolution: an ancient stellar population in which most of the group’s bright galaxies have merged
into one luminous galaxy. They therefore termed their finding a "fossil" group. This evolutionary scenario seems a plausible one for isolated parts in our universe where galaxy groups
can evolve undisturbed. Another FG formation scenario has been suggested by Mulchaey &
Zabludoff (1999). Here, FGs could merely be "failed" groups in which the majority of the baryonic mass was accidentally placed in a single dark matter halo, leading to the dominant central
object. Investigations of FGs do not favor this scenario since several studies have revealed that
fossil brightest group galaxies (BGGs) exhibit disky isophotes (Khosroshahi et al. 2006). According to Bender (1988) and Khochfar & Burkert (2005), it is considered that gas-rich mergers
cause this isophotal behavior. This is also supported by Aguerri et al. (2011) and Méndez-Abreu
et al. (2012), who find that the Sérsic index of BGGs in FGs is significantly smaller than that
in central galaxies of clusters. According to Hopkins et al. (2009), small Sérsic n stem from
gas-rich mergers.
Investigations based on the criteria by Jones et al. (2003) have generally led to the conclusion
that FGs formed early and have not experienced any major merger event for several Gyrs
(Sanderson et al. 2003; Khosroshahi et al. 2004). According to simulations, they accreted the
1.6 thesis outline
majority of their mass at high redshifts (e.g., 50% at z > 1; D’Onghia et al. 2005; Dariush et al.
2007; Díaz-Giménez et al. 2008). Fossil groups would therefore constitute the top end of the
hierarchical evolution of galaxies on group scales.
Some more recent studies suggest that FGs may only be a transient phase in a group’s
evolution (von Benda-Beckmann et al. 2008; Dariush et al. 2010; Cui et al. 2011). Dariush et al.
(2010) argue that most of the early formed systems are not in a "fossil phase" at z = 0, but were
so at some earlier point during their evolution. It is also clear that the observational criteria
for FG classification are to some extent arbitrary, and slight changes to, say, ∆m12 will change
the fraction of environments classified as fossil. Milosavljević et al. (2006) show that there is a
smooth distribution of the luminosity gap among 730 SDSS clusters, in line with the idea that
the observational definition of a fossil group does not necessarily highlight a marked change
in underlying formation histories. Nevertheless, it is clear that fossil groups mark an extreme
environment (in the tail of a smooth distribution), which is only expected in a few percent of
massive dark matter halos (Milosavljević et al. 2006).
Here we are interested in the properties of the faint galaxy population in such an extreme
environment. Early results suggested that FGs also lacked faint satellites (Jones et al. 2000)
that provide potentially interesting constraints on the so-called "substructure crisis/missing
satellite problem" of ΛCDM (D’Onghia & Lake 2004). Recently, Mendes de Oliveira et al. (2009)
has reanalyzed the FG used by D’Onghia & Lake (2004) and found a steeper faint end slope
of −1.6 – comparable to clusters (e.g., Coma cluster: α = −1.4, Secker et al. 1997). Other recent
studies of FGs reveal shallower faint end slopes of α = −1.2 when determined out to ∼ rvir
(Cypriano et al. 2006; Proctor et al. 2011; Eigenthaler & Zeilinger 2012), whereas the restriction to
0.5rvir even reveals declining faint ends, i.e., α > −1.0 (Mendes de Oliveira et al. 2006; Aguerri
et al. 2011; Proctor et al. 2011).
However, none of these studies reaches magnitudes fainter than MR ' −17 mag29 , barely
scratching the dwarf regime. Therefore they cannot provide meaningful constraints on the
asymptotic faint end slope of the galaxy luminosity function. To investigate this faint galaxy
population of an FG, we provide here a photometric analysis of the NGC 6482 group down to
MR ' −10.5 mag – to our knowledge the deepest FG study yet.
thesis outline
This thesis can be divided into to parts. The first part is observational, where we will study the
properties of NGC 6482, in particular its satellite system. In the second part, for FG candidates
is searched in the SAM of Guo et al. (2011) in order to study their properties and histories. The
goal of this thesis is to test the hypothesis that a FG is an early formed galaxy group which
has evolved without interactions of other groups, i.e., fossil groups are indeed exceptional. We
also compare properties of NGC 6482 with the SAM FGs in order to draw conclusions on this
FG and FGs in general in a final chapter.
29 Deeper observations of FGs exist with the HST ACS, but their much more constrained spatial coverage makes them
inappropriate for the study of widely distributed dwarf galaxies.
Part II
Chapter taken
from Lieder
et al. (2013)
ngc 6482
NGC 6482 is the nearest known FG (z = 0.0131; Smith et al. 2000), so it is well suited for a
ground-based study of its dwarf galaxy population. If adopting the cosmological parameters
H0 = 70.0 km s−1 Mpc−1 , ΩM = 0.3, and ΩΛ = 0.7, NGC 6482’s distance is m − M = 33.7
mag (d = 55.7 Mpc), resulting in a physical scale of 0.263 kpc arcsec−1 . We use these numbers
throughout the paper.
We anticipate here that we measure MR = −22.7 mag for the BGG and for the second ranked
galaxy MR = −20.5 mag. Together with the X-ray luminosity of LX = 1.0 · 1042 h−2
70 erg s
(Böhringer et al. 2000) NGC 6482 meets the fossil definition by Jones et al. (2003). Chandra
observations imply a virial radius of 310 kpc, a hot gas mass fraction of fgas = 0.16, and a
total mass of M200 ≈ 4 × 1012 M , with an R-band mass-to-light ratio at rvir of 71 ± 15 M /L
(Khosroshahi et al. 2004). These data are consistent with the ROSAT study of Sanderson et al.
(2003), but we note that their larger field-of-view constraints result in a slightly larger rvir and
in fgas ≈ 0.07, which are more consistent with its TX ∼ 0.6 keV.
On 5 June 2008, R-band images of NGC 6482 were acquired using the Suprime-Cam wide field
imaging instrument at the Subaru telescope (Table 1). The Suprime-Cam camera is a mosaic of
ten 2k×4k CCDs with a pixel scale of 0.202 arcsec pix−1 , and it covers an area of 34 0 × 27 0 per
field (Miyazaki et al. 2002). The field-of-view corresponds to a physical scale of 624 x 458 kpc
at the distance of NGC 6482, reaching the virial radius at the field edges. Eighty-five percent
of the area that is enclosed by rvir is covered. After a chip replacement in July 2008, B-band
images were obtained on 4 August 2008. Both observations were obtained in service mode
under run ID S08B-150S (PI Hilker).
In either band, two short (R: 60s, B: 120s) and four long (R: 540s, B: 1020s) exposures were
acquired, all centered on NGC 6482. The average seeing in the R-band was 0.6 arcsec FWHM
and 1.0 arcsec in the B-band.
data reduction
Suprime-Cam’s reduction pipeline SDFRED was used to carry out overscan correction and Appendix A
flatfielding. As mentioned above, the B-band data were taken after a chip replacement. For for a general
this data set, each of the ten individual CCDs had four separate readouts, hence four different description of
Table 1: R−band observation time line from 5 June 2008.
Image type
Exp. time
60 s
60 s
540 s
540 s
540 s
540 s
Notes. HST: Hawaii Standard Time, (a): expected fluxscale deviates from THELI’s applied fluxscale by ∼ 28%,
(b) large scatter in flux measurements of standard stars.
gains. Unfortunately, accurate individual gains were not provided with the data1 . We adjusted
the four gains within each CCD relative to each other such that sky brightness differences
were less than 1% after the flatfielding step. This adjustment was determined with the long
exposures for which gain variations dominate the relative count difference between the four
stripes per chip. The relative gain corrections were then applied to all other B-band exposures
(flats, standards, and short science exposures). The knowledge of the absolute gain value for
the B-band data is not necessary because absolute photometric calibration was achieved with
the standard star exposures, themselves corrected with the same relative gain as the science
The THELI image reduction pipeline (Erben et al. 2005) then was used for the remaining
steps of data preprocessing. The astrometric calibration from the THELI reductions was based
on cross-correlation with the PPMXL catalog of point sources using the scamp software. It also
corrected for geometric distortions in the outermost parts of the Suprime-Cam fields. After
the THELI photometry step, which is based on SExtractor (Bertin & Arnouts 1996) and which
adjusts the brightness levels of all chips and all exposures to each other, background subtraction
was carried out using THELI.
After the THELI processing, instrumental magnitudes were computed from observations of
standard stars taken in all four nights of the observing run, and from the photometry calibrated
on the Cousins B and R magnitude system of Landolt (1992).
The average 1σ noise per pixel for the 36-minute coadded image in R-band corresponds to
a surface brightness of µR = 27.2 mag/arcsec2 , and µB = 28.4 mag/arcsec2 for the 68-minute
composite image in the B-band. We thus have similar surface brightness sensitivities in B and
R, since typical early-type galaxy colors are around B − R 6 1.5 mag.
1 "For all data, S_GAIN[1-4] and GAIN values at FITS header have errors greater than 10%. Those values are only for reference
and should not be used for data analysis." (
2.4 calibration
The R-band and B-band data were observed on different nights. Each night, standard star
fields were observed at two different points in time and for a range of different airmasses. At
each airmass, two exposures per field were obtained. A significant extinction coefficient was
found in the B-band, while for the R-band it was consistent with zero. Thus, the atmospheric
extinction term in R-band is absorbed by the zero point (Table 2).
For the night of 5/6 June 2008 when R-band data were taken, there were unfortunately some
transparency variations due to the presence of clouds (Table 1), which prompted us to take special care in the photometric calibration: the standard star exposures in the R-band around 03:00
Hawaii Standard Time (HST) showed huge sensitivity variations at an average zero point fainter
than the mean of the other standard star exposures. We discarded these measurements and instead adopted the zero points measured two hours later around 05:00 HST, when conditions
were stable. Fortunately, the R-band science images, taken two hours earlier, were obtained at
almost exactly the same airmass, so that we do not introduce a luminosity offset when not considering the atmospheric extinction term. The observations of multiple standards throughout
the night therefore allowed exclusion of those standard images with a notable drop in throughput. The used calibration parameters are displayed in Table 2. Systematic uncertainties due to
photometric calibration arising from this table are given by σR = 0.04 mag and σB = 0.12 mag
(uncertainties for Schlegel extinction are not provided).
We then proceeded to check for the presence of clouds in the R-band science data taken between 02:07 and 02:56 HST. In general, THELI compensates for varying atmospheric transmission during a sequence of images that are to be coadded. Relative flux offsets are determined
and logged via the fluxscale parameter, from comparing the same sources in the individual
images. All images are then normalized to the highest transmission within the stack of images.
For a correct compensation of possible cloud effects, it is necessary to have at least one cloudless exposure in the stack of images that are coadded. THELI found that the first of the four
long R-band exposures (540 s) taken at HST 02:11 was indeed affected by a significant flux drop
(∼ 28%) with respect to the other three long exposures. This was corrected by THELI in the
final coadded image via the fluxscale parameter. We consider this correction as robust, since
the other long exposures had relative fluxes consistent with each other at the 5% percent level.
The two short R-band exposures were taken immediately before the one long exposure that
was apparently affected by reduced atmospheric transmission, between 02:07 and 02:11 HST.
Among themselves, these short exposures (later used only for fitting the centers of the brightest
galaxies) did not show any notable relative variation in the flux. However, given their fast
cadence, this does not exclude that they were affected by clouds. To test for the presence of
clouds, we ran SExtractor on both the short coadded image and the long coadded image, both
normalized to 1s integration time. The ratio of object fluxes between those two images shows
that the short exposures had a 24% lower sky transmission than the long exposures. When
we used the short time exposures for our analysis – only for the three brightest galaxies in our
sample – we corrected the R-band flux by that offset factor of 1.31 (=1/(1-0.24)). For consistency
reasons, we applied the same procedure to the B-band data and found that the long time flux
is ∼ 6% less than the short time flux. This difference is within the typical variation on a clear
night, suggesting that no clouds were present during these observations. To be consistent with
the treatment in the R-band, we corrected all B-band longtime fluxes upward by a factor of 1.06.
Table 2: Photometric calibration parameters.
ZP [mag]
27.37 ± 0.02
27.07 ± 0.06
κ [mag]
−0.124 ± 0.046
1.056 ± 0.018
2.006 ± 0.318
−0.001 ± 0.019
0.147 ± 0.033
A [mag]
0.22 . . . 0.31
0.35 . . . 0.50
Notes. ZP: zero point; κ: atmospheric extinction coefficient; X: mean airmass of exposures contributing to a coadded image;
CT: color term; A: Galactic extinction by
Schlegel et al. (1998)
In the following we describe how parameters are extracted from the imaging data in a reproducible way. We search automatically for low-surface brightness objects using the source extraction software SExtractor. The isophotal parameters of galaxies, in particular the boxiness,
are determined via the IRAF tool ellipse.
Source Extractor – SExtractor – is a software that uses automated techniques to analyze astronomical images (Bertin & Arnouts 1996) in order to find objects they contain. This is done in
five steps.
Background estimation. First, SExtractor runs through a grid that covers the whole frame and
determines the local background, i.e., the background in each mesh. This is achieved by clipping the number counts histogram iteratively until it converges around its median at 3σ. In
case of a crowded field, a clipped mode is chosen. The resulting background map is a bilinear
interpolation between the meshes of the grid that have an area BACK_SIZE. "The choice of the
mesh size is an important step. Too small, the background estimation is affected by the presence
of objects and random noise. Too large, it can not reproduce the small scale variations of the
background" (Bertin & Arnouts 1996). Before the interpolation is done, the background values
can be smoothed using the median filter BACK_FILTERSIZE. Effectively, this smooths deviations
in the background map that arise from bright or extended objects. The computed background
can also be used to calculate magnitudes of objects. The BACKPHOTO_TYPE parameter sets how
the background around an object is determined. GLOBAL means, that the background value is
taken from the background map.
Detection by thresholding. DETECT_THRESH is the threshold applied to detect objects. In order to
account for low-surface brightness objects at least a certain number of adjacent pixels, specified
by DETECT_MINAREA must have values above the threshold. We will specify the detection threshold with respect to the RMS of local background within a mesh.
Deblending merged objects. The detection method mentioned above needs to separate neighbors
that have been extracted as a single source. A typical example for the issue is a pair of galaxies
whose projection puts them close to each other. Any extracted object is re-thresholded in exponentially spaced levels between DETECT_THRESH and the maximum count in the object. The
number of those levels is specified by DEBLEND_NTHRESH. The so obtained light distribution
within the object is stored in a tree structure. Every branch, i.e., when pixels above a threshold level are found, is considered a different object provided that (1) the number count in the
branch is above a certain fraction of the total number count of the composite object, and (2) at
least one other branch above the same level and above this fraction exists. The fraction of the
flux is specified by the contrast parameter DEBLEND_MINCONT. Fig. 6 tries to illustrate the method.
Figure 6: "A schematic diagram of the method used
to deblend a composite object. The area profile of
the object (smooth curve) can be described in a
tree-structured way (thick lines). The decision to
regard or not a branch as a distinct object is determined according to its relative integrated intensity (tinted area). In that case above, the original
object shall split into two components A and B.
Remaining pixels are assigned to their most credible "progenitors" afterwards." Figure taken from
SExtractor manual, p21.
Filtering. This procedure checks if detections would have been made when their neighbors were
not there. It calculates a Moffat light profile for the neighbor. Then the contribution from the
wings of this profile is subtracted. Effectively, this procedure rejects spurious objects and was
basically applied when SExtractor was used.
Photometry. The precise photometry of galaxies will be obtained by an isophotal analysis as
demonstrated in the following section. However, for the detection of galaxies in the image data
we will rely on their location in the surface brightness-luminosity diagram. It would not be
reasonable to carry out the isophotal analysis for ∼ 60000 objects contained in the field of view.
We will use SExtractor’s photometry for a first guess. The peak surface brightness provided
by SExtractor is given by the surface brightness of the pixels with the highest number count.
Its flux is converted to surface brightness by the input of the pixel scale and the zero point (see
Sect. 2.4). The total luminosity of an object is determined by the flux of all pixels the object is
considered to be composed of, subtracted by the background estimated above and applying
the zero point.
ellipse fitting
The light profiles of galaxies can be very complicated. They may consist of different structures
like disk and bulge, light concentration might change as well as the position angle and ellipticity of isophotes. In order to measure the radial light profiles we use the STSDAS isophote
package contained in IRAF. The main task is ellipse that fits a set of elliptical isophotes over
an image in order to generate surface brightness profiles of the object which it contains. The
algorithm uses an iterative method following Jedrzejewski (1987).
Each isophote is fitted along a predefined semi-major axis a, starting from an initial guess
defined by center coordinates, ellipticity and position angle θ. The image is then sampled
along an elliptical path, producing a 1-dimensional intensity distribution that depends only on
the position angle. The intensity variations along the ellipse are fitted by a harmonic function
I(θ) = I0 +
(an cos nθ + bn sin nθ) .
3.2 ellipse fitting
Each of the harmonic amplitudes1 (a1 , b1 , ..., a4 , b4 ) contains information about the deviation
of the isophote from perfect ellipticity, i.e., the galaxy isophotes are not necessarily elliptical.
Each amplitude of the series divided by the semi-major axis a and the intensity gradient of the
light profile is then related to a specific ellipse geometric parameter.
n = 1: deviations with 360 ◦ period, i.e. "egg-shaped" distortions
n = 2: deviations with 180 ◦ period, i.e. "flattened" distortions
n = 3: deviations with 120 ◦ period, i.e. "triangular" distortions, not observed in galaxies
n = 4: deviations with 90 ◦ period, i.e. "boxy" distortions
The parameter a 4 /a describes the boxiness of the isophotal shape, i.e., how boxy (a 4 < 0) or
disky (a 4 > 0) an isophote appears (see Fig. 7). The sine coefficient b 4 corresponds to warped
distortions. For pure boxy or pure disky isophotes, b 4 is close to 0. As mentioned in Sect. 1.4,
this parameter is of particular interest since those fourth order deviations of isophotal shapes
are signatures that are related to galaxy mergers (Bender 1988; Khochfar & Burkert 2005).
Figure 7: Illustration of isophotes with disky shape (a4 /a = +0.1, left panel) and boxy shape (a4 /a = −0.1, right
panel) as compared to perfect ellipses. Figure taken from Bender et al. (1988).
ellipse offers to mask pixels that shall not be considered during the fitting process. The
reason for the mask are obvious foreground stars or artifacts that distort the isophotes of
the object of interest. For spatially small galaxies those masks were created manually using
ellipse’s interaction mode. In the case of galaxies with spatially large extend with many small
"companions", however, SExtractor was used.
There are many parameters to be set to fit the isophotes. The method applied to obtain the
light profile is the following:
1. The initial fit was performed with variable ellipticity, position angle and position center of
the measured light profile in order to get a first guess for those parameters. The starting
point for the fit was basically near the effective radius of a galaxy.
2. After the first guess for the center coordinates, they were fixed at the position where the
S/N was smallest and/or the position did not change significantly over a large range of
the fit.
1 The ellipse task uses An coefficients of the sine and Bn of the cosine terms, in contrast to the general notation in
literature we have used here.
3. Subsequently, the same method was applied to ellipticity and position angle. In some
cases there was an isophote twist observed such that position angle was allowed to vary.
Similarly, in some cases better results were obtained by applying variable ellipticity.
4. We checked the obtained isophotal fit with the isopall task in order to find a guess for
the isophotal parameters. After that, a model of the light profile was created using the
bmodel task and subtracted from the original image. The model was finally fine-tuned
(by fixing model parameters with the best guesses) in order to get a residual image that
contains the least signatures.
Basically, ellipse provides an output table that contains all parameters of an isophote as a
function of the semi-major axis. These tables will be used to analyze the surface-brightness profiles (see Sect. 4.3), and also to derive accurate galaxy magnitudes from the cumulated intensity
of the isophotes.
Chapter taken
from Lieder
et al. (2013)
sextractor and morphological classification
SExtractor (Bertin & Arnouts 1996) was used for detecting dwarf galaxy candidates in the
field of view, followed by visual inspection. To optimize SExtractor’s parameters, we simulated
seeing convolved dwarf galaxies with exponential surface brightness (SB) profiles and circular
morphology (ellipticity=0) and added them to the R-band Subaru field. We put only 50 artificial
galaxies on randomly chosen fields of 1 arcmin2 to not saturate the already crowded field with
objects. That process was repeated 100 times. Later in this section, we also use these simulations
for completeness determination.
Dwarf galaxies are found to be relatively homogeneous in terms of their photometric scaling
relations (Misgeld & Hilker 2011) among different environments. As input for our simulations,
we used the µ-mag relation found by Misgeld et al. (2009) for dwarfs in the Centaurus cluster1
with a simulated scatter in µ of ± 0.96 mag around the fiducial relation. This scatter corresponds
to the 2 σ width of the relation found by Misgeld et al. (2009). The goal of this exercise is to
determine the location of typical dwarf galaxies in SExtractor’s MU_MAX-MAG_BEST space, in
order to establish a distinction from the crowd of small faint objects whose apparent sizes are
close to the resolution limit of our data (Fig. 8). The parameter space occupied by the simulated
dwarf galaxies is clearly offset from the bulk of faint sources, which allows defining a fiducial
separation line as indicated in Fig. 8. All objects below the green line in that plot are considered
as possible members of the NGC 6482 group. A small minority of simulated dwarf galaxies
have recovered SExtractor parameters above that line, because they are superposed on another
object – mostly a brighter foreground star.
1 µV,0 = 0.57 · MV + 30.90 and converted to R-band by adopting V − R = 0.6 mag
Table 3: Optimized SExtractor parameters for dwarf galaxy detection.
Notes. This parameter set is sensitive to faint extended objects but many more unresolved objects
are found. Photometric output parameters are reliable in general, but individual outliers of up to
0.5 mag between input and recovered magnitude
can occur due to the rather extreme setting of background determination.
sample selection and photometric procedures
Overall, the analysis of SExtractor’s findings showed that even with extreme settings, only
up to 80 − 85% of the simulated galaxies for the brightest galaxy bin are discovered (see Fig. 9).
This is due to a crowding completeness limit imposed by the high foreground star density
towards NGC 6482 owing to its low galactic (l = 48, b = 23) latitude (see, e.g., Fig. 10). In
the halo of bright stars, an automated detection algorithm like SExtractor tends to "overlook"
individual sources. In addition to the crowding incompleteness, the usual surface-brightness
incompleteness begins at MR ∼ −13 mag. We used an analytical expression to describe the surface brightness incompleteness, normalized to the crowding incompleteness level. This function
is shown in Fig. 9. It reaches a 50% completeness at MR ≈ −10.5 mag and was used to correct
the luminosity function (LF) for incompleteness.
The SExtractor detection parameters were varied (see Fig. 9 and Table 3) in order to find the
optimal set in terms of recovered simulated galaxies with respect to all detections classified as
galaxy – given in Fig. 8. We stress that for the actual photometry of dwarf galaxy candidates,
individual aperture photometry was performed. The automatic magnitudes measurements by
SExtractor are only used for the preselection of probable dwarf galaxy candidates.
The optimal SExtractor parameter set for dwarf galaxy detection is displayed in Table 3, and
yielded a total of 621 galaxies below the green line, out of a total of 61120 detections in the field
of view. Those 621 objects were a preselection and were subsequently inspected visually by two
of the authors (SL and SM) in an independent manner in order to reject artifacts (see Fig. 11).
The majority of sources were indeed readily identified artifacts in the halos of bright stars, see
e.g., the lefthand panel of Fig. 11. Another goal of the visual inspection was to reject obvious
background galaxies, such as low surface-brightness spiral galaxies, interacting low surfacebrightness galaxies (merging events), or small, very faint galaxies that appear too compact
(compare right center panel and right bottom panel of Fig. 10). In particular, the last distinction
has an impact on the number counts at the faint end of our sample. It is well known that faint
dwarf galaxies (at MR > −12 mag) are diffuse, while their effective radius does not change
Figure 8: SExtractor MAG_BEST and peak surface brightness for all non-saturated objects
detected in the long exposure of the Subaru NGC 6482 field of view, including simulated dwarf galaxies with apparent sizes
corresponding to the distance of NGC 6482.
The SExtractor object detection parameters
are given in Table 3. Black contours: all
detected objects. Red dots: discovered simulated dwarf galaxies. Green dashed line:
separation line adopted between galaxies
and unresolved objects at the faint end
(µpeak = 30 + 0.7 × MR ).
4.2 color-magnitude diagram
significantly with luminosity (see Misgeld & Hilker 2011). As a result, we implicitly assume for
our visual inspection that the faint dwarf galaxies should exhibit such a diffuse appearance.
Of the 621 SExtractor detections, 83 remained as visually confirmed candidate dwarfs. Twelve
other sources were rejected because either a spike of a nearby foreground star covered the
object’s center, a structure was visible after the subtraction of the modeled galaxy (see Sect.
4.2.1), or there was no counterpart found in B-band, or only a very weak one (∼ 1σ above sky).
Furthermore, two obvious dwarf galaxies (with MR ∼ −11.5 mag and −10.7 mag) not detected
by SExtractor and all bright galaxies (six galaxies brighter than MR = −18 mag and a diffuse
dE with MR ∼ −15.6 mag) were included in the sample since SExtractor was tuned to find faint
galaxies with MR > −14 mag. Overall, 80 galaxies in the absolute magnitude range −8.8 mag
to −22.7 mag at NGC 6482’s distance were selected for detailed photometric analysis.
The morphological classification we adopted during visual inspection follows the extended
Hubble scheme by Sandage & Binggeli (1984). In the dwarf regime, we simplify it by labeling
early-type dwarf galaxies generally as "dE" and irregular dwarf galaxies as "dIrr". Examples
of our classification are shown in Fig. 12. The morphological classification type of each group
galaxy is provided in Table 6.
color-magnitude diagram
The morphologically preselected sample was cleaned of further probable nonmembers via color
selection criteria. In the following section 4.2.1, we describe the photometric procedures applied
for the color measurement and in 4.2.2 discuss the selection of the fiducial sample based on the
distribution in color-magnitude space.
4.2.1 Photometric procedure for magnitude and colour measurement
To correct for the light blurring due to the PSF, we degraded the R-band images to the worse
seeing of the B-band images (1.0 arcseconds) using IRAF task psfmatch. By doing this, we expected to measure the flux within the same physical isophotes. Since the observed field is very
Figure 9: Determination of optimal SExtractor parameters.
Upper panel: selection of tested SExtractor parameter
sets. Colored curves show SExtractor detection number
counts for different setups (TH: detection threshold; A:
minimum area of pixels above threshold; DBTH: number
of deblending subthreshold; DBCONTR: deblending contrast). The black, dashed histogram indicates the number of simulated galaxies in each magnitude bin. The
red solid line represents our final choice, since it provides an optimal balance between the fraction of recovered objects and the detection of spurious ones. Lower
panel: the red, solid histogram shows the fraction of
recovered simulated galaxies using the optimal parameter set. The black solid line is a fit to the red histogram
(i.e., our completeness function). Owing to crowding
incompleteness (high foreground star density), the recovery completeness saturates at 80% for the brightest
sample selection and photometric procedures
Figure 10: Illustration of example SExtractor detections. In each case the yellow circle has a diameter of 20 arcsec
and is centered on the object in question. Numbers in the upper right corner denote absolute R-band magnitudes.
Upper panel: simulated galaxies placed into deep science images. Middle panel: objects accepted as possible
members after visual inspection. Lower panel: rejected objects because of compact appearance or visible structure
typical of background grand-designed spirals or mergers.
crowded, the light of a very bright foreground star’s reflection halo partially contaminates the
light of a selected dwarf galaxy in many cases (see, e.g., left image of Fig. 11). In those cases the
star was modeled in both passbands (using ellipse) and subtracted from the image in order
to obtain more reliable values for the galaxy’s luminosity. All galaxies were photometrically
analyzed using the ellipse task (Jedrzejewski 1987) that is included in the STSDAS package of
IRAF. All ellipse fits were performed with fixed parameters for center coordinates and position angle but variable ellipticity. In some cases, like the central galaxy NGC 6482 itself, optimal
results were obtained when the position angle was allowed to vary. Because the seeing of the
R-band images was better, we did a first ellipse run for the undegraded R-band images. Those
4.2 color-magnitude diagram
Figure 11: Illustration of preselected SExtractor detections considered as possible members (red circles) and artifacts/background sources (yellow circles). Left: many objects are rejected since they are detected in the refraction
halo of a foreground star and in the shadows along instrument suspension. Right: a field not affected by artifacts
where detections close to spikes of foreground stars were rejected. Only a few objects remain and are considered
as possible group members (red circles).
(a) E
(b) SBc
(c) dIrr
(d) dE,N
Figure 12: Examples of morphological classification (provided in subcaption).
were used for the surface brightness analysis in Sect. 4.3. Another ellipse run was performed
to fit the degraded R-band images. We then applied the obtained isophote table to the B-band
image of the same object to measure the flux within the same physical isophotes. Obvious faint
foreground stars and background galaxies were masked, and ellipse fits were performed far
beyond the galaxy’s edge to see whether the signal reaches the amplitude of the background
noise. Using that level, an individual background adjustment was done for every galaxy. The
result of this background estimation is shown in the three panels of Fig. 13. The intensity levels
out at zero and associated error bars become as high as the signal; i.e., the signal is dominated
by background noise (note the logarithmic scale of the intensity – right axis).
The ellipse output tables were used to determine all astronomical quantities that are presented in this study. The truncation radius of a galaxy was defined to be the last isophote
at which the intensity is still higher than its error. The radial profiles of the cases shown in
Fig. 13 are displayed out to that truncation radius. The flux enclosed by that ellipse is used
as (measured) total flux f. Using that flux the apparent magnitude of an object is calculated.
Finally, the apparent magnitude of an object was corrected for galactic extinction by applying
the foreground extinction map of Schlegel et al. (1998). In Table 2 quantities determined for the
sample selection and photometric procedures
Figure 13: Intensity profiles (open symbols, right y-axis) and cumulative flux (solid symbols, left y-axis) of three
arbitrarily chosen galaxies in the sample. Shown are all data points used for determining the total flux.
photometric calibration are listed. The photometrical uncertainties of the dwarf spheroidals
(dSph) are dominated by sky noise.
The half-light radius r50 is determined as the radius enclosing 50% of the measured total flux
f. We determine the mean B − R color of each object using the flux within r50 as determined
in R-band. Within r50 the signal-to-noise ratio is higher than for the total flux. In light of
the crowded field and the transparency variations (see Sect. 2.4) in some cases a variable sky
background can occur, making r50 more reliable for our color estimation, especially for very
low surface-brightness targets for which total fluxes are difficult to determine.
Fiducial sample definition via color-magnitude selection
The colors of all objects with B − R < 1.75 mag and brighter than MR = −10.5 mag are shown in
the color-magnitude diagram (CMD) in Fig. 14. We consider redder galaxies to be background
contamination2 . Galaxies fainter than this limiting magnitude have very large B − R color errors and are in the luminosity regime where the detection completeness is below 50%. The
colors represent the integrated value within the half-light radius r50 . Only the color of the
BGG, whose inner arcsec is saturated in R-band, is represented by its value at r50 . The B − R
value of the disrupted galaxy (at MR ≈ −17.7 mag) comes from SExtractor analysis. It is clearly
visible in the plot that three disky galaxies fall almost exactly on the red sequence (RS hereafter). These are the S0 host of the disrupted galaxy, an S(lens)0 and a dusty edge-on spiral –
the bright blue square in Fig. 14. See ID 3, 6, and 2 in Table 6. The sample also contains two blue,
almost face-on spirals and three dIrrs denoted by filled blue squares. The four brightest galaxies are spectroscopically confirmed group members (and indirectly the disrupted galaxy, see
Sect. 5.5). Nicely visible in the CMD is the two-magnitude gap in R-band between the BGG and
the second-ranked galaxy – one of the fossil criteria. Also noticeable is that the second brightest early-type galaxy has MR = −17.7 mag – five magnitudes fainter than the BGG, already
entering the dwarf galaxy regime.
To improve on the purely morphological constraints of group membership described in the
previous section, we color-restrict our sample to galaxies that lie within 3σ of the red sequence
(RS), whose location we determine with a least square fit to the data points shown in Fig. 14.
2 A 12 Gyr-old stellar population with super-solar metallicity ([Fe/H] = +0.2 dex) – typical of luminous early-type
galaxies – has a B − R color of ∼ 1.75 mag (Worthey 1994).
4.2 color-magnitude diagram
Figure 14: Color-magnitude diagram of all objects brighter than MR = −10.5 mag (our 50% completeness limit) and
bluer than B − R = 1.75 mag. B − R colors represent the integrated value within the half-light radius determined
in R-band, except for the BGG –where the color is determined at r50 –, and the disrupted galaxy (see Sect. 5.5).
Red data points denote red sequence galaxies that we consider to be group members (circles: elliptical galaxies,
squares: S0 galaxies), blue data points for blue cloud galaxies (circles: blue dSphs, squares: spirals and irregulars),
respectively. Black data points are galaxies considered to be background galaxies. The open blue square denotes
the disrupted galaxy of Sect. 5.5. Open circles (one blue, one red) represent galaxies with uncertain photometry
because the galaxy is superposed on a brighter object (BGG or refraction halo of a star) that could not be fully
modeled. Because of their morphology, those galaxies are included in the sample. The solid black line is a best
fit for our red sequence CMR for galaxies brighter than MR = −14 mag (see text). The dashed lines illustrate the
3σ level of confidence, which is used to reject background galaxies from the sample on the red side.
To not be affected by the larger scatter of faint galaxies we fit the RS only to galaxies brighter
than MR = −14.0 mag, and exclude the obvious blue sequence objects, as well as three photometrically uncertain galaxies.
We obtain the following least-square fit for the color-magnitude relation (CMR) of the RS in
the NGC 6482 group
B − R = (−0.029 ± 0.008) · MR + (1.05 ± 0.13)
with an RMS of 0.06 mag. The index r50 given to the color legend (B − R) on the y-axis indicates that the values are the average within the half-light radius. The CMR fits the relation
defined by the brightest early-type galaxies in our sample well, down to MR ∼ −14 mag, and
is also consistent with the color distribution of the fainter galaxies – even though these exhibit
a larger scatter. In the following, every object within the 3σ RMS of the fit and brighter than
MR = −10.5 mag is considered to be an RS member of the group. We furthermore include two
galaxies in this fiducial sample with uncertain photometry that formally places them redward
sample selection and photometric procedures
(a) dE(,N?)
(b) dE,N
Figure 15: Galaxies with uncertain photometry due to BGG’s halo and several stars in close proximity. We believe
both galaxies are part of the group. In the righthand figure, we could not account for additional brightness
gradients from the BGG and a very bright foreground star.
of the above 3σ range, but they morphologically resemble diffuse dwarf galaxies at the group’s
distance 3 (see also Fig. 15). Galaxies belonging to the blue cloud are labeled with blue datapoints. After selection around the red sequence, twelve out of 80 galaxies were considered to
be background galaxies on the basis of their extreme red colors. Three of those are visible as
black datapoints in the CMD. When only considering galaxies brighter than the 50% completeness level at MR = −10.5 mag, 22 further galaxies are disregarded. Finally, including the two
probable members with uncertain photometry mentioned above, this yields a fiducial sample
of 48 probable group member galaxies (see Table 6).
surface brightness profiles measurements
Surface brightness (SB) profiles of all investigated galaxies were analyzed using the analytic
expression suggested by Sersic (1968). In our case we fitted single Sérsic profiles to the R-band
SB obtained from the undegraded images (see Sect. 4.2.1), that is,
" #
Rc 1/n
µ(R ) = µe + 1.0857 · bn
−1 ,
where µe is the SB of the isophote at the effective radius re . The constant bn is defined in terms
of the parameter n that describes the shape of the light profile. As shown by Caon et al. (1993),
a convenient approximation relating bn to the shape parameter n is bn = 1.9992n − 0.3271 for
1 6 n 6 10, which we applied in our calculations. The c in the variable
Rc denotes that we
performed the Sérsic fits with respect to the circularized radius Rc = a 1 − , where a is the
major axis of the isophote with its ellipticity . We note that a multiple Sérsic fit would be more
appropriate in the case of the S(lens)0 galaxy in our sample (ID 6 in Table 6) (see Kormendy &
3 These galaxies are listed in Table 6 with IDs 20 (MR = 14.2 mag, B − R = 2.48−1.13
mag) and 22 (MR = 14.1 mag,
B − R = 1.74 ± 0.13 mag
4.3 surface brightness profiles measurements
Bender 2012 and Janz et al. 2012). Thus, the errors of a single Sérsic fit are rather large for this
galaxy. For consistency with the rest of the sample, we stick to a single fit as reference. We note
at this point the importance of a reliable background estimation for the SB fits to dwarf galaxies.
Caon et al. (2005) show that incorrect sky background estimates lead to significant differences
in the Sérsic fitting parameters. We are confident that the individual curve-of-growth method
described above gives a robust background estimate for each galaxy.
The Sérsic fits were performed with different fitting ranges. The standard fit excluded the
inner two arcseconds (i.e., one arcsecond of Rc ), which is about three times the seeing, and was
performed until the intensity reaches µR = 26.5 mag/arcsec2 . For some very faint SB profiles,
the fit did not converge so that either only the inner arcsecond was excluded or the limiting
SB was set to µR = 25.0 mag/arcsec2 . Nonetheless, we tried to perform the fit with all of the
three settings to get robust error estimates that are provided in Table 6. For nucleated galaxies,
only the main body of the galaxy was fitted, excluding the central luminosity spike. Total
luminosities were not computed from those fits, but from information of the total galaxy flux
given by the ellipse outputs.
The results of these measurement are used to analyze the photometric scaling relations of
dwarf galaxies in the fossil group NGC 6482, and to identify galaxies in our sample that exhibit
centrally concentrated light profiles – typical of intrisically luminous galaxies – resulting in
high Sérsic n (more than 2). In particular for galaxies with faint total magnitudes, this would
indicate that they are background galaxies following Lieder et al. (2012).
Chapter taken
from Lieder
et al. (2013)
That galaxies are brighter in the R-band than in the B-band (∼ 1.5 mag) roughly compensates
for the missing depth in the R-band (∼ 1.2 mag). Since the seeing is better in the R-band, we
present all results related to the according R-passband quantities.
spatial distribution
In Fig. 16 we present a B − R color-coded, luminosity-scaled spatial distribution of all galaxies
within the field of view that are considered group members. There is another spectroscopically
confirmed group member outside the field of view with an apparent B-band magnitude of
mB = 15.5 mag (Zwicky et al. 1963) – comparable to the other spirals in this study.
Figure 16: Lower panel: Spatial distribution of all galaxies
considered group members (blue and red sequence, see
Sect. 4.2.2). Spectroscopically confirmed group members are denoted by dotted shapes. All objects are colorcoded with respect to their B − R color, and the size
of each galaxy is scaled to its luminosity by roughly
L0.03 . Ellipticity and position angle are represented by
its value at the half-light radius. The solid circle represents the area that is completely covered by our field of
view (r = 229 kpc). The size of the dotted circle corresponds to the virial radius (rvir = 310 kpc). The arrow
in the southwest corner indicates that another spectroscopically confirmed cluster member lies outside the
field of view. Upper panel: Angular distribution of all
galaxies shown in the lower panel within the solid circle. The 0 deg position is north in the lower panel and
the angle grows clockwise. The errors in this plot are
The investigation of the angular distribution of the group galaxies (only within the fully
covered circle of 229 kpc) shows a preferred location of galaxies towards the west (90 deg
position; see upper panel of Fig. 16). There are five galaxies in the far southwest end whose
projections look very clustered. Those five galaxies may constitute an intruding subgroup.
Another constraint on the group membership of the mentioned galaxies arises from Fig. 17.
There we plot the cumulative radial distribution of galaxies of certain magnitude intervals
with respect to their distance from the BGG, to test whether they are clustered towards the
BGG. From this plot it is evident that the bright galaxies (MR < −15 mag) are concentrated
around the BGG as compared to an uniform distribution of galaxies. This also holds for all
galaxies we suppose to be group members.
5.2 photometric scaling relations
Figure 17: Radial distribution of investigated galaxies represented by their cumulative fraction with respect to
their distance to the BGG. Only galaxies within the
solid circle in Fig. 16 (largest completely covered annulus) are taken into account as long as they obey
the membership constraints of Sect. 4.2.2. Green: bright
galaxies (MR < −15 mag). Red: faint galaxies (MR >
−10.5 mag). Light blue: all galaxies brighter than MR =
−10.5 mag. The black solid line represents a uniform
distribution as would be the case for background galaxies.
photometric scaling relations
In Fig. 18 we present the most relevant photometric scaling relations of the galaxies presented
in the CMD and the additional probable member with uncertain photometry at B − R = 2.48,
ID 20 in Table 6, including effective SB µe at the effective radius re , effective radius, Sérsic index
n, and total luminosity. The top panel in particular shows the correlation between effective SB
and effective radius, also known as the Kormendy relation (Kormendy 1977). We stress here
that all quantities except the total magnitude are values that arise from single Sérsic fits to
the light profiles of the undegraded images (see Sect. 4.2.1) down to µR = 26.5 mag/arcsec2 .
We disregard central bright components like nuclei; i.e., only the main body of the galaxy is
considered. Galaxies whose properties constitute strong outliers in these plots are typically
candidates for background galaxies. There is one source that is an outlier in three of the four
plots: this is the S0 galaxy (MRK 0895), the host of the disrupted galaxy (see Sect. 5.5), a
spectroscopically confirmed cluster member. It has a comparatively high surface brightness
and small size compared to the main body of group member galaxies that might be related to
the edge-on view, which is simply an effect of its high inclination (see Fig. 21). We note that
this galaxy is well fit by a single Sérsic profile (as seen in the right panel of Fig. 21). That the
grand design spiral galaxies tend to deviate from the photometric scaling relations given by
the early types is also visible in these plots. The spirals tend to have larger half-light radii and
fainter effective SBs as expected from the early-type relations, resulting in lower concentration
parameter n. This is expected since our Sérsic fits consider the disks alone. Two other outliers
represent the probable members with uncertain photometry. These are the galaxies displayed
in Fig. 15. For the galaxy with two foreground stars in the center, the low SB can be due to
difficult masking that took most of its light.
Clear trends are visible in all relations in the sense that brighter galaxies are larger (re ) and
have brighter SB at the half-light radius and more centrally concentrated light profiles (Sérsic
n). There is no faint galaxy with high Sérsic n that would qualify it as background galaxy.
This is a consequence of our applied µ − mag selection criterion (see Sect. 4.1), which initially
rejects faint galaxies with high central light concentration. Another point is worth mentioning.
We do not see any galaxy within the interval −14 < MR < −13 mag. A similar dip in the
Figure 18: Photometric scaling relations of all investigated galaxies. Except for the total magnitude (curveof-growth), all quantities arise from single Sérsic fits.
In the case of spiral galaxies, the fit was performed to
the disk; for dE,N only the main body was fitted. Symbols as in Fig. 14. While re is the effective radius, µe
represents the effective SB (at re ). The gray line in the
µe − MR -plot gives the relation of Misgeld et al. (2009).
The disrupted galaxy is not shown in this plot (no light
profile available).
galaxy luminosity function around this magnitude was reported by Hilker et al. (2003) for the
Fornax cluster. We, however, refrain from addressing the statistical significance of the gap and
its origin owing to the low number statistics at these low luminosities.
luminosity function
In Fig. 19 we show our completeness uncorrected galaxy luminosity function (1 mag bin width,
steps of 1 mag). The sample used for the LF are the 48 galaxies considered as likely members,
see Sect. 5.2. For a better visualization of the LF we use a binning-independent sampling of
the completeness-corrected LF, performed by an Epanečnikov kernel (Epanečnikov 1969) with
a bin width of 1.0 mag – displayed with red colors in Fig. 19.
Figure 19: R-band luminosity function of member considered galaxies (see Fig. 14). The black histogram represents the observed data (bin width: 1 mag). The red dotted line is a binning-independent representation of the
counts (Epanečnikov kernel of 1 mag bin width), while
the red solid line is its completeness-corrected (see Sect.
4.1) counterpart with the 1σ uncertainty limits (dashed).
The vertical dotted line is our 50% completeness limit
at MR = −10.5 mag. For comparison, some faint end
slopes are illustrated in the top left corner of the plot.
The best fit slope to our data is α ∼ −1.3, see text.
5.4 the brightest group galaxy ngc 6482
Because of the missing L∗ galaxies in a FG, the bright end of the LF looks different from
normal cluster LFs. Thus, a Schechter fit to the LF will only be poorly constrained at the bright
end. Nevertheless, it is meaningful for the faint end. We performed a fit to the galaxy number
count distribution (assuming Poissonian errors), including completeness correction for galaxies
fainter than MR = −15 . The fitting interval was chosen to end with MR = −10.5 mag (our 50%
photometrical completeness limit). We fit the number count distribution of all galaxies in our
imaging survey, noting that this only 84% of rvir is covered by our dataset. The faint end
slope of an error weighted Schechter function fit reveals α = −1.32 ± 0.05. A similar fit to the
luminosity function within the circular region fully covered by our data (0.74 rvir , see Fig. 16),
yields a marginally steeper slope α = −1.49 ± 0.13.
There is a hint of an upturn in the LF fainter than MR = −12 mag, but completeness correction starts to play an important role in this magnitude range, such that we do not discuss it in
more detail.
the brightest group galaxy ngc 6482
The radial SB profile of the BGG (see Fig. 20) is well described by a single Sérsic fit as the
deviation of the photometric data to the fit (second panel) within the inner 100 arcsec remains
at values smaller than ∆µ = ±0.1 mag/arcsec2 . We fit the light profile with respect to the
circularized radius and exclude the inner 3 arcseconds (the inner 2 arcseconds are obviously
affected by saturation) from the fit. Its Sérsic n = 2.82 ± 0.03 – the light concentration parameter
– is rather small for such a giant elliptical galaxy, given that a Sérsic n = 4 represents the typical
de Vaucouleurs profile. In particular it is smaller than reported by Alamo-Martínez et al. (2012)
who find values of ∼ 3.9 in g- and z-band. However, smaller values of n for fossil group central
galaxies were already reported by the FOGO collaboration (Aguerri et al. 2011; Méndez-Abreu
et al. 2012), who obtain a mean Sérsic index of n ∼ 3 for a sample of 21 FGs.
The inner isophotes (10 00 6 Rc 6 50 00 ) of NGC 6482 exhibit a moderately large ellipticity
( ∼ 0.3), and turn into almost spherical isophotes in the outskirts (Rc > 70 00 ). The elevated
overall ellipticity is accompanied by a disky shape in the inner galaxy part (lower panel in
Figure 20: Radial profiles of the BGG NGC 6482. Top
panel: SB profile, including a plot of logarithmic radial
scale in the inset. In both cases the red line represents
the single Sérsic fit, the fitting results are provided too.
The second panel displays the deviation of the data
from the Sérsic fit. The third panel shows the ellipticity with respect to radial distance and the bottom panel
illustrates the a4 /a parameter that describes the deviation of the isophote from a perfect ellipse.
Fig. 20). This is seen from the a4 /a parameter, for which positive values denote disky isophotes
(Bender 1988).
a disrupted galaxy around mrk 895
In one particular case we observe a galaxy being disrupted by the confirmed group member
galaxy MRK 895. This is an edge-on S0 galaxy as shown in Fig. 21. For the disrupted galaxy we
can only provide SExtractor-based photometry. We tuned SExtractor to detect the whole debris.
The obtained flux represents only a lower limit because we have masked point sources, as well
as the hosting S0 galaxy. This fact is denoted by the arrow on this galaxy in the color-magnitude
diagram (Fig. 14).
We masked the tidal debris for the ellipse investigation of the S0 galaxy in the outer regions,
but did not mask it where the debris crosses the bright isophotes along the disk of the galaxy.
Thus, the isophotes might be affected by light from the tidal debris. But this effect should not
be significant for the total brightness of the S0 galaxy since the galaxy itself is very bright (see
light profile in the right panel of Fig. 21).
The projected diameter of the debris is ∼ 35 kpc. We investigated the B − R colors of both the
debris and the overdensity close to the northwest corner of MRK 0895. While the overdensity
shows B − R ∼ 1.4 mag, the rest of the debris shows B − R colors of ∼ 1.2 mag. The S0 galaxy
itself has B − R ∼ 1.69 mag as shown in Fig. 14 (the third brightest galaxy is the host). As a
result, the debris is on average 0.3 mag bluer than its host. The disrupted galaxy is obviously
not on the red sequence. The progenitor could have been a relatively luminous late-type and/or
metal-poor system, since the flux of the whole debris adds to MR = −17.7 mag.
Figure 21: Detection of a galaxy being disrupted. Left: S0 galaxy MRK 895 by which the dwarf galaxy is being
disrupted (north up, east left). Center: Image with different contrast settings to illustrate the tidal debris. Right:
Light profile of the S0 galaxy. The red line visualizes the best Sérsic model to the data.
Chapter taken
from Lieder
et al. (2013)
brightest group galaxy
We find B − R = 1.73 for the BGG NGC 6482, a color typical of metal-rich old stellar populations.
Such a red color was also found for NGC 6482 by Alamo-Martínez et al. (2012) (g − z = 1.85 at
r50 ). Another finding of our study is the relatively low Sérsic index of n ∼ 2.82 for NGC 6482,
in agreement with the studies of the FOGO group, who find Sérsic indices around n ∼ 3 for
FGs (Aguerri et al. 2011; Méndez-Abreu et al. 2012). They argue based on Hopkins et al. (2009)
and Kormendy et al. (2009) that low Sérsic indices for giant ellipticals (n ∼ 2.5) are tracers
for dissipational mergers. Bender et al. (1988) and Khochfar & Burkert (2005) find that disky
isophotes of giant elliptical galaxies are the result of wet, gas-rich mergers, i.e., mergers with
participation of spiral or irregular galaxies. We clearly see disky isophotes in the BGG (a4 /a ∼
0.05) and Alamo-Martínez et al. (2012) identify a dust lane in their HST images of NGC 6482
– favoring the merger scenario of our FG as originally claimed by Ponman et al. (1994). But
that does not necessarily disfavor the "failed group" scenario of Mulchaey & Zabludoff (1999).
Dekel et al. (2009) suggested that inflows of cold streams might have been the major formation
scenario in the early Universe. A rotational disk would have stayed intact while giant starforming clumps merged into the center to form a massive spheroid. These star-forming clumps
– one could call them galaxies – could leave an imprint on the BGG’s morphology, such as disky
isophotes or dust lanes. Oser et al. (2010) show in simulations that the majority of stars of an
intermediate mass central galaxy (like our NGC 6482) have been formed ex-situ in clumps, thus
they have been accreted. In this sense, a massive dark matter halo accompanied by cold gas
streams would reflect the "failed group" scenario but should also show merger signatures. A
difference in both formation scenarios would then become washed-out.
photometric scaling relations
We adopt the µ-mag relation of Misgeld et al. (2009) to simulate galaxies in order to discover
dwarf galaxies in the NGC 6482 group. These relations agree well with the sample properties
of the recovered dwarfs as seen in Fig. 18. Disregarding disky galaxies (i.e., spirals and S0s),
most galaxies in the sample follow the same photometric scaling relations, indicating that they
truly belong to the NGC 6482 group. However, at the faint end of the distribution background
contamination should play an important role. We accounted for that by applying a certain color
range for group members, following the CMR of the bright galaxies.
In general, the photometric scaling relations are very similar to those found in galaxy clusters.
This includes the distribution in CM space (see Fig. 14) where both the red and the blue sequence are distinctly defined. Our best fit of the CMR to the RS has a slope of −0.029 ± 0.008,
comparable to similar slope determinations in B − R/R in some galaxy clusters(−0.045 ± 0.028
discussion and conclusions
for Coma; Adami et al. 2006; (−0.055 ± 0.009 for Perseus; Conselice et al. 2002), possibly somewhat to the shallow side.
luminosity function
Little is known about the faint satellite systems of FGs. The deepest observational study of
a FG in the literature reaches Mg = −16 mag (Mendes de Oliveira et al. 2006) – that is four
magnitudes fainter than the group’s characteristic magnitude (M∗ + 4 mag). Therefore no solid
constraints on the dwarf galaxy regime can be drawn from these studies. Particularly the faint
end slope of the LF has been poorly constrained up to now by other FG studies, and varies
strongly from −0.6 to −1.6 (Cypriano et al. 2006; Mendes de Oliveira et al. 2006, 2009; Proctor
et al. 2011; Eigenthaler & Zeilinger 2012).
Our study is, to our knowledge, the first one to deeply probe into the dwarf galaxy regime of
a fossil group, extending the available literature studies by 6-7 mag in total luminosity. Our
investigation reveals dwarf galaxies as faint as MR = −10.5 mag. We find a faint end slope of
α = −1.32 ± 0.05, fully within the range of values typically found in cluster environments (Table 4), such as Coma or more unevolved clusters like Virgo and Hercules. The faint end slope
of a composite LF, averaged over 60 nearby galaxy clusters, reveals a similar value of α = −1.28
(de Propris et al. 2003). Previous studies have suggested that indeed the faint end slope of the
LF is independent of environment: Trentham & Tully (2002) show such an almost invariable
faint end slope in their study of five different environments with varying galaxy density and
morphological content. They find a composite faint end slope of α = −1.19 for their entire sample. The result of our study, the first deep one in a fossil group, is consistent with the average
slope found in a range of environments, and lends further credence to the notion that the faint
end slope of the galaxy luminosity function depends only very little on environment.
Another useful parameter for describing the LF shape is the dwarf-to-giant ratio (Phillipps et al.
1998; Sánchez-Janssen et al. 2008). We compared our data with the study of Trentham & Tully
(2002), adopting their definition of the d/g ratio as d/g = N(−17 < MR < −11)/N(MR < −17).
By taking the completeness correction into account, we obtain d/g = 4.1 ± 0.6. The error acounts
for color and magnitude uncertainties that could propagate into our group membership determination. The dwarf-to-giant ratio we find is consistent with the average d/g = 3.2 (rms 1.2)
reported in Trentham & Tully (2002), and in particular matches the values they find for virialized systems like NGC 1407 and the Virgo cluster.
We do not find any galaxy in the magnitude range of −14 < MR < −13 mag, best seen in
Fig. 18. While this interesting feature of NGC 6482 might be due to the low number counts
(Fig. 19), we note that a similar dip has been found by Hilker et al. (2003) in the Fornax cluster.
As already noted by these authors, this magnitude range is the transition from dE to dSph.
Another two properties of dwarf galaxies are the fraction of early- to late-types and the fraction of nucleated dEs. Trentham & Tully (2002) find evidence that dynamically more evolved
systems have a higher fraction of dE as compared to dIrr (see also Mahdavi et al. 2005). The percentage of dwarfs in the range −17 < MR < −11 mag classified dE as opposed to dIrr is 89+1
percent, comparable to the fraction Trentham & Tully (2002) that find in the central 200 kpc of
Virgo cluster. The errorbars arise from photometric errors. Among the dEs, 38% are nucleated
within the same magnitude range. This is comparable to the 40% of a combined nucleation rate
of four groups in the Trentham & Tully (2002) sample but only half the nucleation they find for
the Virgo cluster (70%).
We conclude that the NGC 6482 fossil group shows photometric properties consistent with
those of regular galaxy clusters and groups, including a normal abundance of faint satellites.
6.3 luminosity function
Table 4: Luminosity function faint end slopes in literature.
Sandage et al. (1985)
Secker et al. (1997)
Hydra I
Misgeld et al. (2008)
Misgeld et al. (2009)
Sánchez-Janssen et al. (2005)
Hilker et al. (2003)
Penny & Conselice (2008)
Trentham & Tully (2002)
de Propris et al. (2003)
NGC 6482
this study
Notes. Faint end slopes α were derived by a single Schechter function fit.
† Composite LF (linear fit) of five different environments with varying
galaxy density.
The potential missing satellite problem in this fossil group is thus on a similar scale to those in
other environments.
Part III
the millennium-ii simulation
The Millennium-II Simulation (MS-II) (Boylan-Kolchin et al. 2009) is a dark matter N-body simulation that incorporates ΛCDM cosmology. It is based on the Millennium Simulation (MS)
(Springel et al. 2005b) as data structure and particle number (∼ 1010 ) are the same. Both simulations were carried out in a periodic cube, i.e., a particle that escapes at one side will enter it
through the opposite side. As compared to the MS, MS-II has the advantage of a five times better spatial resolution and thus a 125 times better mass resolution. The box size is 100 h−1 Mpc,
somewhat smaller but approximately the scale of the acoustic peak from BAO (Eisenstein et al.
2005; Beutler et al. 2011). At redshift zero, and accounting for the adopted cosmological parameters1 in MS-II, this scale corresponds to a side length of 137 Mpc. A DM particle has a
attributed mass of 6.9 × 106 h−1 M . The resolution limit of a halo is 20 particles which corresponds to a lower mass limit of 1.38 × 108 h−1 M . With this mass resolution, halos similar
to those hosting the Local Group dSphs are resolved (Mateo 1998; Strigari et al. 2008a). Fig. 22
illustrates the variety of structure that arises from MS-II, from the large-scale cosmic web down
to the smallest satellites embedded in larger DM halos.
The simulation data is preprocessed "on-the-fly" in order to identify DM halos. This is
achieved by the friend-of-friends (FOF) algorithm, a technique originally invented to search for
overdensities in spectroscopic galaxy surveys, later modified to look for structures in simulated
galaxy data sets (Huchra & Geller 1982; Davis et al. 1985). The FOF approach is straightforward.
It looks for particle pairs that are closer than a given cut-off separation. In the MS-II this linking length is chosen to be 20% of the mean particle separation. If at least 20 particles could be
linked that way, it was considered a halo and retained for later analysis. At z = 0, in the full
MS-II about 60% of all DM particles belong to ∼ 107 FOF groups. Those FOF halos are teemed
with substructure, as illustrated in the lower-left panel of Fig. 22 which shows the largest FOF
group in the simulation.
In a post-processing step, it was searched for that substructure within FOF groups using the
SUBFIND algorithm that identifies "substructure candidates as regions bounded by an isodensity
surface that traverses a saddle point of the density field" (Springel et al. 2001). All self-bound
substructures containing at least 20 particles were stored as subhalos. The most massive subhalo
within a FOF group is called the main (sub)halo of the group, and usually contains most of its
mass. Each subhalo found in a given output was then linked to one descendant subhalo in the
following output. The so constructed merger trees thus mimic structure growth by merging of
subhalos, and not by merging of halos. Sometimes a subhalo is not identified by SUBFIND when
passing through the center of the FOF halo (Boylan-Kolchin et al. 2009), but found again in the
subsequent output. However, those cases are very rare.
1 Ωm = 0.25, Ωb = 0.045, ΩΛ = 0.75, and H0 = 73 km s−1 Mpc−1
Figure 22: A sequential zoom through the Millennium-II simulation. The upper-left panel is a 15h−1 Mpc thick slice
of the full 100h−1 Mpc simulation (in comoving coordinates). The sequence is centered on the most massive halo
of the simulation (8.2 × 1014 h−1 M ) – similar to the Coma cluster (Colless & Dunn 1996). The cosmic web is
clearly seen and even on the smallest scale 0.5h−1 Mpc a rich variety of substructure is visible. Figure taken from
Boylan-Kolchin et al. (2009), their Fig. 1.
Beside the total mass of all FOF group members MFOF , MS-II provides three more definitions
to determine a mass within a spherical region. The center of a FOF halo is in every case defined
as the position of its main subhalo. We will stick to the definition of the virial mass Mvir given
in Sect. 1.2, i.e., the mass within the largest sphere with the mentioned center and a mean
overdensity that exceeds 200 times the critical value. The radius of this sphere is the virial
radius Rvir . Both are linked to each other by
G Mvir
100 H2 (z)
whereas G is the gravitational constant and H(z) is the redshift dependent Hubble constant.
Hence, the virial mass contains all masses of particles within the sphere, if SUBFIND consideres
them to belong to the group or not (see above). However, Guo et al. (2011) mention that the
virial radius usually lies entirely within the boundary of the FOF group, i.e., the virial mass
always takes masses into account that are physically FOF group members. The reader is re-
7.2 the semi-analytic model of Guo et al. (2011)
ferred to Springel et al. (2005b) and Boylan-Kolchin et al. (2009) for a detailed description of the
Outputs are saved in 68 epochs, so-called snapshots. 65 of those snapshots are spaced according to
log10 (1 + zN ) =
N(N + 35)
(0 6 N 6 64)
and three snapshots at high redshift z = 40, 80 and 127. The latter corresponds to a lookback
time of ∼ 13.6 Gyr. Table 7 shows that the snapshots are not equally spaced in time.
the semi-analytic model of Guo et al. (2011)
We will use the semi-analytic model provided by Guo et al. (2011) (G11 hereafter) to investigate
properties of FGs in general but also to compare the results of our observations to predictions
of simulations/SAMs. The model uses the MS-II and bases on the SAM by de Lucia & Blaizot
(2007) (DLB07), which successfully described the homogeneity of local BCGs properties and it
has drawn a link between those and high redshift galaxies. The DLB07 model utilized the MS
with its lower mass resolution. Guo et al. updated and extended the DLB07 model, and applied
it additionally to the MS-II in order to put constraints also on the dwarf galaxy population.
Their galaxy formation model incorporates following baryonic processes.
Reionization is included by a model that describes how the baryon fraction in a halo depends on
mass and redshift (Gnedin 2000). A universal baryon fraction of 17% is adopted, based on the
first year WMAP results (Spergel et al. 2003). It is shown that reionization has no major impact
on galaxy formation, except, maybe for the faintest satellite systems.
Cooling happens as diffuse gas joins a halo. At early times and in low mass halos, the material is
essentially available in free-fall time by cooling. In massive galaxies (> 1012 M ) a shock front
occurs in the outer regions of the galaxy, creating a hot atmosphere of infalling (and shocked)
gas. This gas is then accreted by cooling flows. The gas accretion rate on a halo for both regimes
is estimated by models of Springel et al. (2001) and de Lucia et al. (2004). This makes condensation on the center smooth in time and not instantaneously. The important difference to DLB07
is that satellite galaxies are allowed to have gas halos which can be removed gradually (see
The disk of a galaxy is distinguished between gas disk and stellar disk. Both are allowed to grow
in mass and angular momentum. While the gas disk grows by gas accretion or minor mergers,
the angular momentum of the stellar disk can only be changed by star formation, transferring
mass from the gas disk to the stellar disk. Both the gas and the stellar disk are assumed to
be thin, to have exponential density profiles, and to have maximum circular velocities of the
surrounding DM halo. The derived stellar light concentrations and sizes of both discs in this
simple model are fairly in agreement with observations (Guo et al. 2011).
Star formation is assumed to happen from cold gas according to an empirical relation which
links star forming regions of star forming galaxies to high surface mass density regions contained in the cold gas disk (Kennicutt 1998). The process is efficient if a certain threshold for
local instability in the rotationally supported disk is exceeded. The G11 model assumes that
a few percent of cold gas is turned into star each rotation period of the disk. This model is
basically similar to the one imposed by DLB07 but the revised cooling treatment leads to a
smoother evolution of the star formation rate, i.e., star formation histories are generally less
Supernova (SN) feedback is adjusted to observed stellar mass functions such that the efficiency of
gas reheating and ejection increases when galaxies become more massive. This is done in order
to account for the observed suppression of star formation in low-mass galaxies. The ejected
hot gas can be retained in an ejecta reservoir and fall back on the galaxy by cooling, which is a
substantial difference to the DLB07 model.
Satellite galaxies are divided into "satellites" and "orphans". While satellites or type 1 galaxies
have a dominant DM component, in orphan galaxies (type 2) the DM halo is not existent anymore, i.e., below the resolution limit. All galaxies are born as type 0 galaxies, become type 1
as they fall into a group or cluster and turn into type 2 when they get merged onto the cluster
center. Basically, the central galaxies of groups/clusters associated with the main subhalo of a
FOF group are in every case type 0 galaxies, but not vice versa. When a "normal" type 0 galaxy
becomes member of a FOF group its label is switched to type 1.
Tidal and ram-pressure stripping is enabled when a satellite galaxy (type 1) enters the virial
radius of the main halo of the central galaxy (type 0). Only within the virial radius thus a
satellite galaxy can become gas stripped. In the model, hot and ejected gas is continuously
stripped equally at each time-step. This is not a realistic setting, since ram-pressure stripping
can already occur at earlier stages of the infall (Bahé et al. 2013) and ram-pressure depends on
the density of the intracluster medium (ICM) which increases inwards. Additionally, the cold
gas component is (unrealistically) not affected by ram-pressure stripping. Only material that is
located outside a stripping radius2 remains in the subhalo.
The improvement to DLB07 manifests in the on average later gas loss of satellite galaxies
which is incremental rather than abrupt. When they enter a FOF group one thus expects that
they continue star formation for longer time as compared to DLB07. However, Guo et al. (2011)
show that the so achieved morphology-density relation is still too strong as compared to observations, i.e., real satellite galaxies retain their gas longer in dense environments, resulting in a
larger fraction of star forming galaxies in clusters. They argue, this is a result of the enhanced
SN feedback which was imposed to match the observed stellar mass function.
Disruption of the stellar component can only occur after the DM halo of the satellite has been
stripped completely, i.e., the satellite (type 1) has become an orphan (type 2). This galaxy orbits
within the potential of the main DM halo. As soon as the DM density of the main halo exceeds
the baryon density of the remaining (stellar and cold gas) halo, the orphan galaxy is disrupted
instantaneously. That is, disruption does not occur continuously. In particular, the cold gas is
added instantaneously to the hot gas atmosphere of the central galaxy, not being able to form
stars anymore. Furthermore, Guo et al. (2011) mention that dynamical friction on the satellites
is not accounted for properly since it only considers the DM particles. Often, the DM subhalo
is less massive than the stellar component, falsifying the expected decay of the galaxy.
Mergers in the model can occur both between centrals and satellites and among satellites. As
soon as the DM mass drops below the baryonic mass of the galaxy, the merger countdown is
triggered. Merging bases on dynamical friction and the merging time for a satellite is estimated
by the formula given by Binney & Tremaine (2008), taking into account both DM and baryonic
2 The stripping radius of a satellite galaxy is a value that takes tidal forces as well as ram-pressure stripping into
account. It essentially becomes smaller with decreasing distances to the main subhalo.
7.2 the semi-analytic model of Guo et al. (2011)
mass. Orbits of type 2 galaxies decay linearly with time as it is expected from a satellite that
spirals to the center of a larger host. During a major merger (baryonic masses of galaxies differ
by less than a factor of three) the discs of the participating galaxies are destroyed and an ellipsoid is created. In the case of a minor merger, in turn, the disk of the larger galaxy remains
intact. In both cases a starburst is triggered, following Somerville et al. (2001). That is, a fraction
of the cold gas contained in both galaxies is converted into stars. These are added to the disk
of the remnant in the case of a minor merger. A major merger, on the other side, expels (almost
all of) the remaining cold gas from the remnant by the strong SN feedback.
Bulge formation is achieved in Guo’s model by either a merger or secular evolution of a disk.
While a major merger ends up in an ellipsoid, a minor merger remnant forms a bulge that consists of all stars from the minor progenitor. The other possibility to transfer mass from the disk
to the (possibly already existing) bulge is to apply a criterion for disk instability (Efstathiou
et al. 1982) which was slightly modified. It is shown in the paper that disk instability is the
major contributor to bulge formation for intermediate-mass galaxies, while mergers dominate
the other mass regimes. However, the comparison with SDSS data reveals that the agreement
with observed stellar mass concentrations "is fair, at best" (Guo et al. 2011). In particular the
light of low-mass galaxies is too strong dominated by the disk. This is explained by the possible
dissipation of gas during mergers, not taken into account.
Black hole growth and AGN feedback occur in two modes, following (Croton et al. 2006): "quasar"
mode and "radio" mode. Quasar mode applies to black hole growth owing to gas-rich mergers,
and is adjusted in order to match the observed relation between black hole mass and bulge
mass. Feedback is not modeled explicitly but incorporated in the starburst that follows the accretion onto the black hole. Radio mode growth is related to hot gas accretion onto the central
black hole of galaxies which deposits energy in relativistic jets which in return heat the hot
gas atmosphere. This AGN feedback is able to disrupt type 2 galaxies, and, moreover, can also
operate in low-mass satellite galaxies since they are also associated with hot gas. Essentially,
the quasar mode dominates black hole growth in any case.
Metal enrichment by supernovae happens as both heavy elements and a fraction of the star’s
mass are deposited instantaneously in the cold gas component of a galaxy. Metals are then
carried into the hot gas atmosphere by SN winds. This atmosphere can then be stripped subsequently, which enhances metals in the inter cluster medium. The model is adopted from
de Lucia et al. (2004).
Stellar population synthesis by the models of Bruzual & Charlot (2003) adopting a Chabrier initial
mass function is employed in order to compute the photometric properties of the model galaxies – like stellar masses and realistic magnitudes. Dust extinction is kept redshift dependent in
order to account for observations.
In their paper, Guo et al. (2011) focus on evaluating improvements as compared to DLB07 and
differences between MS-II and MS. We are interested in comparing our photometrically obtained results to the Guo model. There are two particular photometric properties that shall
be mentioned here. First, the LF at redshift 0 deviates at both ends when comparing it to the
SDSS data of the nearby universe. This is displayed in Fig. 23. The abundance of dwarf galaxies
is underpredicted by the model, independent of the observed band. G11 speculate that either
assigned mass-to-light ratios are too large for dwarfs, or the observational data overcorrects for
Figure 23: Galaxy luminosity functions in the SDSS compared to Guo’s SAM. Black data points are SDSS lowredshift data from Blanton et al. (2005). The green line is the prediction by the Guo model. While data with
absolute magnitudes fainter than −20 results from MS-II alone, the bright end is results from MS+MS-II in order
to cancel out cosmic variance. While the model underpredicts the abundance of faint galaxies, the number of
bright galaxies is overpredicted as compared to the nearby galaxy sample. Figure taken from Guo et al. (2011),
their Fig. 8.
incompleteness at the faint end, or cosmic variance3 influences the observational data. Possibly,
all of the reasons are applicable. Similarly, there are too many bright galaxies at present time
predicted by the model, in particular in the g band. This might be indicating that the applied
dust model fails to predict sufficient extinction.
The other point concerns the colors of galaxies. As illustrated in Fig. 24, low-mass galaxies
are too red in the G11 model, while luminous galaxies are too blue in turn. For the latter
difference, the paper makes K-corrections4 and the uncertain photometry of the observational
sample responsible. For lower masses it is mentioned only that the dwarfs are finishing star
formation too early which makes them passive and red. This picture is supported by the finding
of an "overly high redshift of the peak of the star formation history" (Guo et al. 2011), i.e.,
3 Cosmic variance is the uncertainty in observational estimates for the volume density of galaxies. It arises from the
limitation of the volume, even in large surveys, which do not cover large-scale density fluctuations (see Somerville
et al. 2004).
4 The flux of an astronomical source within a given band(width) varies with redshift owing to the shift of its spectrum.
The K correction accounts for this flux difference when comparing the flux of two objects at different to each other
(see Hogg et al. 2002).
7.3 selection of clusters and groups
dwarf galaxies form too early in the model. Another particular hint is provided by Weinmann
et al. (2011) who find that the red fraction of dwarf galaxies in model clusters is too high.
They show that this is owing to environmental effects. Ram-pressure-stripping is too strong in
the G11 model and tidal disruption may be insufficient so that too many red dwarfs survive.
However, Fig. 24 also tells us that the majority of galaxies in the intermediate mass range
9.5 6 log M∗ 6 11.0 are "in reasonable agreement with observations". It is mentioned by Guo
et al. (2011) that the reddest galaxies are dominated by passive galaxies containing a disc, in
particular at intermediate mass.
For the sake of completeness, it shall be mentioned that Guo et al. (2013) updated MS and MSII by scaling structure growth in a ΛCDM universe to the cosmological parameters consistent
with seven-year WMAP results (Komatsu et al. 2011) and applied their SAM to those scaled
versions. In particular the matter density Ωm and σ8 , the RMS density fluctuation amplitude
of a top-hat sphere of 8h−1 Mpc radius, have changed significantly since the first-year WMAP
results originally adopted in both simulations. It was already realized by Guo et al. (2011)
that clustering at scales below ∼ 1 Mpc is overpredicted, suggesting that the implemented σ8
value was too high. However, the effects of the change in both parameters cancel out, i.e., the
predictions with updated cosmology are very similar to those of the original model.
We will stick to the Guo et al. (2011) model in this work. Although some critical points
were raised in the above text, it is a state-of-the-art SAM that incorporates many aspects of
galaxy formation and evolution and its comparison to observations is generally in reasonable
selection of clusters and groups
We aim to investigate not only fossil groups but also their link to "normal" galaxy groups,
if there is. On the other hand, we are interested in comparing our observationally obtained
results of NGC 6482 to FGs in the Guo SAM. Prior to the investigation of FGs we additionally
aim to compare our results to those of the FG studies in the framework of the Millennium
Gas Simulation by Dariush et al. (2010). They investigated only "FGs" more massive5 than
∼ 2 × 1013 h−1 M , hence "fossil clusters" (see their Fig. 1). Therefore, we select galaxy groups
from the Guo catalog with virial masses6 larger than 1012 h−1 M . That is, we pick the 3542
most massive galaxy groups and clusters from the ∼ 107 FOF groups in the MS-II.
5 Note, that we will use the cosmological parameters specified in the MS-II, in particular the dimensionless Hubble
parameter h = 0.73
6 The virial mass provided by the Guo tables is taken from MS-II and therefore takes only dark matter into account.
Figure 24: "u − i color distributions as a function of stellar mass. Solid black curves show distributions predicted
by Guo’s model, applied to the MS (above log M∗ = 10.0) and MS-II (at lower masses), while dashed red curves
are distributions compiled from SDSS/DR7. The range in log M∗ /M is indicated at the top right-hand side."
Clearly, the model overpredicts red low-mass galaxies but underpredicts red high-luminosity systems. Figure
taken from Guo et al. (2011), their Fig. 12.
the x-ray luminosity criterion
We recall the definition of a fossil group from Sect. 1.5. There has to be a central elliptical
galaxy that dominates the group by a magnitude gap to the second ranked galaxy of two or
higher. It has to be associated with a hot gas halo that exceeds a certain X-ray luminosity LX .
The latter turns out to be a problem in the G11 tables since no LX is provided in the publicly
available data. On the other hand, the definition by Jones et al. (2003) also provides a clue to
solve it. The only reason to apply the X-ray luminosity criterion was to ensure that we deal
with the central galaxy in the group. The G11 tables provide a parameter type which is the
galaxy type mentioned in Sect.7.2. A type zero galaxy is supposed to be the central galaxy in
the FOF group because it contains the most bound DM particle. In reality, this is similar to, e.g.,
the Virgo cluster, where the central galaxy M87 is associated with the largest DM halo traced
by the hot gas in the X-ray (Böhringer et al. 1994). Hence, we translate the X-ray luminosity
criterion of the fossil definition into: a galaxy being identified as a type zero.
Another approach to obtain an X-ray luminosity is provided by Stanek et al. (2010). They
make use of the Millennium Gas Simulations1 , a resimulation of the MS with gas particles. For
the (more realistic) PH simulation which includes preheating and cooling of gas along with
shock heating, they provide a relation between the virial DM halo mass and the bolometric
X-ray luminosity Lbol of the associated hot gas component at z = 0.
hln Lbol i = −1.653 + 1.868 × ln Mvir
whereas Mvir is given in units of 1014 h−1 M and Lbol in units of 1044 erg s−1 . Dariush et al.
(2010) (D10 hereafter) investigate fossil cluster properties utilizing the SAMs of Croton et al.
(2006) and Bower et al. (2006), based on X-ray luminosities originating from the above mentioned PH simulation. In their Fig. 1 they provide a visualization of Eq. 7 including its scatter
(see Fig. 25). There are three points to make about this plot.
1. Above log(Mvir /h−1 M ) ∼ 13.5 all clusters fulfill the X-ray luminosity FG criterion.
2. When using Eq. 7, the virial mass of a cluster, which scratches the X-ray luminosity limit
of 0.25 × 1042 h−2 erg s−1 , is log(Mvir /h−1 M ) ∼ 13.2. Of course, the scatter around the
relation introduces an uncertainty to the mass.
3. Most important, clusters below log(Mvir /h−1 M ) ∼ 13.2 do not accumulate enough hot
gas to exceed the FG X-ray luminosity. In other words, NGC 6482 should not exist as a
group with FG X-ray luminosity. But we have to admit, there are not many halos with
masses lower than that.
1 The Millennium Gas Simulations should be treated with care because there is no publication available describing
it, even unrefereed.
definition and literature evaluation of fossil systems
Figure 25: "The relation between the mass
of group haloes (within R200 ) at z = 0
from the Millennium DM simulation, and
the bolometric X-ray luminosity of the corresponding haloes in the Millennium gas
simulation. All groups have M(R200 ) >
1013 h−1 M at z ∼ 1.0. The vertical dashedline corresponds to the X-ray luminosity
threshold LX,bol = 0.25 × 1042 h−2 erg s−1
generally adopted to define fossil groups.
Of the 17866 groups matched in the two catalogues, 14628 groups lie above this threshold." Figure taken from Dariush et al. (2010),
their Fig. 1.
This thesis’ focus is on the mass regime of NGC 6482, i.e., on FGs with masses lower than
1013 M , which are not considered in the analysis of D10. We will avoid the LX criterion for
FGs because we know, when a galaxy resides in the center of a cluster and is not accidentally
a bright galaxy in its outskirts. However, we will discuss the results of D10 in the context
of our study. Knowing that fossil clusters can occur at masses log(Mvir /h−1 M ) > 13.2 ≈
2.2 × 1013 M , we talk about galaxy clusters in the following when this mass is exceeded. It
is roughly a tenth of the Virgo cluster virial mass and half as massive as the Fornax cluster
(McLaughlin 1999; Drinkwater et al. 2001; Urban et al. 2011). Using this definition, we find 180
clusters in the MS-II at z = 0.
the magnitude gap
The most distinct property of fossil groups is the large magnitude gap between the first and
second ranked galaxy. In this section this gap is investigated to get an insight to fossil groups
and to figure out how these can be distinguished from "normal" groups. We will specify the
magnitude gap ∆m12 as the difference in r band luminosity between the central galaxy of
a FOF group and the brightest group member within half the virial radius given in the G11
tables. Of course, ∆m12 is the gap between the first and second ranked galaxy. For fossil groups
it is indeed larger than 2. Generally, a galaxy brighter than the central one may reside within
0.5 rvir though. This is the case, for instance, if two groups encounter or a nearby giant galaxy
has a significant star burst. In conclusion, values ∆m12 < 0 may occur.
In Fig. 26 we visualize the magnitude gap at present time as a function of the assembled
mass fraction at z = 1 to the value at z = 0. This study has been performed by D10 for the
SAM of Bower et al. (2006) (see Fig. 26a), and we compare it to the G11 model in Fig. 26b. The
basic finding in the cluster regime of the MS is that the most massive clusters form late. They
have assembled only about 20% of their final mass at z = 1 (bluish data points). Less massive
clusters (reddish data points) tend to assemble earlier but, generally, the majority of all clusters
assemble their masses late if we define "late" as "assembling more than half of their masses
during the last 7.7 Gyrs". The plot also tells us that low-mass clusters are more likely to form
8.2 the magnitude gap
(a) Dariush et al. (2010)
(b) this work
Figure 26: Magnitude gap m12 between the first and second ranked galaxy within 0.5 rvir at z = 0 versus the ratio of
the virial mass at z = 1 to the mass at z = 0. (a) X-Ray bright clusters (fulfilling the LX criterion for FGs) from the
Millennium Gas Simulations. Basically, all data points belong to clusters with masses log(Mvir /h−1 M ) > 13.2.
Cluster masses are color coded from low-mass to high-mass, red through blue, respectively. The horizontal dotted
line marks the transition between fossil and non-fossil clusters. Clusters have typically ∆m12 < 2 and the major
fraction of clusters assemble the majority of their mass after z = 1 (vertical dashed line), with low-mass clusters
tending to assemble their mass earlier. (b) Similar plot based on the G11 model, except color coding. Black
contours (determined in squares of 0.1 × 1.2 in levels in factors of 15) illustrate the distribution of the low-mass
regime – basically groups, while red data points belong the 180 clusters. The cluster distribution is comparable
to that of D10, although negative magnitude gaps occur. Low mass systems show significantly higher ∆m12 and
typically assembled 70% of their mass before z = 1. Using the ∆m12 criterion, an overwhelming majority of low
mass systems in the G11 SAM is fossil, also by means of the assembly time. Note the different scalings for ∆m12
in (a) and (b).
∆m12 > 2 as compared to the most massive clusters in the study of D10. However, it is clearly
seen in Fig. 26a that the overwhelming majority of clusters is non-fossil.
The same analysis in the G11 model is presented in Fig. 26b. There is general agreement with
the investigation of D10. The majority of clusters (red data points) have ∆m12 < 2, 14% could
be labeled (optical) "fossil" when the magnitude gap criterion is applied. The median assembled mass fraction is ∼ 0.6, in qualitative congruence with the low-mass systems of Fig. 26a
(70% of our clusters have masses log(Mvir /h−1 M ) < 13.6). The low-mass halo sample (black
contours) continues the trend when compared to the high-mass sample in the following sense:
the lower the mass of a system the earlier it has formed the majority of its final mass and the
higher its magnitude gap. 74% of all low-mass systems (log(Mvir /h−1 M ) < 13.2) are optically "fossil" with magnitude gaps up to ∆m12 ∼ 10. The extreme behavior is not surprising as
the fraction of solely optically determined fossils is known to increase with decreasing mass
(see Cui et al. 2011 and references therein). Most notably, low-mass systems seem to prefer to
have assembled ∼ 70% of their final mass at z = 1 as it visible from the increasing density of
the contours. However, it is also evident from Fig. 26b that basically the whole parameter space
is available to low-mass systems.
But there are also differences between both plots. By our definition of ∆m12 we allow negative values. This is apparently not the case in the analysis of D10. They mention that their ∆m12
is the gap between the first and the second ranked galaxy in the system, i.e., the central galaxy
has not necessarily been taken into account. However, only 5% of low-mass systems have a
definition and literature evaluation of fossil systems
negative magnitude gap and 10% of the clusters. We could have treated the magnitude gap
accordingly by flipping all negative values but it illustrates another difference between both
plots. The low-end of our ∆m12 distribution correlates with the fraction of assembled mass at
z = 1. It seems a consequence of the above mentioned trend that earlier assembled systems
have on average higher magnitude gaps.
The trend is even stronger for low-mass systems. The above mentioned flipping of negative
magnitude gaps can wash out this trend at least for systems that have assembled more than
∼ 60% of their masses before z = 1. In fact, this behavior could indicate an evolution process,
which argues in favor of FGs such as fossil means "majority of mass early assembled". Other
explanations are plausible as well, e.g., that this regime is dominated by field galaxies which
have only few (and much fainter) companions. Furthermore, we have to keep in mind that
this plot is "constructed" as it considers only galaxies that reside within half the virial radius.
The plot does not provide an information about the general magnitude gap in groups. In the
outskirts, another bright galaxy may reside but not within half rvir . However, the correlation
among groups found in Fig. 26b is not obvious in Fig. 26a.
Another point worth mentioning is that some systems loose mass since z = 1, particularly
in the low-mass regime. These systems are not shown in Fig. 26b and would be located at
assembled mass fractions > 1. However, they are so sparse that no contour does appear. On the
other hand, without exception, clusters in the G11 model gain masses if comparing the z = 0
snapshot with that one at z = 1, in qualitative agreement with Fig. 26a.
In Fig. 27, the sample is divided in four virial mass ranges (vertical lines) in order to investigate the mass dependence of the parameters of Fig. 26a. The plots contain a fossil sample (red
data points) and a non-fossil sample (back data points), with the transition ∆m12 = 2. Because
the distributions are not Gaussian (it is rather a tail of a Gaussian distribution), only the inner
two quartiles of each distribution is displayed by lines. The intersection of these lines denote
the location of the median of a distribution. It is evident in the figure that the masses of fossil
systems are on average smaller than those of non-fossils as red data points are offset from black
data points to the left, except, in the most massive bin.
The bottom panel illustrates the magnitude gap distribution (∆m12 ). Low-mass fossils have
significant higher magnitude gaps in comparison to high-mass fossils. Non-fossils do not show
any trend in this plot, their median is ∼ 1 within every mass bin. The top panel shows the
assembled mass fraction at z = 1 as compared to z = 0, the same parameter as in Fig. 26. It is
obvious in the plot that fossils have assembled a higher fraction (∼ 70%) of their final mass at
z = 1 as compared to non-fossils (∼ 50%). There is a weak mass dependence in fossil systems
but the assembled fraction of the most massive non-fossils drops significantly (∼ 35%). This is
in agreement with the study of D10. In Fig. 26a the most massive systems (bluish) have smaller
assembled fractions.
In the density panel of Fig. 27 we compute2 the local average mass density of the systems
at z = 0 when including all masses3 within a sphere of 5h−1 Mpc radius. For supercluster
volumes this radius has been found to be a constant in the MS (see Einasto et al. 2007, and
Liivamägi et al. 2012 for a different approach to the diameter). The plot shows the expected
mass dependence. The more massive a system the denser its environment. Interestingly, there
2 The estimation has to be done with caution because those huge volumes can overlap with the bounding surface
of the periodic MS-II cube. Therefore, a simple query within a sphere delivers wrong numbers. One fourth of all
systems is affected by this issue when estimating the mass density.
3 We think that mass density is a better tracer for environment since gravitation accelerates all systems, increasing
velocities and therefore increasing the probability for encounters.
8.2 the magnitude gap
Figure 27: Mass dependence of fossil (∆m12 > 2, red data points) and non-fossil systems (∆m12 < 2, black data
points). The samples were subdivided in four mass ranges as indicated by the vertical dotted lines. Shown are
the inner two quartiles of each distribution. The center of the crosses denotes the location of the medians. Panels
in top to bottom order. (1) Fraction of final assembled mass at z = 1 (see Fig. 26). (2) Local density within a
sphere of radius 5h−1 Mpc, normalized to the lowest density found among all groups and clusters. (3) Fraction
of fossils within the mass bin. (4) Magnitude gap distribution. The most massive mass range contains only one
fossil system, displayed by the red dot.
is no or very small difference between fossils and non-fossil. From a statistical perspective both
types reside in similar environments.
The remaining f∆m12 > 2 panel represents the fraction of fossil system within each mass bin.
It shows that the fraction of (by the magnitude gap) identified fossils increases continuously
with decreasing virial mass as already suspected from Fig. 26a. This is in agreement with both
observational and semi-analytical studies which consistently claimed the mass dependence of
the optical fossil fraction (Milosavljević et al. 2006; D’Onghia et al. 2007; van den Bosch et al.
2007; Yang et al. 2008; Dariush et al. 2010). On the other hand, there is inconsistency about
the actual value of the fraction (10 ∼ 60% for masses ∼ 1013 M .). We find even 80% in the
lowest mass bin to be "optical" fossils. Using the GIMIC simulations (utilizing the MS), Cui
et al. (2011) have shown that it is necessary to invoke the X-ray luminosity to shrink the optical
fossil fraction from 70% to a X-ray matched fraction of ∼ 10%. X-ray data is not available for
the G11 SAM. Therefore, we will use a different approach to account for the hot gas emission
as outlined in the following section.
definition and literature evaluation of fossil systems
finding elliptical galaxies
In this section we want to investigate the properties of the central group/cluster galaxies in
order to find fossil groups in our sample. This addresses photometric properties but also star
formation and merger histories. Beside the identification of systems which should be X-ray
bright, the aim is to find central galaxies to be identified with ellipticals. The latter is the third
and obvious selection criterion of FGs.
Ellipticals as passive galaxies
Elliptical galaxies are known to be non-star forming. Hence their light is dominated by old
stars, which let an elliptical appear red. We recall from the previous chapter that in the G11
model star formation is driven by either disk instabilities or merger events. Galaxies become
passive/non-star forming if the merger event is strong enough to expel the cold gas from the
disk to the hot gas reservoir.
Photometric properties. A first approach is to investigate the dependence between star formation
and color, illustrated in Fig. 28 where star formation rate (SFR) versus u − r color of central
galaxies is plotted. Red data points represent central galaxies of clusters and black contours
belong to central galaxies of groups with masses lower than log(Mvir /h−1 M ) = 13.2. There
are 26 clusters in the SAM exhibiting the FG magnitude gap larger than 2 mag within half
the virial radius. Those clusters are divided into "candidate" and "true" FGs and marked with
green and blue crosses, respectively. A true fossil is a massive cluster one expects to have a
sufficient bright FG X-Ray luminosity as outlined in Sect. 8.1.
As expected from the stellar population model, group centrals occupy two regions in the
plot. There are red and passive galaxies but there is also a significant number of blue and starforming centrals, if we consider the notations "blue" as u − r < 2 mag and "star-forming" as
SFR > 1 M yr−1 . The latter is the commonly referred to the SFR of normal spiral galaxies (Lee
et al. 2009).
The identification of active galaxies being blue holds not for cluster centrals. Star-forming
central galaxies of clusters remain red, although the scatter increases towards more bluish
colors. In particular, it turns out that even central galaxies of fossil clusters can be star forming.
This behavior can be explained by their lower specific SFR (per unit stellar mass, SSFR hereafter)
as displayed in Fig 29. Star forming central galaxies of clusters have on average a factor of ten
higher stellar masses as compared to those of the groups. The same amount of new born stars
contributes a smaller fraction to the total light in the case of cluster centrals, i.e., the light
remains dominated by older, red stars so that their SSFR is small compared to actively starforming spiral galaxies. Again, typical values for normal spiral galaxies are SSFR > 10−11 yr−1
(Lee et al. 2009), denoted by the horizontal dotted line. Fig. 29 shows that the two classes of
central galaxies (star forming and passive) in groups remain intact. On the other side, even
the central galaxies of fossil clusters can be actively star forming in the SAM of G11 although
they are red. However, we are interested in ellipticals which are known to be passive galaxies.
Fig. 29 therefore suggests that SSFR 6 10−11 yr−1 is also reasonable in the G11 model in order
to distinguish passive from star forming galaxies.
Another interesting point regards the luminosities of fossil cluster centrals. They are generally brighter than Mr = −22 mag. This is in agreement with the observational studies of
Zarattini et al. (2014) and Santos et al. (2007) who find only 1 out of 25 (1 of 34, respectively)
fossil clusters whose central galaxy is fainter than that. We use this finding in the following as
8.3 finding elliptical galaxies
Figure 28: u − r over SFR of central galaxies in the SAM of G11. Shown are only
galaxies with SFR > 0 at z = 0. Red
dots represent the central galaxies of clusters (log(Mvir /h−1 M ) > 13.2). Purple
data points belong to those clusters with
SFR > 1 M /yr. Blue crosses represent
clusters which fulfill ∆m12 > 2 and have
masses log(Mvir /h−1 M ) > 13.5, i.e., they
would certainly be bright enough in the Xray to qualify them as FG according to D10
(see Sect. 8.1). Similarly, green crosses are
the less massive clusters which fulfill the
magnitude gap of fossil groups. Black contours belong to the data from groups with
masses log(Mvir /h−1 M ) < 13.2. The
green dashed lines represent the divisions
between blue and red, and star forming
and passive, respectively. In groups, blue
central galaxies are star forming. In contrast, star forming cluster centrals are significantly redder, likewise the fossil clusters.
constraint for centrals galaxies of fossil groups.
Star formation histories. What are typical SFRs of elliptical galaxies in the G11 model? Since elliptical galaxies are formed by mergers, we compare the star formation history (SFH) of central
galaxies to their merger history in order to figure out what level of SFR can be expected for an
elliptical galaxy.
For the last 7.6 Gyr (z = 1) this analysis is shown for 16 examples from group mass scale
through cluster scale in Fig. 30 for a "fossil sample" with ∆m12 > 2 and in Fig. 31 for a "control
sample" which obeys |∆m12 | < 0.5. In each subfigure (of similar mass) the histories of two
central galaxies are plotted. Denoted in blue is a galaxy that has SFR > 1 at z = 0, while black
lines/symbols belong to a galaxy with SFR < 1 at z = 0. The top panel of each subfigure shows
the SFH of the central galaxy (by means of SSFR) and the bottom panel illustrates its merger
A merger event was considered to take place one snapshot after the mergeon flag of an
infalling galaxy was set to either 2 (merging galaxy is type 2) or 3 (merging galaxy is type 1),
and its descendant was the central cluster/group galaxy. According to G11 we define major
mergers (baryonic4 mass ratio larger than 1:3) and minor mergers (mass ratio between 1:3 and
1:10). We also consider mergers that have not been significant (masses differ by more than a
factor of 10). These three regimes are separated by horizontal dotted lines in bottom panel of
each subfigure.
Both figures show clearly that mergers trigger star formation, as described in Guo et al. (2011).
The SSFR peak remains for one snapshot only (roughly 0.3 Gyr) and can reach a level similar
to that of spiral galaxies (dotted line) regardless of the type of merger. Even a non-significant
merger in the most massive groups can trigger a spiral-like SSFR.
4 We take only stellar mass and cold gas mass into account to determine the merger mass ratio as we have found
only those masses are relevant to destroy a disk in agreement with the G11 definition of a major merger. The hot
gas halo attached to a galaxy is apparently neglected in this calculation, although Guo et al. (2011) write: "Major
mergers are those between galaxies with baryonic masses differing by less than a factor of 3."
definition and literature evaluation of fossil systems
Figure 29: SSFR versus Mr of central galaxies
with SSFR > 0. Labels as in Fig. 28. Black
contours on a grid of 0.4 × 0.4 mag with contour level 20. Within the cluster sample, FGs
and possible FGs occupy only total magnitudes brighter than Mr 6 −22 mag and are
most likely passive with SSFR 6 10−11 , emphasized by the green dashed lines.
The low mass groups in the top left panels of figures show that it is possible to have a
SSFR > 10−11 yr−1 without a merger event. We note that roughly half of all groups with
∆m12 > 2 containing a bright central galaxy (Mr < −22 mag) have such high SSFRs. When
(presumably) the first merger occurs the SFR of such a system is quenched as evident in the
top left panel of Fig. 30 (black line). The time scale of this quenching process, however, seems
to depend on the mass ratio of the merger.
The prescription of G11 converts a certain percentage of cold gas in the disk of a galaxy into
stars each snapshot. This fairly constant (high) SSFR in the low mass centrals, which have not
been disturbed by a merger, belongs to star formation by disk instability. As soon as a merger
occurs, a fraction of the cold gas is converted into stars and the remaining cold gas is either
completely expelled (major merger) or a part of it remains in the surviving disc (minor/nonsignificant merger) (Guo et al. 2011).
There are two points to make about these these figures. First, there is no difference between
the fossil sample and the control sample. The star formation history (SFH) is similar with
respect to merger events. Likewise, the frequency of mergers does not differ significantly either,
when comparing systems of equal mass. Second, SSFR > 10−11 most likely seems to indicate
an ongoing merger event in clusters. At the group mass scale, SSFR > 10−11 in the central
galaxy can also mean, that it has never experienced a merger. Thus, defining fossil groups by
only the magnitude criterion and "not having experienced a merger since z = 1" introduces
a bias because the majority of these "fossils" are star forming. In the G11 model it seems that
these star forming central galaxies are comparable to field galaxies or groups like the Local
Group5 . We will return to this topic in Sect. 9.2.
However, a general SSFR level for passive galaxies is not easy to define from the small
number of investigated galaxies in Figs. 30 and 31. We therefore investigate the merger history
of central galaxies of central galaxies in the group mass regime since z = 1, which is presented
5 The Local Group fits indeed the adopted mass range as it has a total mass of Mtot ∼ 1.3 × 1012 M (Karachentsev
& Kashibadze 2006).
8.3 finding elliptical galaxies
Figure 30: The effect of mergers on the SSFR in central galaxies of groups/cluster with ∆m12 > 2. Subfigures
correspond to virial masses as indicated, equally spaced in log space. The top panel in each subfigure shows the
SFH of a central galaxy. Snapnum is the snapshot number (see Tab. 7), SSFR in units of yr−1 . SSFR > 10−11 is
typical for spiral galaxies and indicated by the dotted line. The bottom panel of a subfigure shows baryonic mass
ratio of the merging galaxies in logscale. The space between both dotted lines in this plot denotes the ratio range
of minor mergers. Above 1:3 (∼ −0.5 in logspace) a merger event is a major merger. Below 1:10 (= −1 in logspace)
a merger event is "not significant". Blue data points and lines belong to a central galaxy with SFR > 1 at z = 0,
a central galaxy with SFR < 1 at z = 0 is indicated in black. Clearly, SFR peaks in central galaxies are related to
in Fig. 32 for systems with ∆m12 > 2 mag. Plotted is the SSFR at present time (z = 0) with
respect to the lookback time since the last merger involving the central galaxy has happened.
Central galaxies whose last merger event was a major merger belong to red data points, minor
mergers are represented by green data points, and if the last merger was non-significant it is
denoted by blue data points.
If a merger is ongoing (at z = 0) Fig. 32 shows clearly that the SSFR is basically comparable to
that of spiral galaxies (above the dashed line). It is also evident in the plot that major mergers
quench star formation to a level lower than SSFR = 1012 yr−1 . On the other side, non-significant
mergers do not affect the SSFR of central galaxies. These galaxies have generally SSFR on
the same level, which is similar to spiral galaxies. This suggests that these galaxies have not
experienced any other significant merger event in the past. Minor mergers, in turn, inhibit star
formation significantly to a level of −12 6 log(SSFR/yr−1 ) 6 −11, unless the merger took not
definition and literature evaluation of fossil systems
Figure 31: Same as Fig. 30 but for groups/clusters with ∆m12 < 0.5 (control sample).
place during the last 1 Gyr. This suggests that minor mergers inhibit star formation on larger
time scales.
Unless there is no ongoing merger event, the SSFR certainly drops below 10−11 yr−1 if a minor or major merger took place in past. However, Figs. 30 and 31 suggests that central galaxies
in the cluster regime tend to have −12 6 log(SSFR/yr−1 ) 6 −11. This is also supported by
Harrison et al. (2012) who find BCGs of fossil clusters to have SSFR up to 10−11 yr−1 . In the
group mass regime of Fig. 32 a level is not clearly seen either. We thus can not constrain the
SSFR of passive galaxies further and remain with condition that elliptical galaxies must have
SSFR < 1011 yr−1 , which basically means that the central galaxy has undergone a merger in
the past.
Ellipticals as bulge-dominated systems
The other approach to obtain elliptical galaxies is to search for galaxies whose disk has been
destroyed. In the G11 model, this is achieved by major mergers, i.e., mergers with baryonic
mass ratios larger than 1:3. G11 calculate the bulge-to-total (B/T) stellar mass ratios of the
galaxies and adopt B/T > 0.7 to be ellipticals. In Fig. 33 the distribution of the B/T ratios of
3681 central galaxies of most massive groups/clusters is illustrated. It is surprisingly not a
smooth distribution. Basically, no central galaxy with 0.5 6 B/T 6 0.9 is found, in contrast
8.4 fossil groups as relaxed systems
Figure 32: Specific star formation rate at z = 0 vs. lookback time of the last merger involving the central galaxy.
Plotted are only groups with 1012 6 Mvir /h−1 M 6 1013 , ∆m12 > 2 mag and SFR > 0 M yr−1 , which have
had at least one merger event with a galaxy brighter than Mr = −16 mag since z = 1. While major mergers are
those between galaxies with stellar and cold gas mass differing by less than a factor of 3, a non-significant merger
is characterized by mass ratios smaller than 1:10. Minor mergers have mass ratios between those limits. Red,
green and blue data points represent merger events as indicated in the diagram. Solid symbols denote central
galaxies that have experienced only one merger during the last ∼ 7.7 Gyrs, while open symbols show galaxies
with more than one recorded merger since z = 1. If a central galaxy experiences a major merger, the SSFR at
z = 0 is below 10−12 yr−1 unless the merger is not ongoing. Minor mergers quench star formation although less
strong. On the other side, if there was only one non-significant merger in the past since z = 1 star formation is
not quenched, i.e., the SSFR is generally higher than 10−11 yr−1 . The horizontal line denotes the approximate
limit of SSFR in spiral galaxies (Lee et al. 2009).
to observations. We therefore refrain from adopting B/T values and focus on the definition of
passive galaxies as ellipticals, outlined in the previous section.
fossil groups as relaxed systems
Fossil groups are considered to be relaxed as they are dominated by an elliptical galaxy, which
was once formed by a major merger, but obviously not in interaction with another galaxy
anymore. The timescales for obvious strong visual features of mergers range from ∼ 0.2 Gyrs
for dry mergers (Bell et al. 2003) up to ∼ 0.8 Gyrs for major mergers of gas-rich disk galaxies
(Lotz et al. 2008; Bridge et al. 2010). In order to account for this morphological criterion, we
consider groups as potential fossil candidates only if their last merger event (major, minor or
non-significant) happened at least 1 Gyr in the past.
definition and literature evaluation of fossil systems
Figure 33: Bulge-to-total ratios of all central galaxies of groups/clusters with virial
masses larger than Mvir = 1012 M . The
G11 model provides a bimodality as bulgedominated galaxies are clearly distinct from
disk-dominated galaxies.
summary of selection criteria
Here we summarize the criteria which have been applied to the central galaxies of clusters and
groups contained in the SAM of Guo et al. (2011) at z = 0 to obtain fossil groups and clusters.
1. Mr < −22 mag because no fossil cluster was found with central galaxies fainter than that.
In addition X-ray luminosity scales with optical luminosity. Optically bright (elliptical)
galaxies are accompanied by a bright X-ray halo (Cox et al. 2006; Harrison et al. 2012;
Girardi et al. 2014).
2. ∆m12 > 2 within 0.5 rvir , the magnitude gap criterion for fossil groups.
3. SSFR 6 10−11 yr−1 to account for a passive (elliptical) galaxies and to reject spiral-like
4. The last merger involving the central group/cluster galaxy happened at least 1 Gyr in the
past to account for relaxed systems and to avoid visual merger features, which could still
be visible in the observed counterparts.
The selection criteria and the resulting samples are summarized in Tab. 5.
8.5 summary of selection criteria
Table 5: Rejections due to selection criteria for different samples.
magnitude gap
star formation
relaxed systems
Notes. Selection criteria originate in findings of Figs. 29 and 32.
The group mass range is 1012 6 Mvir /M 6 1013 and clusters have masses log(Mvir /h−1 M ) > 13.2. Within 0.5rvir , a
magnitude gap of ∆m12 > 2 mag is adopted for fossil and field
groups, |∆m12 | 6 0.5 mag for control samples. A luminosity cutoff is not imposed on the control samples but for fossils it is
Mr < −22 mag. log(SSFR/yr−1 ) < −11 is adopted for fossil and
control groups, while log(SSFR/yr−1 ) > −11 is the condition for
field groups. Relaxed systems are mimicked by the adoption that
the last merger involving the central galaxy happened at least 1
Gyr in the past.
In this chapter we want to analyze fossil systems and compare these to non-fossil groups which
are referred to as control sample. In literature control samples often have ∆m12 < 0.5 mag (e.g.,
Dariush et al. 2010; Díaz-Giménez et al. 2011). Owing to our definition of ∆m12 in Sect. 8.2,
negative values are allowed as well. Thus, we will define a control group/cluster as −0.5 6
∆m12 6 0.5 mag. Except the luminosity constraint which is put on the fossils, the control
samples have been selected in a similar manner (see Tab. 5). We have already made use of this
notation in Sect. 8.3.1.
fossil clusters
In the previous chapter some constraints were imposed on the centrals galaxies in order get a
tighter sample of ellipticals. In this section we aim at examining global properties for the cluster
mass regime, i.e., log(Mvir /h−1 M ) > 13.2. Four parameters are investigated for a fossil and a
control sample, as they were defined in the previous chapter (see Tab. 5). In Fig. 34 the analysis
of the mass distribution, local densities, the distribution of the central’s luminosities and the
B/T ratios are presented. In each panel the fossil sample is displayed in red and the control
sample in black. Both the control and the fossil sample contain systems of which we believe an
undisturbed elliptical resides in the center.
It has to be stressed at this point that we are facing low number statistics in the cluster regime
(see Tab. 5) as the fossil sample contains only 12 clusters and the control sample consists of 29
clusters. The findings presented here must be seen in this light.
The mass distributions in the top left panel of Fig. 34 shows the employed cut-off at the lowmass end. A first difference between both samples is revealed. While the fossil sample has
a narrow (low-)mass range, the control sample contains clusters which are on average more
massive. In the top right panel of Fig. 34 the average local mass density is computed as already
done in Sect. 8.2. The different mass distributions do also manifest in different density distributions. The distributions look similar but shifted to each other. Fossils tend to reside in lower
density regions. The median overdensity of the fossil sample is ∼ 23, while the value is roughly
a factor of 1.5 larger for the control clusters.
The bottom panels of Fig. 34 illustrates properties of the central galaxies. Control centrals
are fainter than their fossil counterparts, being on average ∼ 0.3 mag brighter. Note, that the
fossils BCGs are generally brighter than Mr = −22 mag (see Fig. 29) and no artificial cut-off
is introduced in this plot. The B/T ratios of both fossil and control cluster centrals converge
to 1 which indicates that the majority of those galaxies have experienced a major merger (or
9.1 fossil clusters
Figure 34: Properties of clusters with masses log(Mvir /h) > 13.2 at z = 0. Top left panel: mass distribution of the
virial masses. Top right panel: distribution of the local environment as mass density within a surrounding sphere
of 5h−1 Mpc radius (see text). Bottom left panel: r band luminosity distribution of the central galaxy. Bottom
right panel: B/T ratio distribution of the central galaxy. Red data belong to the fossil cluster sample and black
data represent the control sample. Fossil clusters have lower masses and reside in less dense environments. While
their BCGs are brighter than those of control clusters, both types are ellipticals.
repeated minor mergers) such that the G11 model considers the disk of those systems to be nonexistent, i.e., they are ellipticals at present time. On the other hand, this result is not surprising
since only 13 out of 180 cluster centrals are not ellipticals when considering B/T = 0.7 as
transition to disk galaxies.
The fossil phase
As pointed out in Sect.1.5, simulations revealed that fossil groups are merely a phase in the
evolution of galaxy groups and clusters (e.g., von Benda-Beckmann et al. 2008). It is a basic
intention of this thesis to address this finding. D10 emphasize this as they find only very few
clusters that remain fossil after 7.6 Gyrs, or in return, fossils we see today were not fossils
at z = 1. In Fig.35 we present the same analysis. In order to be comparable, we choose the
magnitude gap criterion only to define a fossil and a control cluster. The figure shows the same
trend Dariush et al. (2010) found. After ∼ 7.6 Gyrs the majority of fossil systems is not fossil
anymore. Similarly, a fossil cluster at z = 0 was unlikely fossil at z = 1. Control clusters behave
history and properties of fossil systems
Figure 35: Evolution of fossil and
control clusters (see text). We select control and fossil clusters at
z = 0 (left column) and z = 1
(right column) and explore what
fraction remains fossil or control
at the other epoch. It is clear that
the "fossil phase" does not last in
80% of all cases.
in the same fashion as they do not belong to the control sample anymore when looking back
(or forward) in time.
While the relative numbers for the control sample (∼ 15% remain in the control sample after
7.6 Gyrs) are in agreement with the D10 analysis of clusters, they are not in the case of fossil
systems. In either case, about 20% of all fossil clusters remain fossil. This is a factor of ∼ 10
more than the fraction Dariush et al. (2010) found to remain fossil. It has to be noted again
that the numbers have to be treated with care (5 of 25 remain fossil). Even the Poissionian
error can push the fraction to the level of D10. Additionally, compared to their study we are
biased towards low-mass systems within the cluster regime. As pointed out in Sect. 8.2, the
fossil fraction increases with decreasing halo mass. However, the general message of the figure
is that galaxy clusters in the G11 model evolve in terms of their magnitude gap.
Progenitor halos
Oser et al. (2010) showed in simulations that the stars in galaxies are formed within the galaxy
during a phase of infalling gas before z = 2 which is followed by a phase of accretion of stars
formed outside the virial radius, essentially in other galaxies. Inspired by their work we want
to investigate whether differences exist between the formation of progenitor DM halos that
eventually merge in the central DM halo among a fossil and a control cluster. In Fig. 36a such
an analysis of progenitor halos as identified by subfind is presented for a fossil (red) and a
control cluster (black) of similar mass (log(Mvir /h−1 M ) ≈ 13.6) and environment. We plot
the "formation" time (in terms of redshift) over the distance to the DM halo (in terms of factors
of rvir ) that is considered to be the root of the central halo (bottom left panel).
9.1 fossil clusters
(a) mass origin
(b) mass assembly
Figure 36: Origin and assembly of mass for a fossil (red) and a control cluster (black) of comparable mass
(log(Mvir /h−1 M ≈ 13.6) and similar environment at z = 0. (a) Origin time (in redshift) and place (in terms
of distance to the central halo) of all DM halos that eventually merge in the central DM halo of the cluster. The
formation of the progenitor DM halos of a cluster is clumpy in space and time. The formation time distribution
of both samples is comparable, while the progenitor halos of the control cluster form more distant as compared
to the fossil. (b) Mass assembly of the same clusters with respect to redshift. Before z = 3 the fossil cluster is
roughly an order of magnitude more massive than the control cluster.
There is a correlation in Fig. 36a between formation time of the progenitor halos and their
distance to the central halo. The earlier a DM halo is formed the more distant from the central
halo it happens. This is owing to our definition of distance to the central halo in terms of its
virial radius. The higher the redshift the smaller the virial mass of the central halo (see Fig. 36b)
and therefore the smaller its virial radius (see Eq. 5). Although the absolute distances in factors
of h−1 Mpc may be similar, our relative defined distances must increase with redshift.
However, there is a shift between the distance distributions of both clusters (see top panel
of Fig. 36a). The control cluster seems to be capable to accrete DM halos that have formed in
greater distance, although its final mass is the same as that of the fossil cluster. To explain this
behavior, Fig. 36b is needed. The fossil cluster (red) assembles more virial mass before z ∼ 3, the
period when almost all progenitor halos are formed. Before z = 3, the virial mass of the fossil
cluster is almost an order of magnitude larger as compared to the control cluster. Hence, its
virial radius is larger. This makes the fossil cluster assigning a smaller relative distance (in terms
of rvir ) to an object located at the same physical distance as compared to the relative distance
the control cluster assigns. This accounts for the shift in the formation distances distribution,
which is ∼ 3 as expected from Eq. 5.
Generally, the progenitor halos of the central cluster halos are equally distributed in time but
the distribution is different in space with respect to the central halo. That the control cluster
assembles its virial mass later than the fossil cluster suggests that the central halo originates
from a less dens environment and needed thus more time to assemble its mass.
history and properties of fossil systems
fossil groups
In order to compare our observationally obtained findings of NGC 6482 to the G11 model, we
are particularly interested in properties of fossil groups in the group mass range. We have
selected 59 FGs and 141 control groups as they are specified in Tab. 5. The central galaxy
of the control sample has not a luminosity constraint but needs to be non star forming in
order to compare it to the red FG sample. Additionally, we will investigate the star forming
"fossils" whose centrals look like spiral galaxies, simply because we are curious about those.
The star forming "fossil" sample is accordingly defined, except for their high SFR, and consists
of 298 groups. While the representation of fossils (red) and controls (black) is adopted from the
previous section in plots, the star forming "fossils" will be displayed in blue throughout this
In Fig. 37 the properties of the groups are presented similar to Fig. 34. The mass distributions
in the top left panel provides first insights. Clearly seen is the adopted mass range for groups
(1012 6 Mvir /M 6 1013 ) which cuts the distributions on both edges. While the control
sample shows a uniform mass distribution blue "fossil" and red FG distributions are very
different from each other. The masses of the passive FGs are basically higher than 1.6 × 1012 M
and fairly uniformly distributed up to the cut-off at the high mass end. The mass distribution
of the active "fossils" looks like the tail of a Gaussian distribution, cut at the low mass end.
There is actually not a single star forming "fossil" more massive than 4.5 × 1012 M .
The local density distributions (see Sect. 8.2) in the top right panel of Fig. 37 show that environmental differences among the samples are not as strong as one would expect it from
their mass distributions, although they exist. Again, the control sample and the red FGs have
strikingly similar distributions. The median overdensity a group resides in is ∼ 13 for the FG
sample and ∼ 14 in the case of the control sample. In contrast, the median local density a blue
"fossil" resides in is ∼ 10. Obviously, these "fossils" reside in on average lower density regions as
compared to the other samples. This again indicates that we are facing a kind of "field groups".
In addition, the comparison to the cluster environment (see Sect. 9.1.1) shows that groups tend
to reside in less dense environments, although they also cover the range of environmental
densities in which clusters are situated.
The distribution of the centrals’ luminosity in the bottom right panel of Fig. 37 reveals the
magnitude cut which was imposed on the fossil systems. Their distribution is similar to a tail of
a Gaussian. Remarkably, the centrals of star forming "fossils" are on average slightly brighter in
the r band than those of red FGs. This is not a "projection" effect. If we were plotting the whole
distribution without applying the luminosity cut-off, a gap of ∼ 1 mag would be visible between
the mean Mr -values of both fossil samples. The difference between the median magnitude of
the centrals of our luminosity limited samples is ∼ 0.1 mag – not a large gap. The centrals of
the control sample, in contrast, have a much lower median r band luminosity, even compared
to their cluster counterparts they are much fainter. Of course, there is always another similarly
bright galaxy nearby. This seemingly implies that it is very unlikely that those non-star forming
control groups harbor a central galaxy brighter than Mr 6 −22 mag (1 of 141 groups).
For the sake of completeness, B/T ratios of the central galaxies are provided in the lower
right panel of Fig. 37. It shall be stressed here that the B/T might not be reliable since Guo et al.
(2011) mention that the reddest galaxies are passive but contain a disk. This is seen for the red
FG sample in the figure. The majority has B/T ≈ 1, i.e., they are ellipticals. On the other hand,
9.2 fossil groups
Figure 37: Same as Fig. 34 but for groups with masses 1012 6 Mvir /M 6 1013 at z = 0. Red data are FGs, black
data represent the control sample while blue lines belong to the star forming "fossil" sample (see text). Control
groups and FGs have similar mass distribution and similar environment. The properties of their central galaxies
differ (see text). The blue "fossil" sample are low mass groups in low dense regions with central disk galaxies.
∼ 40% of all red FGs have disks in the model although we consider all centrals in the red FG
sample to be ellipticals because they are passive (see Sect 8.3.1).
The control sample central galaxies is even stronger affected by galaxies with B/T < 0.7,
although the same constraints were imposed on both samples, except for the luminosity cut-off.
70% of control centrals are (passive) disk galaxies but supposedly ellipticals. This is expected as
Guo et al. (2011) note that (passive) disk galaxies dominate particularly the intermediate stellar
mass regime of the reddest galaxies (9.5 6 log M∗ 6 11.0), which is similar to the stellar mass
range of the control centrals. The lower stellar mass range as compared to FGs is indirectly
seen in the bottom left panel of Fig. 37 since their luminosities are on average more than 1 mag
fainter. In any case, the blue and star forming "fossil" centrals are purely disk galaxies.
There are two points to emphasize regarding Fig. 37. The passive FG sample and the passive
control sample have similar masses and reside in similar environments, they are thus comparable. Their different central galaxies are expected since FG centrals are outstanding in terms
of their luminosity as we have imposed a luminosity cut-off on these. The other point to make
concerns the blue "fossils". They reside in low density regions, have low masses, and their centrals are star forming disk galaxies. We now may identify these "fossils" as loose groups, their
centrals may represent field galaxies.
history and properties of fossil systems
Figure 38: Magnitude gap distribution. The magnitude
gap of field groups is on average larger than that of
fossil groups.
Figure 39: Fraction at z = 1 of the final assembled mass.
While most of the field groups have assembled more
than 70% of their final mass at z = 1, almost no control group assembles more than 65% of its final mass
at z = 1. The fossil groups distribution looks split.
The major fraction are late assemblers but also a significant fraction of the fossils has assembled most of
its final mass at z = 1.
In Fig. 38 the magnitude gap distribution of the samples is shown. Of course, the cut-offs
which are imposed on the samples are visible. The figure also shows that the field groups have
on average larger magnitude gaps than the fossil groups – represented by the shift between
both samples. The field distribution peaks at 6 ∼ 7 mag. This is a giant gap between the BGG
and the second ranked galaxy, justifying the terminology "field group". However, the fossil
group’s ∆m12 -distribution looks bimodal, maybe due to low number statistics but more likely
because of the imposed criteria (in particular the SFR criterion).
We therefore also examine the fraction of assembled mass at z = 1 as opposed to the final
mass achieved at z = 0, illustrated in Fig. 39. Clearly, field groups have assembled the major
fraction of their final mass already ∼ 7.6 Gyr in the past. The median of the distribution is
a fraction of 71%. Control groups assemble their mass on average later. The median control
group has assembled 48% of its final mass at z = 1. On the other hand, roughly half of the
control groups have assembled half of their final mass or more at z = 1.
The picture for the fossil groups again looks more complicated, maybe bimodal. They seem
to follow the distribution of the control groups. But there is a significant fraction of fossil groups
which have assembled ∼ 80% of their final mass already at z = 1. There is no correlation with
the two peaks of the fossil distribution in Fig. 38. Roughly half of the fossil groups with a high
assembled mass fraction have ∆m12 < 4, so do not behave like the field groups as one could
have expected from the assembled mass distribution. Similarly there is no correlation with B/T
ratios either (not illustrated in the figures).
However, as seen in Fig. 39 at the high fraction tail, there are (fossil) groups that had assembled more mass at z = 1 as compared to z = 0, i.e., they have lost mass. Therefore, the process
of mass loss provides an reasonable explanation for shifting groups within the figure. On the
9.2 fossil groups
Figure 40: Time spent in fossil phase since
z = 1 for groups as indicated in the figure. The broadened distributions of both
the passive FG and control sample "peak" at
∼ 5 Gyrs and are similar to each other. The
inlay plot shows the ∆m12 history for two
arbitrarily chosen fossil and control groups.
It illustrates the transient character of the
fossil phase. In stark contrast, almost all star
forming field groups have spent the complete 7.6 Gyrs in the fossil phase.
other side, only 5 of 16 fossil groups with α1.0 > 0.7 experience a significant mass loss since
z = 1 (more than 20% between two arbitrary snapshots).
The fossil phase
In Sect. 9.1.2 we have found evidence in the G11 model that the fossil phase seems indeed
transient in a cluster’s evolution. In this section this phase shall be examined in more detail.
We thus extract from the SAM1 how often a group was in the fossil phase since z = 1. Fig. 40
displays the distribution of time which a group has spent in the fossil phase, i.e., during that
time there was no other bright galaxy – according to the magnitude gap of 2 – within half the
virial radius.
The distributions of the passive fossil and the control sample are strikingly similar. They
span the whole range of values, but none of the fossil groups has spent less than ∼ 0.8 Gyrs
in the fossil phase. Most of the groups in both samples have spent at least ∼ 2 Gyrs in a fossil
phase, in some cases several times. Interestingly, even ∼ 8% of all control groups were fossils
for more than 7 Gyrs. A bright galaxy has entered their 0.5rvir -sphere only recently as they are
labeled "control". However, the similar distributions of the control and the fossil sample are a
manifestation of the transient fossil phase.
The picture is completely different for the star forming field groups. Almost all of those
have spent more than ∼ 7 Gyrs in the fossil phase, which is in this case not transient. Although
we know that they did not experience any major merger in the past (see Sect. 8.3.1, this is
1 In this calculation a group is considered to remain fossil for the whole time period between two snapshots, as
indicated by the inlay plot of Fig. 40. This introduces an uncertainty of up to 0.35 Gyrs within a snapshot. However,
this uncertainty applies to both situations. Groups can leave or enter the fossil phase. On average and for a large
sample both uncertainties might cancel out unless there was no preference of galaxies to cluster as they attract each
other, biasing the magnitude gap. That is, one of both regimes might be entered one time more as compared to the
other. Therefore, the mentioned uncertainty applies which is a maximum error of ∼ 5% as compared to the whole
"observation" period of 7.6 Gyrs.
history and properties of fossil systems
somewhat surprising since it apparently also excludes that any other bright galaxy was nearby
during the last 7.6 Gyrs. This is another evidence that they must be "loose groups" of field
The faint satellite system
As the LF is a key tool to study the faint satellite system of a cluster or group it is a crucial
point of this work to figure out what values for faint end slopes can be obtained from the
galaxy groups of the G11 SAM, particularly in the light of the normal slope that we found in
our study of NGC 6482 (see Sect. 5.3). As fossil groups are special due to their magnitude gap,
a Schechter function will not be appropriate to fit their LFs. In a first approach, we instead
fit the faint end only and use a simple linear approximation whose slope represents the faint
end slope. In order to compare the groups to each other, the LF is normalized to the volume a
group occupies, determined by its virial radius. Hence, the galaxy number is scaled to the virial
volume in order not to overweight the number density of massive groups (or underrepresent
less massive groups) in the calculation. After that the LF is examined in two different ways.
The first method fits a linear function (in log-number-magnitude) to the faint end of the LF
of each group within a sample (−18 mag 6 Mr 6 −10 mag). Errors on the number counts
are treated as Poissonian, and are incorporated as weights into the liner fitting. After that, the
obtained functions are statistically analyzed, represented by mean and standard deviation. We
only provide 1σ confidence levels because the distributions are not Gaussian (we return to this
issue later).
The other determination method collects all galaxies within a given magnitude bin from
all groups of a sample and sums them up (normalized by volume and number of considered
groups). This treatment returns a composite LF, i.e., all galaxies in the sample are considered
to belong to one single group. It provides a smooth distribution which is less affected by low
number statistics as compared to the first method. In order to account for the Poissonian error
on a single number count that a group galaxy contributes, errors are propagated accordingly.
While the latter method provides a view on the global properties of the sample LF, the former
method gives insights into the scatter around those global properties.
The resulting luminosity functions are presented in Fig. 41. The results of the first computation method are displayed by lines – dashed for the mean linear fit, solid for the corresponding
1σ scatter. The data points belong to the composite LFs. The mean slope of all single LF fits
within a sample is given in the top left corner and the slope of the composite LF (linear fit) is
provided in the bottom right corner.
The absolute numbers differ significantly from those given in Fig. 23, where Guo et al. (2011)
compare the overall abundance of galaxies within the whole SAM and compare it to a SDSS
volume of 7.6 × 105 h−3 Mpc3 . Of course, within those volumes, universe is on average less
dense as compared to our study, yielding lower numbers for Φ – the galaxy number density.
Disregarding the different samples in the top left panel of Fig. 41, the overall shape of the LF
looks like a Schechter function, i.e., two power laws at both the faint and the bright end. Of
course, there are differences. At the bright end, each sample departs from a normal Schechter
function, owing to the environment we are looking at – the centers. The brightest galaxies are
known to reside in the centers of groups and clusters, so we always catch the BGG.
The bright end of the field LF provides a surprise since a data point is missing at Mr =
−21.5 mag. This is not expected since we are consider all galaxies within the complete virial
radius. The missing data point indicates that even within the virial radius the fossil criterion
still holds for the field groups. In the case of fossil groups the magnitude gap is washed out
9.2 fossil groups
Figure 41: Luminosity functions on the group mass scale. Top left panel: data points represent the composite LF
of each sample assuming Poissonian errors (see text). The remaining three panels are close-ups of each sample
(color coding as indicated) to emphasize the faint end. Dashed lines represent the mean value which is obtained
when evaluating the function values of the linear fit to the luminosity function of each single group in the sample.
Solid lines denote the corresponding 1σ scatter. Numbers in the top left corner of each panel provide the slope of
a linear function which is fitted to the mentioned mean values, including 1σ scatter. Numbers in the bottom right
corner provide the slope of a linear function fitted to the composite LF in the interval −18 6 Mr 6 −10 mag.
because in some cases there are apparently bright galaxies nearby. This is not a sampling effect,
since all magnitude bins are centered accordingly. All BGGs of the fossil sample are cumulated
in the −22.5 mag bin. In return, the number densities at the bright end of the control sample
are generally high as compared to the other samples. This is owing to (a) the broad range of
central galaxy luminosities (see bottom left panel of Fig. 37) and (b) their definition – there has
to be a comparable bright galaxy nearby.
The focus of the figure, however, is on the faint satellites. Therefore, close-ups of the faint end
of the LFs for each sample are presented in the other three panels of Fig. 41. The composite LF
of the control sample follows tightly the mean LF of the individual groups, i.e., the composite
LF is a good representation of individual LFs. This is also reflected in the same slopes for the
mean LF and the composite LF. Furthermore, we note that the scatter around the mean LFs is
of similar scale for all three samples.
In the case of fossil groups the picture is similar to that of control groups, except that the
composite LF tends to lie systematically above the mean individual LF, at least for −18 6 Mr 6
history and properties of fossil systems
−14 mag. However, the both LFs follow each other and their faint end slopes are of the same
The field sample looks different. The "bright end" of the composite LF around Mr ∼ −17 mag
deviates significantly from the mean LF of the field sample. Bright dwarfs are underrepresented
in field groups as one would expect from a linear faint end. It is therefore not a good representation of field groups. In fact, the faint end dominates these groups. Often, bright dwarf galaxies
are missing in those groups. However, at the "faint end", the mean LF and the composite LF
agree fairly well.
The different computation methods for both LFs provide an explanation for the different
faint end slopes obtained for the field sample (α = −1.41 for the mean individual LF and
α = −1.52 for the composite LF). The composite LF slope averages all data points and is not
well constrained as the LF is curved rather than linear. On the other side, the linear fit of the
individual LFs often takes only the faintest three bin into account since brighter galaxies do
not reside within the virial radius. The low number of data points to be fit is reflected in the
larger scatter (solid lines) as compared to the other samples.
In reality, the spatial distribution of galaxies in groups and clusters is hard to obtain. In observations the line-of-sight coordinate information gets lost and only a 2d-projection is obtained.
The information of the third missing coordinate is generally achieved by spectroscopy of individual galaxies. The Doppler shift contains recessional velocity information. If a large number
n of galaxies within a cluster can be spectroscopic surveyed the radial velocity dispersion σr
centered on the mean recessional velocity v̄ of the galaxy cluster can be calculated by
(vi − v̄)2
whereas vi are the radial velocities of the individual cluster galaxies. The radial velocity dispersion is also a projection of the true 3-d velocity dispersion of the cluster. If the virial theorem
applies to a galaxy cluster, the mean velocity of galaxies within the virial radius is about 3
times the 3-d
√ velocity dispersion σ200 of the cluster. This implies a 1-d velocity dispersion of
σr = σ200 / 3 which is commonly used in the community (see e.g. Cypriano et al. 2006; Evrard
et al. 2008).
In order to be comparable to observational studies we want to determine the LF for FGs
when they are projected. The virial radius shall be known (e.g. from X-ray observations). We
then determine all line-of-sight velocities of all galaxies whose projections are located within
the virial radius. From those σr is calculated. In order to account for the radial extent of the
group, we then reject all galaxies from a projected sample which have
√ radial velocities which
deviate from the velocity of the central group galaxy by more than 3σr . To make this model
more realistic we assume that spectroscopic data is only available for galaxies brighter than
Mr = −18 mag and so that all dwarf galaxies with projections within the virial radius are
taken into account for the LF determination. For the three cartesian projections we calculate
the composite LF as done for Fig. 41. The analysis is presented in Fig.42.
The comparison to the unprojected LF of the fossil groups shows that projection does not
affect the overall shape of the LF. Within error bars the number densities remain the same at the
bright end but are generally higher for the projected LFs. There is also systematical overabundance of dwarf galaxies in every projection. However, the introduced offset does not change
the shape of the LFs. In particular, within error bars (∼ 0.01) the faint end slope remains the
same for each projection. The luminosity distribution of the additionally considered galaxies
must thus have a LF similar shaped as the unprojected LF.
9.2 fossil groups
Figure 42: Luminosity functions of fossil groups projected along an axis as labeled in the top of each panel. Shown
are the composite LFs as of Fig. 41. Numbers in the bottom right corner are slopes of a linear fit to the faint
end of the LF (−18 6 Mr 6 −10 mag). Top left panel: Comparison between all LFs. The other panels show the
comparison of the unprojected LF (gray) and one particular projection (see text). Projection generally overpredicts
the number of galaxies. The faint end slope, however, remains unaffected.
As pointed out by Lieder et al. (2012), there is an offset between the LF faint end slope of a
Schechter fit and an simple linear fit (in log space) such that linear slopes exceed the values
of the Schechter slopes. As already mentioned, the Schechter fit is not a good choice for fossil
groups or small spatial covered samples. On the other hand we want to compare our results to
other studies which generally adopt a Schechter function to fit the LF (see Tab.4). Therefore, in
Fig. 43 we present the Schechter faint end slopes which are still meaningful as the faint end is
numerous occupied. The figure shows the distribution of the particular mean LFs of Fig. 41.
While the distributions of the Schechter faint end slopes are fairly symmetrical for the control
and the fossil groups sample, the distribution is clearly skewed for field groups. Hence, the
mean LF is not a good representation for the whole sample of the field group LFs. The median
(or even better the mode) are better representatives of a skewed distribution. Median slopes are
−1.44, −1.42 and −1.31 for the fossil, control and field sample, respectively. These offsets are
visible in Fig. 43, with field groups tend to have smaller slopes as the mode of the distribution is
α ∼ −1.2. The differences between the Schechter slope and the linear slope are thus of the order
of ∼ 0.1, in agreement with Lieder et al. (2012). The basic result of Fig. 41 and Fig. 43, however, is
the same. The faint satellite system of fossil groups and control groups is comparable in terms
history and properties of fossil systems
Figure 43: Faint end slopes from Schechter fits to the LF
of each fossil (red), control (black) and field groups
(blue). While the distributions of the fossil and control sample is fairly symmetric, the field Schechter
slope distribution is negatively skewed. Field groups
have on average smaller faint end slopes as compared
to the control and fossil sample. For comparison, the
derived Schechter faint-end slopes for NGC 6482 (see
Sect. 5.3) are illustrated by vertical green dotted lines.
Figure 44: Cumulative distribution of d/g ratios of samples as indicated in the bottom right corner. d/g ratios of control and fossil groups are clearly offset. For
comparison, the d/g value of NGC 6482 derived in
Sect. 6.3 is denoted by the green dotted line.
of their abundance and luminosity, they have the same faint end slope. The number of faint
satellites of field groups, in contrast, increase less strong with decreasing luminosity.
We finish this section with a consideration of dwarf-to-giant ratios for all group samples. The
d/g ratio is determined according to Sect. 6.3. Only dwarf galaxies brighter than Mr = −11 mag
are considered, and the transition between dwarfs and giants is Mr = −17 mag. The cumulative
d/g distributions obtained within the virial radius are displayed in Fig. 44.
The overall appearance of the three distributions look similar, statistical variance is thus on
similar scale among each sample. Therefore, the clear offset between the d/g of fossil and
control groups is significant. While the median d/g of fossil groups is 12.5, it is only 8.0 for
control groups. Assuming the number of dwarf galaxies is similar among both samples as
suggested by Fig. 41, the significant difference can only arise from a different number of bright
galaxies. The difference in both d/g ratios could therefore suggest that the number of giants in
control groups is a factor of ∼ 1.5 larger than that in fossil groups. This appears to be reasonable
since control groups are defined to contain more bright galaxies (similar to the central galaxy).
On the other hand, field groups have d/g ratios similar (but somewhat higher, median d/g =
9.0) to those of control groups. This is somewhat surprising and we can only speculate about
the reason. The magnitude gap of 2 mag even within rvir suggests a lack of bright galaxies and
the shallower faint end slopes may indicate a lower number of dwarf galaxies as compared to
the control sample. As a consequence, the d/g ratios of field groups happen to be comparable
to those of control groups.
fossil clusters
Many publications have been investigating fossil "groups" in the MS using all available SAMs
(e.g., Dariush et al. 2007; Sales et al. 2007; Díaz-Giménez et al. 2008; Dariush et al. 2010; DíazGiménez et al. 2011; Cui et al. 2011). All of these studies find percentages in the range of 3 ∼ 13%
for (optical) fossil groups among clusters with masses higher than Mvir ∼ 101 3h−1 M . In the
given mass range, this is in agreement with the occupation statistics of 2dFGRS observations
but the fossil fraction of 18% ∼ 60% in the SDSS is (somewhat) higher (van den Bosch et al.
2007; Yang et al. 2008). According to our definition of a cluster (log Mvir /h1 M > 13.2) and
our selection criteria (see Tab.5) we find a fraction of ∼ 14% of optical fossil clusters in the SAM
of Guo et al. (2011), in agreement with the quoted studies. When we employ more conditions
in order to account for X-ray luminosity and relaxed systems the fractions drops to ∼ 7%, in
agreement with the optical and X-ray study of Jones et al. (2003). However, we stress that this
number is confronted with low-number statistics as 12 of only 180 clusters are fossil.
It is known, from a semi-analytical perspective, that fossil clusters assemble their mass earlier
than "normal" clusters (Dariush et al. 2007; Díaz-Giménez et al. 2008, 2011). Our study confirms
that behavior for the cluster mass regime, clearly visible in Figs. 27 and 36b. Our finding that
fossil clusters reside in less dense environments as compared to "normal" clusters, additionally
favors the picture that the "surroundings of fossil groups could be responsible for the formation
of their large magnitude gap" (Díaz-Giménez et al. 2008).
von Benda-Beckmann et al. (2008) have shown in simulations that fossil groups are not an
end product of galaxy evolution in a group or cluster environment. New galaxies may infall
into the cluster making its fossil status a fossil phase. We confirm that picture of the fossil phase
as ∼ 80% of all fossil clusters at z = 1 are non-fossil after 7.6 Gyrs, and vice versa, ∼ 80% of fossil
clusters at z = 0 have been non-fossils at z = 1. Although our clusters are afflicted with low
number statistics, there is general agreement with the fractions of clusters that remain fossils
in the study of Dariush et al. (2010). However, control clusters behave in a similar way as they
are "non-controls" after the considered time period. This could indicate that fossil clusters can
evolve into control clusters, giving rise that no differences should exist between both cluster
types. This has found to be true for the BCG properties in SAMs (Cui et al. 2011) and in
observations (Harrison et al. 2012; Zarattini et al. 2014; Girardi et al. 2014), and is supported by
our finding that both merger histories and star formation histories for both types of BCGs are
similar from a statistical point of view (see Figs. 30 and 31).
fossil groups
As far as we aware of, there is no study of fossil groups in the SAM of Guo et al. (2011). Beyond
that, the group mass regime with masses 1012 6 Mvir /M 6 1013 has not been explored so
discussion and conclusions
far, except for Cui et al. (2011). On the other hand, those groups are just as massive as NGC 6482
we aim to compare with.
In contrast to the cluster regime, no significant differences exist between control groups and
fossil groups. They reside in similarly dense environments, have comparable star formation
and merger histories, have similar mass distributions and their faint satellite system is similarly
distributed with respect to luminosity. This is in agreement with Cui et al. (2011) who find that
the satellite number distribution between fossils and non-fossils is not different. It has already
been stated by Miles et al. (2004) that the faint end slope of the LF should not be affected by
(possible) merging activities at the bright end.
Control groups differ from fossil groups by definition. This is reflected by the bright end
upturn of their composite LF. In particular, we find that control groups are unlikely to form a
central galaxy brighter than Mr < −22 mag, the imposed cut-off for fossil centrals. That fossil
centrals are on average more than twice as luminous as control centrals could indicate that in
fossil groups the two brightest galaxies have merged, making a control group fossil. The same
argumentation is used by Zarattini et al. (2014) who also find that the fraction of light enclosed
in BGGs of (observational) fossil groups is larger than in non-fossil systems.
However, the most striking similarity between fossil and control groups is that they have
spent the same time periods in the fossil phase, from a statistical perspective. This is somewhat
surprising since control groups are not merely non-fossils, they are sort of counterparts because
another galaxy similar bright as the central galaxy has to be located nearby. If the fossil phase
is part of the evolutionary process of galaxy groups and clusters as pointed out by von BendaBeckmann et al. (2008), it gives rise to an identical evolution of fossil groups and control groups.
Galaxy groups are favorite sites for major mergers because in low-mass environments peculiar
velocities of galaxies are slower which makes encounters more likely (Dubinski 1998; Zabludoff
& Mulchaey 1998). Fossil groups in this picture can be fueled by environment with another
bright galaxy and become non-fossils. After a certain time period both galaxies have merged
and the group becomes fossil again.
At z = 1 control groups have assembled ∼ 50% of their final mass. This is basically in
concordance with the major fraction of fossil groups, again emphasizing the similarity among
both samples. On the other hand, half of both the fossil and the control groups could be labeled
"fossil" if assigning an assembled mass fraction α1.0 > 0.5 to fossil systems – which is the way
to account for the original intention of what a fossil group means (Ponman et al. 1994). This
has already been shown for the cluster mass regime by Dariush et al. (2010) who found a much
higher fraction owing to the low number of (optical) fossil groups. However, in our study a
significant fraction of fossil groups has achieved ∼ 80% of their final mass at z = 1, resembling
the typical assembled mass fractions of field groups, which reside in less dense environment
as compared to fossil groups and contain a star forming central disc galaxy, i.e., a spiral.
The field groups are actually fossil by both meanings. They have assembled ∼ 70% of their
final mass already at z = 1 and stand out by huge magnitude gaps between the first and
second ranked galaxy, visible in Fig.41. These field or poor groups would fit into the picture of
the "failed" group model proposed by Mulchaey & Zabludoff (1999). All baryons are initially
used up in a single luminous galaxy. We find that field group centrals are overluminous and
have not experienced a major or any merger during the last 7.6 Gyrs. In addition, even within
the virial radius there is no other bright galaxy nearby, and the overwhelming majority of field
groups has spent almost the whole time since z = 1 in the fossil phase. Their faint satellite
systems are less unique, as there is a large scatter in the faint end slopes of their LFs. This is in
agreement with the finding that LF properties experience a significant variation in low-density
10.2 fossil groups
regions Zandivarez & Martínez (2011). These authors note that "galaxy evolution in groups
may follow different paths depending on where the group inhabits."
However, field groups are unlikely to have accumulated a significant hot gas halo since
gas was not expelled by a major merger. In addition, Cui et al. (2011) show that high X-ray
luminosity requires are dense environment. Field groups are thus not fossil in the sense of
galaxy evolution as intended by Ponman et al. (1994) but they are fossil by means of their
history. They remained almost untouched by environmental influences and resemble groups
which should not have changed significantly since their formation.
In a nutshell, fossil groups and non-fossil groups are strikingly similar suggesting that they
are two representations of the same evolutionary process of galaxies. Field groups, on the other
hand, are likely to have not changed significantly their appearance since they were formed. An
indication that fossil groups (or non-fossil groups) may be merged field groups is given by
Fig. 43. The number density of faint satellites in fossil (and control) groups increases stronger
than that of field groups, represented by their LF faint end slopes. While giant galaxies merge,
the faint satellite systems of two groups do not (Zabludoff & Mulchaey 1998). This could
eventually account for the steeper slope for fossils and controls as opposed to field groups.
However, this argumentation is not robust as we find that dwarf-to-giant ratios are too high in
galaxy groups of the G11 model as compared to observations. The observational study of d/g
ratios in different environment shows that typical values for non-fossil systems are d/g ∼ 2 − 5
Trentham & Tully (2002). These would be rather extreme cases when compared to d/g ratios
of control clusters in the G11 model (see Fig. 44).
Part IV
In this thesis various aspects of fossil groups were studied. We provide here a photometric
analysis of the nearest fossil group NGC 6482 down to Mr ' −10.5 mag — to our knowledge
the deepest fossil group study yet. Additionally, we investigate the fossil groups in the state-ofthe-art semi-analytical model of Guo et al. (2011) in order to compare it with the observationally
obtained results and to draw conclusions on the evolution of galaxies in groups. The semianalytic model provides high resolution and is the first one that allows to study the faint
satellite systems of fossil groups to luminosities as faint as our observational study. As far as
we are aware of, there is no other study of fossil groups in the semi-analytic model of Guo et al.
We found that present day fossil clusters with masses higher than Mvir ≈ 2 × 1013 M show
properties in agreement with previous semi-analytic studies of fossil clusters (cf. Dariush et al.
2007; Díaz-Giménez et al. 2008, 2011; Cui et al. 2011). Furthermore we found the history of
fossil and non-fossil systems to be similar in terms of star formation and number of mergers.
In the mass regime of galaxy groups (1011 6 Mvir /M 6 1012 ) the similarity between fossil
and non-fossil systems is even more pronounced. Both types of galaxy groups reside in similar
environments, have similar mass distributions and had assembled similar fractions of mass
∼ 8 Gyrs in the past. In particular, we confirmed the scenario that fossil groups are a transient
phase in the evolution of galaxy groups. Both fossil and non-fossil groups have spent the
same time in the fossil phase. Therefore, this suggests that fossil and non-fossil groups are
representations of the same evolutionary track of ordinary galaxy groups.
In agreement with observations(e.g., Lin & Mohr 2004; Zarattini et al. 2014), we found central
galaxies of fossil groups to be more luminous than those of non-fossil systems where another
bright galaxy is in close vicinity. The luminosity difference between central galaxies of fossil
and non-fossil is compatible with the evolutionary picture that fossil groups may form by a
merger of both bright galaxies in non-fossil systems, which accounts for the overluminous
central galaxy in fossils. By this process, a non-fossil group becomes a fossil group, while the
infall of another bright galaxy into the systems turns a fossil group non-fossil.
There are no differences among the faint satellite systems of fossil and non-fossil systems in
the semi-analytic model. Although Guo et al. (2011) show that their model underpredicts the
overall abundance of dwarf galaxies, our study revealed that the luminosity function faint-end
slopes of both galaxy group types found in the semi-analytic model encompass the observed
values in literature (cf. Tab. 4 and Fig. 43). The missing satellite problem is thus not of statistical
significance in the semi-analytic model of Guo et al. (2011). We particularly found the luminosity function’s faint-end slope of NGC 6482 in agreement with those of fossil groups in the
semi-analytic model (see Fig. 43). However, the dwarf-to-giant ratios the semi-analytic model
assigns to galaxy groups are too high in comparison to observations (by a factor of 2 ∼ 3). This
was already found by Weinmann et al. (2011). Similarly, the dwarf-to-giant ratio of NGC 6482
is very small as compared to those provided by the semi-analytic model for fossil groups (see
Fig. 44). This in particular remarkably since we found the faint end, i.e., the number of dwarfs,
in agreement with observations. Therefore, giant galaxies must be underrepresented in the
groups we have investigated in order to obtain the high ratios.
In NGC 6482 we have not found any dwarf galaxy in the range −14 6 Mr /mag 6 −13. In the
semi-analytic model a deviation in the composite luminosity function for fossil groups in this
magnitude range is not evident (see Fig. 42). The "missing" galaxies in this magnitude range
are thus a peculiarity of the NGC 6482 system and probably due to low number statistics of its
faint satellite system.
Furthermore, we investigated groups in the Guo et al. (2011) semi-analytic model that resemble loose or field groups as they reside in low-density environments and their central galaxy
is star forming like a spiral galaxy. These groups appear "fossil" in the sense that they had
assembled ∼ 80% of their final mass already ∼ 8 Gyrs ago. They have spent almost the whole
time since z = 1 in the fossil phase, and even within the virial radius they remain (optical) fossils manifested by the magnitude gap of 2. However, they are not fossil within the meaning of
Ponman et al. (1994), who suspected the outstanding luminous central galaxy to be a merging
product of all bright galaxies within the central region of the group. As the central galaxies of
our field groups have not experienced any significant merger in the past, they can not contain
an elliptical galaxy embedded in a hot gas halo, which would be bright in the X-ray. Field
groups therefore represent another evolutionary track in the Guo et al. (2011) semi-analytic
model. This is also indicated by their systematically shallower faint-end slopes as compared to
the fossil and non-fossil systems (see Fig. 43).
The latter fact suggests that encounters of field groups form the systems that we label fossil
and non-fossil, i.e., they contain a passive central galaxy. In the course of such an encounter,
the giant galaxies will merge earlier than their faint satellites, yielding a steeper faint-end slope.
This particular scenario (which might not be the only fossil group formation scenario) implies
that mergers of gas-rich (star forming) giant galaxies have taken place in fossil groups and is
supported by the finding of wet merger signatures in NGC 6482.
In the future, a major advance of any semi-analytic model would be the incorporation of
the emission by the hot gas, i.e., the X-ray luminosity. It is the crux of this work that the
Guo et al. (2011) model does not provide the X-ray luminosity. Another exercise is to figure out
whether the results of the semi-analytic model presented in our study change when considering
elliptical galaxies by means of their bulge-to-total ratios, instead of the activity by means of
their specific star formation rates. Since the semi-analytic model data is available, we could
also prove whether L∗ galaxies are indeed missing in fossil groups as claimed by D’Onghia &
Lake (2004).
From the available data and the semi-analytic model, fossil groups are merely a phase in the
evolution of galaxy groups. In order to specifically understand its beginning (and its end), we
would need further insight how fossil groups form in the semi-analytic model, and in particular
how their faint satellite system evolves with time.
Part V
Data reduction is the process that turns raw CCD images into science images, free of artifacts
and instrument signatures. Here, all steps of data reduction applied to the Suprime-Cam data
of NGC 6482 shall be described briefly in a general manner to introduce the vocabulary used
in Sect. 2.3. The interested reader is referred to Howell (2006) for a detailed description of data
bias correction
The bias of a pixel is the value that is read out if the CCD was not illuminated, i.e., with an
exposure time of 0 seconds. The A/D converter that translates the analog current signal in a
digital pixel value, introduces a variation which is not gaussian (Howell 2006). Since the A/D
converter can not deal with negative values, each pixel value has to be read in with a positive
offset, in order to account for the "negative introduced" values by the A/D converter. In order
to determine this offset, additional read-out cycles are sent to the electronics which generates
rows or columns of only the signal by the read-out electronics. These ∼ 50 columns or rows are
commonly referred to as overscan region.
As mentioned in Sect. 2.3, after a chip replacement of the Suprime-Cam instrument, the
CCDs contained four read-outs, resulting in 4 different overscan regions per CCD (see Fig. 46a).
We used SDFRED, the Suprime-Cam reduction software, since it was the only one which could
handle four read-outs per CCD. SDFRED determines the median of each overscan row. The bias
is then corrected by subtracting the obtained value from each pixel value in the corresponding
row. The different corrected fields are then sticked together by trimming the overscan regions
as seen in Fig. 46b.
Each pixel of a CCD differs from its neighbor in quantum efficiency and gain, i.e., the conversion
factor of initially read-out electrons in a pixel related to the final number count reported by
any software. The process to correct for these pixel-to-pixel variations in a detector is called
flatfielding. That correction is achieved by illuminating the detector uniformly. The response
of each pixel is recorded and called flat field since the illumination is "flat". A side-effect of
flatfielding is the correction for so-called vignetting and time dependent dust accumulation in
the optical path. This different illumination is thus treated as an intrinsic property of a pixel.
Under the assumption that this response does not change with time, the science images can
be divided by the flat fields in order to correct for the pixel-to-pixel variation. Unfortunately,
the assumption does not hold so that before and after a observing night flat fields are taken and
a combination of those is used instead. Moreover, there is a wavelength dependence of a pixel’s
data reduction
response – the quantum efficiency. In order to account for this issue, commonly a combination
of sky flats (at dusk and dawn) and dome flats (recorded in a uniformly illuminated telescope
dome) are taken.
We used SDFRED for the flatfielding step of our data reduction because it was able to flatfield the four fields within one chip separately, including their different brightness levels tailas
Fig. 46c illustrates. The data was not affected by other large-scale illumination effects so that
further superflatting of defringing (see Howell 2006) was not needed.
astrometric calibration
Astrometry is the precise measurement of position and movement of stars. In particular the
precise position of stars is a central but complicated issue in data reduction. There are many
effects to be aware of when mapping the sky on the CCD detector. Here we mention a few:
• Temperature gradients in the whole suspension of a telescope and in particular within
the (cryogen) detector lead to expansion/shrinking of the whole setup. This affects the
effective focal length, and hence the pixel scale.
• The CCDs are slightly tilted to the focal plane that causes the pixels projected on the sky
are slightly rectangular and not squared. This results in different X and Y pixel scales.
• In a mosaic camera the chips can be slightly rotated and tilted to each other so that the
pixels are not aligned along a global instrument axis.
• The outermost CCDs of the detector cover areas that have a large distance from the optical
axis. Also, a spherically curved sky is mapped on a flat detector plane. Field distortions
are introduced anyway.
We use THELI for astrometric calibration. It generates a reference catalog of non-saturated stars
the image data contains. That catalog is then compared to a catalog of standard stars in order
to match relative position and brightness differences within a given tolerance. We have used
the PPMXL catalog (Roeser et al. 2010) because it covered the NGC 6482 field. This matching
is a first order approximation of the astrometry and also imposes a photometric calibration.
Because of the issues listed above, in a second step a polynomial approach is been made by
THELI to obtain a precise astrometric solution (Erben et al. 2005). The pixel scale variation over
the whole CCD array is small but reaches ∼ 2% in the outskirts as seen in Fig. 45. This leads to
an position offset of several pixels when comparing the first order approximation to the third
order solution. If not correcting with that accuracy, in the outskirt the coadding image (see
below) would contain the same object several times according the number of stacked images –
or at least smear over the object significantly.
background subtraction
Background or sky is characterized by photons which are collected by the detector but not
of interest (Howell 2006). Background does not only contain sky, but also photons from unresolved objects read noise and other sources. THELI offers the possibility of either subtracting
a constant sky or model the sky to obtain a spatial varying sky. In either case, SExtractor (see
Sect. 3.1) is applied in order to reject all bright sources from an image. The from the remaining
pixels the sky is estimated. In the case of the model, the background is smoothed by either a
Gaussian or SExtractor. The images of CCDs that contain bright galaxies (number 1-3 in Tab. 6)
A.5 coadding images
Figure 45: Pixel scale distortion map of R band observations. The deviation from
the nominal pixel scale of 0.2 arcsec per pixel is largest in the outskirts of the
CCD array, corresponding to the largest field distortions.
were ignored for the background estimation because the smooth brightness gradients were not
properly accounted for by THELI’s algorithm. This results in an overestimation of the sky (see
Lieder 2010 for a detailed description).
coadding images
Deep imaging date are obtained by long time observation – lasting up to hours. But there are
good reasons to limit a single exposure to 10–20 minutes, and not to take such a long single
• The objects of interest will saturate pixels if too much flux is collected.
• The number of cosmic rays1 hitting the detector increases with time. Those hits are
recorded by the CCD and disturb the actual observation. They occur more likely in short
• Atmospheric conditions may change, leading to flux variations (e.g. a cloud may move
through the image).
• Dark current caused by the heat of the system begins to become important.
The signal-to-noise (S/N) of an object is determined by many parameters like readout noise,
background counts, detector gain, but also the flux of the object of interest (Merline & Howell
1 energy-rich particles originating presumably in supernova explosions (Fermi LAT Collaboration 2013)
data reduction
1995). If the signal is dominated by the object’s flux and the gain is 1 (valid for electrons/photons), the signal-to-noise ratio is simply the Poisson error of its number counts.
S/N = N
Howell (2006) mentions, that the S/N is a useful method to define the difference between a
bright and a faint source. Deep images need a good S/N so that even faint objects on short
exposures look bright on a long exposure. Eq. 9 shows that the relation between exposure time
(flux) and S/N is not linear – making deep exposures (time) expensive.
As several "short" exposures are taken, they have to be stacked to obtain a deep image, i.e.,
with high S/N. The process of stacking the images is called coadding and performed by THELI.
But the exposures might be shifted, rotated and tilted to each other. Therefore, the images have
to be geometrically transformed to one global coordinate system. This step uses the astrometric
calibration, described in Sect. A.3. During this step THELI also checks for flux variations. With
increasing airmass the transmitted flux through the atmosphere decreases. Based on fluxes at
a given airmass2 THELI calculates the expected flux of objects at another airmass. If the flux
differs towards lower values than expected (because of a cloud) THELI corrects the flux by the
fluxscale parameter (see Erben et al. 2005 for a detailed description).
The particular difficulty in coadding arises from the redistribution of the flux, called resampling (see Bertin 2010 for detailed information). The flux of a certain pixel has to be distributed
properly to four pixels by the above mentioned coordinate transformation. However, if the astrometric calibration was accurate and the resampling algorithm advanced, the S/N does not
decrease significantly from what is ideally expected as illustrated in Fig. 46d.
(a) raw image
(b) overscan corrected
(c) flatfielded
(d) coadded
Figure 46: Illustration of the data reduction process for a B band image. (a) The excerpt of the raw image contains
three different readout fields within one CCD, and also three overscan regions are shown. (b) The image is
corrected by the readout bias and trimmed but brightness differences among the readout fields are visible. (c) The
flatfielding step removes not only those brightness differences but also the global brightness gradient (vignetting).
(d) By stacking four 520s exposures the S/N increases, making the tidal debris of the disrupted galaxy not
disappear in the noise. Background has been subtracted and cosmic rays were removed (see lower right corner).
The image is not smeared and no object has a ghost companion, i.e., astrometric calibration, needed for stacking,
was precise.
2 In astronomy, airmass is a number for the optical path length through Earth’s atmosphere.
Table 6: Parameters of all investigated objects.
[mag/arcsec2 ]
267.95346 23.07192
−22.73 ± 0.02
−21.09 ± 0.02
1.73 ± 0.02‡
19.88 ± 0.02
3.73 ± 0.13
2.82 ± 0.03
268.22717 23.21117
−20.54 ± 0.04
−18.92 ± 0.07
1.72 ± 0.07
21.01 ± 0.01
2.42 ± 0.13
1.05 ± 0.01
267.69073 23.13864
−20.26 ± 0.02
−18.64 ± 0.03
1.69 ± 0.02
18.94 ± 0.01
0.85 ± 0.13
1.88 ± 0.02
268.20694 23.01428
−19.69 ± 0.04
−18.53 ± 0.05
1.19 ± 0.06
21.84 ± 0.02
2.88 ± 0.13
1.07 ± 0.03
268.09314 22.87197
−19.15 ± 0.09
−17.97 ± 0.09
1.19 ± 0.07
23.51 ± 0.03
4.99 ± 0.14
0.60 ± 0.03
267.90015 23.07572
−18.38 ± 0.01
−16.75 ± 0.03
1.60 ± 0.01
21.71 ± 0.02
1.36 ± 0.13
1.38 ± 0.03
267.68355 23.14623
1.33 ± 0.13†
267.74030 22.90452
−17.66 ± 0.02
−16.25 ± 0.02
1.53 ± 0.02
22.44 ± 0.01
1.42 ± 0.13
1.42 ± 0.01
267.78040 23.14328
−17.23 ± 0.05
−16.17 ± 0.05
1.07 ± 0.05
23.05 ± 0.01
1.59 ± 0.13
1.12 ± 0.02
267.84186 23.06776
−16.51 ± 0.02
−15.08 ± 0.04
1.55 ± 0.01
23.09 ± 0.01
1.13 ± 0.13
1.34 ± 0.01
268.22913 23.11805
−16.35 ± 0.03
−14.96 ± 0.06
1.52 ± 0.02
23.81 ± 0.01
1.22 ± 0.13
1.09 ± 0.01
267.85382 23.06654
−15.90 ± 0.04
−14.53 ± 0.05
1.42 ± 0.03
24.20 ± 0.01
1.62 ± 0.13
0.74 ± 0.01
267.76700 22.85475
−15.76 ± 0.05
−14.38 ± 0.08
1.47 ± 0.02
23.68 ± 0.01
1.01 ± 0.13
1.20 ± 0.02
267.91089 23.12349
−15.67 ± 0.04
−14.35 ± 0.06
1.41 ± 0.03
23.66 ± 0.02
1.02 ± 0.13
1.54 ± 0.02
267.76242 23.04759
−15.30 ± 0.05
−14.17 ± 0.06
1.11 ± 0.08
23.72 ± 0.02
0.73 ± 0.13
0.55 ± 0.01
267.66498 23.25852
−15.08 ± 0.07
−13.90 ± 0.08
1.19 ± 0.03
23.90 ± 0.02
0.96 ± 0.13
0.85 ± 0.02
267.81354 23.30462
−14.64 ± 0.03
−13.48 ± 0.05
1.14 ± 0.03
23.95 ± 0.02
0.71 ± 0.13
1.08 ± 0.04
267.68402 22.87308
−14.61 ± 0.07
−13.09 ± 0.09
1.55 ± 0.02
24.82 ± 0.02
1.16 ± 0.13
0.87 ± 0.01
268.04355 22.84158
−14.22 ± 0.05
−12.83 ± 0.12
1.48 ± 0.04
24.01 ± 0.01
0.63 ± 0.13
0.99 ± 0.01
25.91 ± 0.09
2.37 ± 0.20
1.32 ± 0.06
267.75461 23.08187
−14.21 ± 0.08
−12.92 ± 0.25
267.69376 22.86386
−14.19 ± 0.07
−12.70 ± 0.08
1.57 ± 0.03
24.22 ± 0.01
0.68 ± 0.13
0.71 ± 0.01
267.93338 23.09780
−14.11 ± 0.15
−12.52 ± 0.35
1.74 ± 0.13
25.84 ± 0.14
2.28 ± 0.27
1.11 ± 0.09
267.84854 23.17222
−12.95 ± 0.21
−11.61 ± 0.19
1.38 ± 0.09
25.47 ± 0.02
0.73 ± 0.13
0.66 ± 0.02
267.72772 23.02693
−12.91 ± 0.10
−11.60 ± 0.14
1.41 ± 0.05
24.16 ± 0.01
0.41 ± 0.13
0.60 ± 0.02
267.82730 23.01918
−12.87 ± 0.05
−11.69 ± 0.10
1.43 ± 0.04
24.56 ± 0.02
0.49 ± 0.13
1.03 ± 0.02
Continued on Next Page. . .
Table 6 – Continued
[mag/arcsec2 ]
267.89713 23.13568
−12.70 ± 0.08
−11.37 ± 0.15
1.48 ± 0.07
25.19 ± 0.02
0.57 ± 0.13
0.60 ± 0.02
268.15881 23.30970
−12.64 ± 0.09
−11.73 ± 0.12
0.78 ± 0.07
24.64 ± 0.01
0.43 ± 0.13
0.71 ± 0.02
267.75369 22.86655
−12.54 ± 0.06
−11.17 ± 0.13
1.50 ± 0.04
25.18 ± 0.02
0.53 ± 0.13
0.78 ± 0.02
267.97821 22.92692
−12.53 ± 0.18
−11.21 ± 0.32
1.31 ± 0.11
27.14 ± 0.08
0.88 ± 0.14
0.88 ± 0.06
267.80301 23.05564
−12.34 ± 0.07
−11.12 ± 0.22
1.43 ± 0.05
25.53 ± 0.04
0.54 ± 0.13
0.86 ± 0.04
268.06989 23.01075
−12.33 ± 0.06
−10.94 ± 0.17
1.52 ± 0.06
25.66 ± 0.04
0.67 ± 0.13
0.81 ± 0.03
267.97345 22.99362
−12.16 ± 0.04
−10.83 ± 0.10
1.37 ± 0.03
24.81 ± 0.02
0.39 ± 0.13
0.84 ± 0.03
267.83710 23.06381
−11.94 ± 0.04
−10.64 ± 0.10
1.46 ± 0.03
24.57 ± 0.01
0.32 ± 0.13
0.63 ± 0.01
268.01102 23.16201
−11.57 ± 0.09
−10.63 ± 0.08
1.12 ± 0.05
24.30 ± 0.02
0.23 ± 0.13
0.69 ± 0.04
267.69958 23.06408
−11.55 ± 0.08
−10.36 ± 0.17
1.36 ± 0.08
25.97 ± 0.07
0.50 ± 0.13
0.59 ± 0.05
267.87686 23.19275
−11.44 ± 0.07
−10.06 ± 0.12
1.54 ± 0.11
24.71 ± 0.01
0.29 ± 0.13
0.34 ± 0.01
267.92081 23.14277
−11.29 ± 0.09
−10.20 ± 0.24
1.34 ± 0.07
26.14 ± 0.13
0.55 ± 0.14
0.64 ± 0.09
268.07532 23.29704
−11.03 ± 0.14
−10.21 ± 0.15
0.96 ± 0.12
25.51 ± 0.03
0.33 ± 0.13
0.42 ± 0.02
268.19034 23.20517
−10.92 ± 0.12
−9.80 ± 0.44
1.23 ± 0.10
26.46 ± 0.37
0.47 ± 0.17
1.01 ± 0.33
268.02652 22.90529
−10.77 ± 0.18
−9.20 ± 0.32
1.49 ± 0.15
26.53 ± 0.34
0.52 ± 0.20
0.72 ± 0.22
267.84235 22.85096
−10.76 ± 0.09
−9.47 ± 0.11
1.52 ± 0.10
24.92 ± 0.02
0.24 ± 0.13
0.36 ± 0.02
267.67389 23.22414
−10.75 ± 0.14
−8.78 ± 0.25
1.54 ± 0.18
26.92 ± 0.21
0.40 ± 0.16
0.34 ± 0.11
267.97455 23.11946
−10.71 ± 0.14
−9.29 ± 0.33
1.46 ± 0.21
27.79 ± 0.27
0.29 ± 0.15
0.67 ± 0.16
267.67850 22.96362
−10.67 ± 0.09
−9.76 ± 0.16
1.07 ± 0.07
25.19 ± 0.01
0.23 ± 0.13
0.29 ± 0.01
267.85178 23.01907
−10.61 ± 0.17
−9.83 ± 0.22
0.95 ± 0.12
27.06 ± 0.14
0.48 ± 0.14
0.62 ± 0.08
268.05835 22.93668
−10.59 ± 0.10
−9.36 ± 0.21
1.53 ± 0.09
25.47 ± 0.04
0.27 ± 0.13
0.52 ± 0.05
268.10507 23.04556
−10.55 ± 0.20
−9.52 ± 0.25
1.31 ± 0.12
25.64 ± 0.04
0.31 ± 0.13
0.47 ± 0.04
268.06409 22.86462
−10.53 ± 0.30
−9.84 ± 0.29
1.08 ± 0.16
25.94 ± 0.08
0.28 ± 0.13
0.76 ± 0.08
Notes. ID: galaxy identification number in our catalog sorted by MR . α (J2000): Right ascension, in units of degrees. δ (J2000): Declination, in units of degrees. MR : absolute R-band magnitude (adopted m − M = 33.71 mag),
errorbars do not include photometric calibration uncertainty of σR = 0.04 mag. MB : absolute B-band magnitude
(adopted m − M = 33.71 mag), errorbars do not include photometric calibration uncertainty of σB = 0.12 mag.
B − R: integrated B − R colour (within half-light radius r50 ). µe : effective surface brightness in R-band from Sérsic
fit in R-band applied to circularized isophotes. re : effective radius from Sérsic fit in R-band applied to circularized
isophotes, errors include uncertainty introduced by seeing. n: Sérsic index. Type: classification type (for member
considered galaxies only; all early-type dwarf galaxies are labeled dE)
∗ objects with NED-listed velocities, qualiyfing the galaxy as a group member
† color determined using SExtractor
‡ color determined at half-light radius
Table 7: Correlation between snapshot number, redshift and lookback time in the Millennium-II Simulation.
Notes. snapnum: number of snapshot (N + 3 in Eq. 6). H(z): Hubble constant as function of redshift
z in km s−1 Mpc−1 . t: lookback time in Gyr. ∆t: time difference to previous snapshot in Gyr. (priv.
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Based on data collected at Subaru Telescope, which is operated by the National Astronomical
Observatory of Japan, under run ID S08B-150S.
This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration.
SQL databases containing the full galaxy data for the semi-analytic model of Guo et al. (2011) at
all redshifts and for both the Millennium and Millennium-II Simulation used in this work and
the web application providing online access to them were constructed as part of the activities
of the German Astrophysical Virtual Observatory (GAVO).
IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the
Associated Universities for Research in Astronomy, Inc., under cooperative agreement with the
National Science Foundation.
This thesis has made use of SExtractor (Bertin & Arnouts 1996), and THELI (Erben et al. 2005).
This research has made use of NASA’s Astrophysics Data System.
Analog-to-Digital (converter)
Active Galactic Nucleus
Baryon Acoustic Oscillations
Brightest Cluster Galaxy
Brightest Group Galaxy
Bulge-to-Total (ratio)
Charge-Coupled Device
Cold Dark Matter
Cosmic Microwave Background
Color-Magnitude Diagram
Color-Magnitude Relation
COsmic Background Explorer
Dwarf-to-Giant (ratio)
Dark Matter
Fossil Group
Friedmann-Lemaître-Robertson-Walker (metric)
Friend-Of-Friends (algorithm)
Hubble Space Telescope
Hawaii Standard Time
Intra-Cluster Medium
Luminosity Function
Millennium Simulation
Millennium-II Simulation
Navarro-Frenk-White (profile)
Point Spread Function
Root Mean Square
Red Sequence
Semi-Analytic Model
Surface Brightness
Sloan Digital Sky Survey
Star Formation History
Star Formation Rate
Specific Star Formation Rate
Signal-to-Noise (ratio)
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