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Mon. Not. R. Astron. Soc. 000, 1–12 (2005) Printed 4 February 2008 (MN LATEX style file v2.2)
The formation history of elliptical galaxies
Gabriella De Lucia1⋆, Volker Springel1, Simon D. M. White1, Darren Croton1†
and Guinevere Kauffmann1
1Max–Planck–Institut fu¨r Astrophysik, Karl–Schwarzschild–Str. 1, D-85748 Garching, Germany
4 February 2008
ABSTRACT
We take advantage of the largest high-resolution simulation of cosmic structure growth
ever carried out – the Millennium Simulation of the concordance ΛCDM cosmogony
– to study how the star formation histories, ages and metallicities of elliptical galaxies
depend on environment and on stellar mass. We concentrate on a galaxy formation
model which is tuned to fit the joint luminosity/colour/morphology distribution of
low redshift galaxies. Massive ellipticals in this model have higher metal abundances,
older luminosity–weighted ages, shorter star formation timescales, but lower assem-
bly redshifts than less massive systems. Within clusters the typical masses, ages and
metal abundances of ellipticals are predicted to decrease, on average, with increasing
distance from the cluster centre. We also quantify the effective number of progenitors
of ellipticals as a function of present stellar mass, finding typical numbers below 2 for
M∗ < 1011 M⊙, rising to ∼ 5 for the most massive systems. These findings are consis-
tent with recent observational results that suggest “down-sizing” or “anti-hierarchical”
behaviour for the star formation history of the elliptical galaxy population, despite the
fact that our model includes all the standard elements of hierarchical galaxy formation
and is implemented on the standard, ΛCDM cosmogony.
Key words: galaxies: formation – galaxies: evolution – galaxies: elliptical and lentic-
ular, cD – galaxies: bulges – galaxies: stellar content
1 INTRODUCTION
Elliptical galaxies are the most massive stellar systems in
the local Universe and appear to define a homogeneous class
of objects with uniformly old and red populations, negligi-
ble amounts of gas, and very little star formation. Their
deceptively simple appearance inspired a ‘classical’ forma-
tion scenario in which they form in a single intense burst
of star formation at high redshifts (z & 5), followed by
passive evolution of their stellar populations to the present
day (Partridge & Peebles 1967; Larson 1975). This so-called
monolithic scenario successfully explains the tightness of the
fundamental scaling relations that elliptical galaxies obey,
like the colour–magnitude relation and the fundamental
plane, as well as the evolution of these relations as a function
of redshift (Kodama et al. 1998; van Dokkum & Stanford
2003).
This classical view has been tenaciously resistant to
challenges by other theoretical models, despite numer-
ous indications for a more complex formation scenario.
⋆ Email: gdelucia@mpa-garching.mpg.de
† Present address: Department of Astronomy, University of Cal-
ifornia, Berkeley, CA 94720.
Toomre & Toomre (1972) suggested that elliptical galax-
ies can form from major mergers of massive disk galaxies.
Detailed numerical simulations (Farouki & Shapiro 1982;
Negroponte & White 1983) later showed that the merger
of two spiral galaxies of comparable mass can indeed pro-
duce a remnant with structural and photometric proper-
ties resembling those of elliptical galaxies. In more recent
years, a large body of observational evidence has been
collected that demonstrates that interactions and merg-
ers indeed represent a common phenomenon at high red-
shifts, and that these processes affect the population of el-
liptical galaxies in the local Universe. Schweizer & Seitzer
(1992) found evidence for bluer colours of elliptical galax-
ies with increasing morphological disturbance in a study
based on a small sample with a strong bias towards iso-
lated systems (see Michard & Prugniel 2004). Later stud-
ies using absorption–line indices have demonstrated that a
significant fraction of cluster early–type galaxies has un-
dergone recent episodes of star formation (Barger et al.
1996). Signs of recent star formation activity have also
been detected in a number of high redshift early–type
galaxies using colours (Menanteau, Abraham & Ellis 2001;
van de Ven, van Dokkum & Franx 2003) and absorption
and emission line diagnostics (Treu et al. 2002; Willis et al.
c© 2005 RAS

2 G. De Lucia et al.
2002). These results favour, at least for a part of the ellip-
tical galaxy population, a hierarchical formation scenario in
which larger spheroidals are assembled relatively late from
the merger of late–type galaxies of comparable mass. Such
a bottom-up formation scenario is naturally expected for
the structure formation process in cosmologies dominated
by cold dark matter.
However, despite an enormous amount of work both on
the theoretical and on the observational side, the debate
concerning the two competing theories for the formation of
elliptical galaxies has remained open. As described above,
a relatively large fraction of early–type systems shows clear
evidence of interactions, mergers, and recent star formation.
However, the data also seem to indicate that only a small
fraction of the mass is involved in such episodes. The lat-
ter observational result has often been interpreted as strong
evidence against the more extended star formation history
naively predicted from hierarchical models. A related issue
concerns the α-element enhancements observed in ellipticals.
The so–called α-elements are released mainly by supernovae
type-II, while the main contribution to the Fe-peak elements
comes from supernovae type-Ia. For these reasons, the [α/Fe]
ratio is believed to encode important information on the
time–scale of star formation. It is now a well established re-
sult that massive ellipticals have super-solar [α/Fe] ratios,
suggesting that they formed on relatively short time–scales
and/or have an initial mass function that is skewed towards
massive stars. The inability of early models of the hierar-
chical merger paradigm to reproduce this observed trend
has been pointed out as a serious problem for these models
(Thomas 1999).
Another contentious issue is related to the significantly
dissimilar evolution of early–type galaxies in different envi-
ronments predicted by early semi–analytic models of galaxy
formation (Kauffmann 1996b; Baugh, Cole & Frenk 1996).
Such differential evolution is a natural outcome of the hi-
erarchical scenario, because present day clusters of galaxies
form from the highest peaks in the primordial density fields,
leading to an earlier onset of the collapse of the dark matter
haloes and to more rapid mergers (Kauffmann 1995).
In recent years, considerable observational progress has
been made in the study of the stellar populations of el-
liptical galaxies in different environments and at differ-
ent redshifts (e.g. Thomas et al. 2005; Denicolo´ et al. 2005;
Treu et al. 2005; van der Wel et al. 2005). One has to bear
in mind however that the derived ages and metallicities de-
pend quite strongly on the models employed in the analy-
sis, primarily because of an essentially unavoidable intrinsic
age-metallicity degeneracy, which appears to be stronger for
older and more metal rich systems (Denicolo´ et al. 2005).
The situation is especially unclear for ‘field’ galaxies, since
here the very definition of ‘field’ is fraught with ambiguities.
Significant systematic uncertainties are also present in theo-
retical models used for studying galaxy formation, where
poorly understood physical processes need to be treated
with coarse approximations in order to predict observable
properties of galaxies.
A detailed analysis of the properties of elliptical galaxies
expected in the framework of hierarchical galaxy formation
has been given in a number of papers (Kauffmann 1996b;
Baugh et al. 1996; Kauffmann & Charlot 1998). This early
work used an extension of the Press-Schechter theory to pro-
duce Monte Carlo realizations of the merger trees of dark
matter haloes, thus allowing the progenitors of a dark matter
halo to be followed back in time to arbitrarily high redshifts.
A drawback of this approach is its lack of spatial informa-
tion on the clustering of galaxies. Another lies in the inher-
ent inaccuracies of the Press-Schechter formalism. Recent
years have witnessed substantial progress in this regard with
the advent of “hybrid” techniques where high-resolution
N-body simulations of structure formation are used to di-
rectly measure dark matter merger history trees from sim-
ulations which are then combined with semi-analytic sim-
ulations of the galaxy formation physics (Kauffmann et al.
1999; Springel et al. 2001; Mathis et al. 2002). This allows
the spatial and kinematic distribution of model galaxies to
be predicted as a function of redshift, providing a more di-
rect and more powerful comparison between theoretical pre-
dictions and observational results. Also, this approach elim-
inates much of the uncertainty introduced by Monte-Carlo
prescriptions for producing mock merging histories.
Most previous semi-analytic studies of the properties
of ellipticals were carried out in the framework of a cosmo-
logical model with critical matter density. This cosmogony
has been replaced in recent years by the ΛCDM scenario,
which has become the de facto standard cosmological model,
thanks to its concordance with a variety of observational
data, including the most recent cosmic microwave back-
ground measurements, distant supernova observations, and
cosmic shear measurements. Given that both the cosmolog-
ical model and the modelling techniques have changed sig-
nificantly, it is interesting to revisit the question of the for-
mation and evolution of elliptical galaxies. In this paper, we
present the results of applying a semi-analytic model that
tracks dark matter halos and their embedded substructures
to the largest high-resolution simulation of cosmic structure
growth ever carried out. Here we concentrate on the analysis
of the star formation histories, the ages, and the metallici-
ties of model elliptical galaxies as a function of galaxy mass
and of environment. In a companion paper, we will study
how the distribution of metallicities and ages depends on
the feedback model and on the chemical enrichment scheme
employed, exploring also the relative contribution of these
two in shaping observed scaling properties like the colour–
magnitude relation.
The layout of this paper is as follows. In Section 2, we
briefly describe the simulation used in our study, and in Sec-
tion 3 we give a concise overview of the semi-analytic model
employed for our analysis. In Section 4, we discuss how the
star formation history of model elliptical galaxies depends
on the stellar mass of galaxies and on the environment, while
Section 5 discusses the dependence of ages and metallicities
on galaxy mass and environment. Finally, in Section 6, we
summarise and discuss our findings, and give our conclu-
sions.
2 THE SIMULATION
In this study, we analyse a large collisionless cosmologi-
cal simulation which follows N = 21603 particles of mass
8.6× 108 h−1M⊙ within a comoving box of size 500 h−1Mpc
on a side (Springel et al. 2005). The spatial resolution is
5h−1kpc, available everywhere in the periodic box. The
c© 2005 RAS, MNRAS 000, 1–12

The formation history of elliptical galaxies 3
cosmological model is a ΛCDM model with parameters
Ωm = 0.25, Ωb = 0.045, h = 0.73, ΩΛ = 0.75, n = 1, and
σ8 = 0.9, where the Hubble constant is parameterised as
H0 = 100 h kms−1Mpc−1. These cosmological parameters
are consistent with recent determinations from the combined
analysis of the 2dFGRS (Colless et al. 2001) and first year
WMAP data (Spergel et al. 2003).
A remarkable aspect of this Millennium Simulation car-
ried out by the Virgo Consortium1 is its good mass reso-
lution combined with a very large particle number, more
than 10 billion. It is the largest high-resolution simulation
of cosmic structure growth carried out so far. This provides
substantial statistical power, sampling the formation history
even of rare objects in a representative fashion. Gao et al.
(2005) have exploited this to show that the clustering of ha-
los of fixed mass does depend on their formation redshift,
an effect that is weak for massive systems but becomes pro-
gressively stronger towards smaller galaxies. We note that
simpler schemes for modelling the galaxy distribution, based
for example on the halo occupation distribution schemes or
on Monte Carlo halo merger trees, do not account for this
effect, highlighting the importance of direct simulations of
structure formation for obtaining fully reliable merger his-
tories.
The simulation has sufficient resolution to track the mo-
tion of dark matter substructures in massive halos, mak-
ing it possible to follow the orbits of cluster ellipticals in
an unambiguous fashion. During the simulation, 64 time
slices were saved, together with group catalogues and their
embedded substructures, the latter defined as locally over-
dense and self-bound structures, identified with the SUB-
FIND algorithm (Springel et al. 2001). These group cata-
logues were then used to construct detailed merging history
trees of all gravitationally self-bound dark matter structures
(Springel et al. 2005). The merger trees describe the assem-
bly of about 20 million galaxies, and form the basic input
needed by the semi-analytic simulation of the galaxy forma-
tion process considered in this study.
3 THE SEMI-ANALYTIC MODEL
Our technique for grafting the semi–analytic model onto the
Millennium Simulation is similar in spirit to that used by
Springel et al. (2001) and De Lucia, Kauffmann & White
(2004), but has been updated in a number of impor-
tant points. A full description of the model is given by
Springel et al. (2005) and Croton et al. (2005), but we here
give a brief account of those aspects that are particularly
relevant for the present study.
One of the key differences of our approach from tra-
ditional semi–analytic models is that we explicitly follow
dark matter haloes even after they are accreted onto larger
systems. This allows the dynamics of satellite galaxies resid-
ing in the infalling haloes to be properly followed until the
parent dark matter ‘substructure’ is completely destroyed
because of tidal truncation and stripping (De Lucia et al.
1 The Virgo consortium (http://www.virgo.dur.ac.uk/) is an in-
ternational collaboration of astronomers dedicated to large scale
cosmological simulation.
2004a; Gao et al. 2004). At this point, we estimate a resid-
ual survival time of the satellite galaxy and track its po-
sition by means of the most bound particle of the subhalo
identified just before the substructure was disrupted. In this
work, we consider as genuine substructures those subhalos
that contain at least 20 self–bound particles. The parent
catalogue of dark matter haloes, which are analysed for sub-
structures and decomposed accordingly, is identified with a
standard friends–of–friends (FOF) algorithm with a link-
ing length of 0.2 in units of the mean particle separation.
In our model, we assume that only the galaxy located at
the position of the most bound particle of the FOF halo -
the ‘central galaxy’ - is fed by radiative cooling from the
surrounding halo, i.e. genuine satellite galaxies cannot re-
plenish their reservoir of cold gas. Gas infall and cooling are
modelled as described in detail in Croton et al. (2005).
Hierarchical merging trees form the backbone of our
semi-analytic model, and are built for all the self-bound
dark matter halos and subhalos in the Millennium Simu-
lation using the methods described in Springel et al. (2005):
the descendant in the next time slice of each dark matter
(sub)halo is identified as the (sub)halo that contains the
largest number of its most tightly bound particles. Individ-
ual trees are stored separately in a self-contained fashion, so
that the semi-analytic code can be run for each of these trees
sequentially, instead of having to process the whole galaxy
population in one single run for the entire simulation box.
This makes the computation feasible even on small work-
stations and allows for easy parallelisation, such that the
computation of the galaxy properties can be repeated with
different physical assumptions in a matter of hours, if de-
sired.
The descriptions we adopted for modelling the various
mixing and exchange processes occurring between different
galactic phases (stars and cold gas, hot diffuse gas in the
dark matter haloes, and intergalactic gas outside virialized
haloes) are essentially the same as those in De Lucia et al.
(2004b). In the present study, we use their ‘ejection slow’
feedback model, which has been shown to reproduce both
the observed relation between stellar mass and cold phase
metallicity, and the relation between luminosity and cold gas
fraction for galaxies in the local Universe, as well as the ob-
served decline in baryon fraction from rich clusters to galaxy
groups. As in De Lucia et al. (2004b), we use metallicity-
dependent cooling rates and luminosities, and we refer the
reader to the original paper for more details on these imple-
mentations.
In the present paper, we adopt new parameterisations
of star formation and of the suppression of cooling flows by
central galaxy AGN activity, as introduced by Croton et al.
(2005). In the following, we briefly summarise the main char-
acteristics of these physical prescriptions where they differ
from those used in our previous work.
Following Kauffmann (1996a) and Croton et al. (2005),
we assume that the star formation occurs with a rate given
by:
ψ = α(Mcold −Mcrit)/tdyn, (1)
whereMcold and tdyn = Rdisc/Vvir are the cold gas mass and
the dynamical time of the galaxy, respectively. The dimen-
sionless parameter α regulates the efficiency of the conver-
sion of gas into stars. Star formation is allowed to occur only
c© 2005 RAS, MNRAS 000, 1–12

4 G. De Lucia et al.
if the gas surface density is larger than a critical value (that
is used to obtain Mcrit in Eq. 1) given by:
Σcrit = 1.2× 107
( Vvir
200 km s−1
)( R
10 kpc
)−1
M⊙ kpc
−2 (2)
Note that in De Lucia et al. (2004b) we did not assume a
surface density threshold for the star formation but we as-
sumed a dependence of the star formation efficiency on the
circular velocity of the parent galaxy. This assumption was
responsible for delaying the star formation in small haloes
until lower redshifts, which correctly reproduces the ob-
served trend for increasing gas fraction at lower luminosi-
ties. As explained in Kauffmann (1996a), the introduction
of a surface density threshold also naturally reproduces the
observed trend of the gas fraction as a function of galaxy lu-
minosity, due to the fact that the gas density always remains
close to the critical gas surface density value. We postpone
a more detailed investigation on how the census of ages and
metallicities is influenced by the assumptions on the star for-
mation and feedback model to a forthcoming paper. With
respect to the trends presented in this paper, we have veri-
fied that the two different assumptions produce very similar
results.
As in De Lucia et al. (2004b), we assume that bulge for-
mation takes place during mergers: in the case of a ‘minor’
merger, we transfer the stellar mass of the merged galaxy to
the bulge of the central galaxy and update the photometric
properties of this galaxy. The cold gas of the satellite galaxy
is added to the disk of the central galaxy and a fraction
of the combined cold gas from both galaxies is turned into
stars as a result of the merger. Any stars that formed during
the burst are also added to the disk of the central galaxy. If
the mass ratio of the merging galaxies is larger than 0.3, we
assume that we witness a ‘major’ merger that gives rise to a
more significant starburst and destroys the disk of the cen-
tral galaxy completely, producing a purely spheroidal stel-
lar distribution. Note that the galaxy can grow a new disc
later on, provided it is fed by an appreciable cooling flow.
Our starburst implementation is based on the ‘collisional
starburst’ model introduced by Somerville et al. (2001) (see
Croton et al. (2005) for details).
Following Croton et al. (2005), we extend the spheroid
formation by assuming that bulges can also grow from disk
instabilities, based on the the analytic model for disk forma-
tion by Mo, Mao & White (1998). We note that the addi-
tion of this chanel for bulge formation does not substantially
modify the trends presented in this paper. However, this ad-
ditional physical mechanism changes the relative fractions of
different morphological types. For the model explored in this
paper, the final fractions of ellipticals, spirals, and lenticu-
lars brighter than −18 in the V–band are 17, 65, and 18 per
cent, respectively, and are very close to the observed rela-
tive fractions 13, 67, and 20 per cent measured by Loveday
(1996). If bulge growth through disk instabilities is switched
off, the above fractions become: 7, 84, and 8 per cent re-
spectively. Considering only galaxies brighter than −20, the
fractions cited above become: 23, 58, and 19 for our default
model and 13, 67, and 20 for a model where bulge growth
through accretion is switched off. These numbers suggest
that this channel of bulge formation may be more impor-
tant for fainter ellipticals. We will come back to this issue
in Sec. 5.
As in previous work, we determine the morphol-
ogy of our model galaxies by using the B–band bulge–
to–disc ratio together with the observational relation by
Simien & de Vaucouleurs (1986) between this quantity and
the galaxy morphological type. For the numbers quoted
above and for the following analysis, we classify as ellip-
ticals all galaxies with ∆M < 0.4 (∆M = Mbulge −Mtotal),
as spirals or irregulars all galaxies with ∆M > 1.56, and
as lenticulars (S0) all galaxies with intermediate value of
∆M . We include in our analysis all galaxies with stellar
mass larger than 3 × 108 M⊙. Note that, although we are
essentially complete down to this mass limit, the less mas-
sive galaxies included in this analysis reside in substructures
whose mass accretion history can be followed back in time
in many cases only for a small number of snapshots. The de-
termination of the morphological type then becomes quite
noisy and uncertain. We estimate that our morphological
type determination is robust for galaxies with mass equal
to a few times 109 M⊙. The inclusion of galaxies below this
limit, however, does not affect our main results of this study.
When necessary, we will explicitly show results including
only galaxies with mass larger than 4×109 M⊙, whose mor-
phological type can be considered ‘secure’. Our final sample
contains 1, 031, 049 elliptical galaxies with stellar mass larger
than 4 × 109 M⊙. 810, 486 of these have stellar mass larger
than 1× 1010 M⊙.
Finally, we use the model of Croton et al. (2005) to de-
scribe central heating by AGN in massive groups and clus-
ters and the associated suppression of cooling flows. In this
model, gas condensation in massive systems is efficiently
suppressed by ‘radio mode’ outflows that occur when a mas-
sive black hole finds itself at the centre of a static hot gas
halo. The importance of these outflows grows with decreas-
ing redshift and with the mass of the system. We refer to the
original paper for full details and the physical motivation for
this feedback implementation. We will later discuss in more
detail the effect that this particular implementation has on
the trends presented in our study.
4 THE STAR FORMATION HISTORY OF
ELLIPTICAL GALAXIES
As discussed earlier, the uniformly red and old stellar pop-
ulations of elliptical galaxies have traditionally been inter-
preted as evidence for a formation scenario in which these
galaxies form in a single intense burst of star formation
at high redshift and then passively evolve to the present
day. Direct observations of the formation and evolution of
early type galaxies are, however, difficult, and are plagued by
the so called ‘progenitor-bias’ (van Dokkum & Franx 1996).
One approach that is adopted to constrain the formation
mechanism of these galaxies is that of studying in detail
their stellar populations by means of population synthesis
techniques. This method has its roots in a pioneering study
by Tinsley (1972), and has become increasingly popular af-
ter the introduction of more detailed population synthesis
models (Bruzual A. 1983; Guiderdoni & Rocca-Volmerange
1987; Buzzoni 1989). Recent improvements have come
through the development of medium to high resolution
spectral models that include quite complete libraries of
stellar spectra and improved treatments of stellar evolu-
c© 2005 RAS, MNRAS 000, 1–12

The formation history of elliptical galaxies 5
Figure 1. Average star formation histories of model elliptical
galaxies split into bins of different stellar mass, normalised to the
total mass of stars formed. The two panels are for galaxies resid-
ing in haloes of different mass, as indicated by the labels. In both
panels, the solid line shows the average star formation history for
all the elliptical galaxies in the sample under investigation. The
long dashed, dash-dotted, dashed, and dotted lines refer to galax-
ies with stellar mass ≃ 1012, 1011, 1010, and 109 M⊙ respectively.
The vertical line in both panels is included to guide the eye.
tionary theory (Vazdekis 2001; Bruzual & Charlot 2003;
Thomas, Maraston & Bender 2003).
The use of these more sophisticated models, together
with the acquisition of better and larger amounts of
data have recently established firm evidence for a mass–
dependent evolutionary history of the elliptical galaxy
population (De Lucia et al. 2004c; Kodama et al. 2004;
Thomas et al. 2005; van der Wel et al. 2005; Treu et al.
2005). The data suggest that less massive ellipticals have
more extended star formation histories than their more mas-
sive counterparts, giving them a lower characteristic forma-
tion redshift, in marked contrast to naive expectations based
on the growth of dark matter halos in hierarchical CDM cos-
mologies. This observational finding is compatible with the
“down–sizing” scenario for star formation proposed earlier
(Faber et al. 1995; Cowie et al. 1996).
In this section, we study in detail the star formation
histories of model elliptical galaxies and their dependence
on stellar mass and environment. In Fig. 1, we show the av-
erage star formation history, normalised to the total mass of
stars formed, for model elliptical galaxies split into different
bins of stellar mass. The two panels are for galaxies resid-
ing in haloes of different mass. In the following we will refer
to galaxies in haloes with mass & 8 × 1014 M⊙ as ‘cluster’
ellipticals and as ‘field’ ellipticals to all model ellipticals re-
siding in less massive haloes. In both panels, the solid line
shows the average star formation history for all the elliptical
galaxies in the sample under investigation. The long dashed,
dash-dotted, dashed, and dotted lines refer to galaxies with
stellar mass ≃ 1× 1012, 1× 1011, 1× 1010, and 1× 109 M⊙,
respectively2. The vertical lines are included to guide the
eye and mark the peak of the 1012 M⊙-ellipticals in the top
panel.
Fig. 1 shows the most important result of this paper:
more massive elliptical galaxies have star formation histories
that peak at higher redshifts (≃ 5) than lower mass systems,
and can reach star formation rates up to several thousands
of solar masses per year for galaxies ending up in overdense
regions. Less massive elliptical galaxies have star formation
histories that peak at progressively lower redshifts and are
extended over a longer time interval.
A comparison of the top and bottom panels of Fig. 1
shows that the qualitative behaviour for ‘field’ and ‘cluster’
ellipticals is the same, but that for fixed mass, the star for-
mation histories of field ellipticals are predicted to be more
extended than those of ellipticals in clusters. This is a nat-
ural outcome of the hierarchical scenario, where haloes in
regions of the Universe that are destined to form a cluster
collapse earlier and merge more rapidly. The star forma-
tion histories shown in Fig. 1 represent averages computed
over all the elliptical galaxies in the simulation box, but the
trends remain true also when a much smaller volume of the
simulation, and hence a much smaller sample size, is anal-
ysed. Fig. 2 shows the star formation histories of randomly
selected elliptical galaxies in different mass bins and in dif-
ferent environments. The figure shows that individual star
formation histories display a much more ‘bursty’ behaviour
than those shown in Fig. 1. This reflects our assumption that
bulge formation takes place during merger-induced bursts,
which naturally gives the star formation histories of individ-
ual systems a bursty nature quite different from the smooth
history seen for the population average. We will comment
more on the implications of this for the scatter of the ages
for the model elliptical galaxies in the following section.
In Fig. 3, we show the star formation histories again,
but this time split into bins of different parent halo mass.
The long dashed, dash-dotted, dashed, and dotted lines are
for elliptical galaxies in haloes of mass ≃ 1× 1015, 1× 1014,
1× 1013, and 1× 1012 M⊙ respectively
3. Only galaxies with
stellar mass larger than 4× 109 M⊙ are used here. The solid
line shows the average mass–weighted star formation history
for all the galaxies in the sample. The faster evolution of
proto–cluster regions produces star formation histories that
peak at higher redshifts for galaxies in more massive haloes.
Given that galaxies of a fixed stellar mass occur in haloes
covering a wide range of masses, it is not surprising that
the dependence of the star formation history on halo mass
is much weaker than that on galaxy stellar mass.
c© 2005 RAS, MNRAS 000, 1–12

6 G. De Lucia et al.
Figure 2. Each panel shows the star formation history for three randomly selected model elliptical galaxies in the given mass bin.
Figure 3. As in Fig. 1, but with model elliptical galaxies split into
bins of different parent halo mass. The solid line shows the average
mass–weighted star formation history for all the elliptical galaxies
in the sample under investigation. The long dashed, dash-dotted,
dashed, and dotted lines refer to galaxies residing in haloes with
mass M200 ≃ 1015, 1014, 1013, and 1012 M⊙, respectively.
5 THE DISTRIBUTION OF AGES AND
METALLICITY
We now turn to an analysis of the distribution of ages and
metallicities of model elliptical galaxies as a function of stel-
lar mass and environment. In Fig. 4, we show the distribu-
tion of the formation redshifts for model elliptical galaxies.
We define the formation redshift as the redshift when 50
per cent (or 80 per cent) of the stars that make up the fi-
nal elliptical galaxy at redshift zero are already formed. The
shaded histograms are for model elliptical galaxies with stel-
lar mass larger than 1011 M⊙, while the open histogram is
for all galaxies with secure morphology (stellar mass larger
than 4× 109 M⊙). The figure clearly demonstrates that the
stars in more massive ellipticals are on average older than
those in their less massive counterparts, but the scatter of
the distribution is rather large and there is a non-negligible
fraction of model galaxies whose stars are formed relatively
late.
It is important, however, to distinguish the early for-
mation times of the stars that make up the elliptical galaxy
population (reflected in the ‘down-sizing’ scenario) from the
assembly time of the more massive ellipticals. If massive el-
lipticals form a large fraction of their stars in a number of
distinct progenitor systems before they coalesce, these two
times may well be quite different. Fig. 5 demonstrates that
2 The actual bin size used for Figs. 1 and 2 is 7 × 10x M⊙ <
Mstars < 2× 10x+1 M⊙, with x = 8, 9, 10, and 11.
3 The actual bin size used is 7×10x M⊙ < M200 < 2×10x+1 M⊙,
with x = 11, 12, 13, and 14.
c© 2005 RAS, MNRAS 000, 1–12

The formation history of elliptical galaxies 7
Figure 4. Distribution of the formation redshifts of model ellipti-
cal galaxies. In the upper (lower) panel, the formation redshift is
defined as the redshift when 50 per cent (80 per cent) of the stars
that make up the elliptical galaxy at redshift z = 0 are already
formed. The shaded histogram is for elliptical galaxies with stel-
lar mass larger than 1011 M⊙, while the open histogram is for all
the galaxies with mass larger than 4 × 109 M⊙. Arrows indicate
the medians of the distributions, with the thick arrows referring
to the shaded histograms. Note that more massive ellipticals typ-
ically form their stars earlier.
this is indeed the case in our model. We here show the distri-
bution of the assembly redshifts for the same galaxies that
we analysed in Fig. 4. We define the assembly time as the
redshift when 50 per cent (or 80 per cent) of the final stel-
lar mass is already contained in a single object. For galaxies
more massive than 1011 M⊙, the median redshift when half
of the stars are formed is ∼ 2.5 (upper panel of Fig. 4), but
for the same galaxies, half of their stars are typically assem-
bled in a single object only at redshift ∼ 0.8 (upper panel
of Fig. 5). In addition, more massive galaxies assemble later
than less massive ones, and only about half of the model
elliptical galaxies have a progenitor with mass at least equal
to half of their final mass at redshifts & 1.5. The assembly
history of ellipticals hence parallels the hierarchical growth
of dark matter halos, in contrast to the formation history of
the stars themselves. Note that the ‘gap’ between assembly
redshifts and formation redshifts for the stars grows towards
more massive ellipticals. Figs. 4 and 5 imply that a signifi-
cant fraction of present elliptical galaxies has assembled rel-
atively recently through purely stellar mergers. This finding
agrees with recent observational results (van Dokkum 2005;
Faber et al. 2005; Tran et al. 2005; Bell et al. 2005).
Table 1 lists, for different mass bins, medians and up-
per and lower quartiles of the distributions of lookback times
Figure 5. As in Fig. 4, but for the assembly redshifts of model
elliptical galaxies. We define the assembly redshift as the time
when 50 per cent (80 per cent) of the stars that make up the
galaxy at redshift zero are already assembled in one single object.
Note that more massive ellipticals typically assemble their stars
later (cf Fig. 4).
corresponding to the formation and assembly redshifts de-
fined above.
The large volume of our simulation allows us to study
how properties of model elliptical galaxies depend on their
stellar mass and on the environment. Fig. 6 shows how the
luminosity–weighted age (panel a), the metallicity of the
stellar component (panel b), and the B−V colour (panel
c), depend on the galaxy stellar mass. In each panel, filled
circles represent the median of the distributions, while the
error bars mark the upper and lower quartiles. In the up-
per panel, the empty circles show the lookback times corre-
sponding to the formation redshifts as defined in the upper
panel of Fig. 4. The ages of model elliptical galaxies range
from ≃ 4Gyr for galaxies with mass a few times larger than
108 M⊙ to ≃ 10Gyr for galaxies with mass ≃ 1012 M⊙. It is
interesting to note that the lookback time corresponding to
the redshift when half of the stars had formed is a very
good approximation to the luminosity–weighted age over
the full range of masses shown. The age of model elliptical
galaxies also seems to flatten at stellar masses ≃ 1010 M⊙.
The same flattening is observed for the B−V colour and,
although weaker, for the stellar metallicity. Note that the
scatter in these quantities (particularly for the colour and
metallicity) is very small, indicating that the main driver of
these trends is the stellar mass, as also reflected in Fig. 1.
We note in passing that our model elliptical galaxies follow
a colour-magnitude relation that is well defined up to z ≃ 1.
c© 2005 RAS, MNRAS 000, 1–12

8 G. De Lucia et al.
Table 1. Formation times and assembly times for model elliptical galaxies in different mass bins. The first two columns indicate the
extrema of the mass bins. The next columns list the lower quartile, the median, and upper quartile for each of the formation and assembly
times defined in the text. Tf50, Tf80 represent the lookback times corresponding to the redshifts when 50 or 80 per cent of the stars
were first formed. Ta50 and Ta80 represent the lookback times corresponding to the redshifts when 50 or 80 per cent of the mass was
first assembled in a single object. All times are in Gyr. Masses are in units of M⊙.
Mlow Mup Tf50 Tf80 Ta50 Ta80
2.5× 109 1.25 × 1010 8.90 10.06 11.01 6.84 8.58 10.06 8.25 9.78 10.79 6.10 8.25 9.78
1.25 × 1010 6.25 × 1010 9.20 10.31 11.01 7.20 8.90 10.06 7.91 9.78 10.56 5.35 7.91 9.50
6.25 × 1010 3.12 × 1011 9.78 10.56 11.22 7.56 9.20 10.31 4.97 7.91 9.78 1.76 4.22 7.20
3.12 × 1011 1.56 × 1012 11.01 11.41 11.76 9.50 10.31 10.79 3.13 4.97 6.84 0.83 2.09 3.85
Figure 6. Median luminosity–weighted age (panel a), stellar
metallicity (panel b), and B−V colour (panel b) of model ellipti-
cal galaxies as a function of their stellar mass. Symbols indicate
the median value of the distributions at each mass, while the er-
ror bars link the upper and lower quartiles. The open symbols in
the top panel correspond to the lookback time of the upper panel
in Fig. 4.
The results shown in Fig. 6 also indicate that this relation
is mainly driven by metallicity, in line with the common in-
terpretation of the evolution of the slope and the zero-point
of the observed relation as a function of redshift. We plan to
investigate the relative contribution of age and metallicity in
Figure 7. The same quantities as in Fig. 6, but now calculated
as mass-weighted average over all galaxies in a halo and shown as
a function of the virial mass of the halo. Only elliptical galaxies
with stellar mass larger than 4× 109 M⊙ are included here.
shaping the observed colour-magnitude relation in a future
paper.
In Fig. 7 we show the same quantities as in Fig. 6 but
as a function of the virial mass of the halo in which the
galaxies reside. Only galaxies with stellar mass larger than
4×109 M⊙ are included here. For each halo, we compute the
mass–weighted average age, metallicity and colour. Fig. 7
shows the median of these values and the upper and lower
c© 2005 RAS, MNRAS 000, 1–12

The formation history of elliptical galaxies 9
quartiles of the distribution. Elliptical galaxies in high den-
sity environments are on average older, more metal rich, and
redder than isolated elliptical galaxies. Elliptical galaxies in
clusters form a homogeneously old population and ellipti-
cal galaxies in groups (haloes with mass ≃ 1013 M⊙) are as
old as or slightly younger than galaxies in massive clusters
(haloes with mass ≃ 1015 M⊙), while elliptical galaxies in
smaller groups exhibit a lower median age. This is in agree-
ment with recent observational results (Terlevich & Forbes
2002; Proctor et al. 2004). The median stellar metallicities
of galaxies in our clusters are higher than the corresponding
values for the field. Elliptical galaxies in these systems show
a remarkably small spread in colour with a median B−V
colour that is almost independent of environment down to
the mass-scale ≃ 1013 M⊙ of groups.
We can also investigate how the properties of model
elliptical galaxies depend on cluster–centric distance. This
is shown in Fig. 8, based on all elliptical galaxies in haloes
with M200 & 8× 1014 M⊙ and with stellar mass larger than
4 × 109 M⊙. We find in total 51 clusters in the whole sim-
ulation box with virial mass larger than this value. Fig. 8
shows that galaxies closer to the centre are on average older
and more metal rich than galaxies at the outskirts of these
clusters. The bottom panel of Fig. 8 shows that this trend
is partly driven by mass segregation. A radial dependence
of galaxy properties is, however, also a natural consequence
of the fact that mixing of the galaxy population is incom-
plete during cluster assembly. This implies that the cluster–
centric distance of the galaxies is correlated with the time
they were accreted onto a larger structure (Diaferio et al.
2001; Gao et al. 2004). The values of the median age, metal-
licity, and colour all flatten at distance ≃ R200. The scatter
shown in Fig. 8 is rather large but in the very centre of the
clusters, where elliptical galaxies are all very old (≃ 12Gyr),
they have about solar metallicity, and have very red B−V
colour (≃ 0.95).
In the hierarchical galaxy formation scenario, elliptical
galaxies form through mergers of smaller units, and larger
systems are expected to be made up by a larger number of
progenitor galaxies. A very interesting question is therefore
how large the number of progenitor systems of galaxies is,
and how this number varies as a function of final mass. To
get a quantitative handle on this question, we define for each
galaxy an effective number of stellar progenitors by comput-
ing the quantity
Neff =
M2final
2
∑
i miMi,form
, (3)
where mi denotes the masses of all the stars that make up a
galaxy of final mass Mfinal =
∑
i mi. The quantity Mi,form
gives the stellar mass of the galaxy within which the star
i formed, at the time of formation of the star. In the case
where all stars form in a single object that grows to the final
stellar mass without experiencing any merger, Eq. (3) can
be viewed as a discretised form of the integral
Neff =
M2final
∫ Mfinal
0
2M dM
,
which evaluates to Neff = 1 independent of the detailed star
formation history. However, if a galaxy is assembled from
several pieces we expect a larger value of Neff , because then
the values of Mi,form that enter the sum in the denomina-
Figure 8. Median luminosity–weighted age (panel a), stellar
metallicity (panel b), B−V colour (panel c), and stellar mass
(panel d) for model elliptical galaxies in dark matter haloes with
mass & 8×1014 M⊙ as a function of the distance from the cluster
centre. Symbols and lines have the same meaning as in Fig. 6.
tor of Eq. (3) become lower. For example, if the stars of a
galaxy were formed in two progenitors of equal final size,
which then merged into a single object without any further
star formation, we obtain Neff = 2. Note that in more gen-
eral cases we will obtain fractional values for Neff due to
the mass-weighting of the progenitors, which is built into
the definition of Neff . For example, if a galaxy is made up of
three pieces that contain one half, one quarter and one quar-
ter of the final stellar mass, respectively, one gets Neff = 8/3,
which is less than the absolute number of progenitors. This
reflects the fact that the majority of the stars formed in a
single object. The mass-weighting hence delivers an effec-
tive count of the progenitors by giving weight only to those
progenitor systems that contribute significantly to the final
c© 2005 RAS, MNRAS 000, 1–12

10 G. De Lucia et al.
Figure 9. Effective number Neff of progenitors as a function
of galaxy stellar mass. Filled circles represent the median of the
distribution in our default model, while the error bars indicate the
upper and lower quartiles. Empty circles and the corresponding
error bars are for a model where bulge formation through disk
instability is switched off. The vertical dashed line corresponds
to the limit above which our morphological type determination is
robust (see Sec. 3).
stellar mass of the galaxy. In contrast, a count of the to-
tal number of progenitors would be dominated by the large
number of negligibly small satellites that fall into a galaxy
during its growth in a hierarchical universe. We therefore
argue that Neff is a more useful proxy for the number of sig-
nificant mergers required to assemble a galaxy. We caution
however that a straightforward interpretation of Neff in the
context of spheroid formation is complicated by the fact that
bulges can also grow in our model without mergers, through
disk instabilities.
In Fig. 9, we show the effective number of progenitors as
a function of galaxy stellar mass. Filled circles represent the
median of the distributions in our default model while empty
circles represent the median of the distributions in a model
where bulge growth through disk instability is switched off.
Interestingly, bulge growth through disk instability seems to
be an efficient process for intermediate mass ellipticals but
rather ineffective for the most massive ellipticals in our sam-
ple. As expected, more massive galaxies are made up of more
pieces. Fig. 9 shows that the number of effective progenitors
is less than 2 up to stellar masses of ≃ 1011 M⊙, indicating
that the formation of these systems typically involves only
a small number of major mergers. Only galaxies more mas-
sive than ≃ 1011 M⊙ are built up through a larger number of
mergers, reaching up to Neff ≃ 5 for the most massive galax-
ies. We recall that these most massive elliptical galaxies are,
however, also the ones with the oldest stellar populations.
We note that the monolithic collapse scenario would predict
Neff = 1 for these large ellipticals, in marked difference to
our hierarchical prediction.
6 DISCUSSION AND CONCLUSIONS
We have combined a large high-resolution cosmological N–
body simulation with semi–analytic techniques to investi-
gate the formation and evolution of elliptical galaxies in a hi-
erarchical merger model. Understanding the formation and
the evolution of these systems represents an issue of funda-
mental interest as 50 per cent or more of the stellar mass in
the local Universe appears to be in early–type systems and
bulges (Bell et al. 2003).
In this paper, we have focused on the dependence of
the star formation histories, ages, and metallicities on en-
vironment and on galaxy stellar mass. In our model, we
find that elliptical galaxies in denser environments are on
average older, more metal rich, and redder than the general
population of ‘field’ ellipticals. This can be attributed to the
fact that high density regions form from the highest density
peaks in the primordial field of density fluctuations, whose
evolution is somewhat accelerated with respect to regions of
‘average’ density. There is also a clear trend for increasing
ages and metallicities, and for redder colours, with decreas-
ing cluster–centric distance. This can again be viewed as
a natural expectation of hierarchical models where the dis-
tance of the galaxies from the cluster centre is correlated
with the time they were accreted onto the larger system.
When this infall happens, we assume that the galaxy is
stripped of its hot gas reservoir so it is no longer able to
accrete fresh material for star formation. The galaxy then
rapidly consumes its cold gas moving towards the red se-
quence.
We have also investigated how the properties of model
elliptical galaxies change as a function of the stellar mass.
We have shown – and this is perhaps the most important
result of our study – that in our model the most massive el-
liptical galaxies have the oldest and most metal rich stellar
populations, in agreement with observational results (see for
example Nelan et al. 2005). In addition, they are also char-
acterised by the shortest formation time–scales, in quali-
tative agreement with the recently established down-sizing
scenario (Cowie et al. 1996). However, these old ages are in
marked contrast to the late assembly times we find for these
galaxies. In fact, our results show that massive ellipticals
are predicted to be assembled later than their lower mass
counterparts, and that they have a larger effective number
of progenitor systems. This is a key difference between the
hierarchical scenario and the traditional monolithic collapse
picture.
Our results disagree with previous semi-analytic models
that found a trend for more massive ellipticals to be younger
than less massive ones (Kauffmann 1996b; Baugh et al.
1996; Kauffmann & Charlot 1998). In order to understand
the origin of this discrepancy we have re-run our model with
different assumptions. Fig. 10 shows the average star forma-
tion histories of all model elliptical galaxies split into bins
of different stellar mass and normalised to the total mass of
stars formed, as in Fig. 1. In the upper panel, we repeat the
results obtained for the ‘standard’ model used in our analy-
sis, which employs the suppression of cooling flows by central
AGN activity as introduced by Croton et al. (2005). In the
middle panel, we show the same results but for a model in
which no AGN feedback and no artificial cooling cutoff is
included. Finally, in the bottom panel, we show results ob-
c© 2005 RAS, MNRAS 000, 1–12

The formation history of elliptical galaxies 11
tained for a model in which galaxy cooling is switched off in
haloes with Vvir > 350 kms−1 - the ad hoc suppression used
in many previous models, including those of De Lucia et al.
(2004b).
Fig. 10 clearly shows that when no suppression of the
condensation of gas in massive haloes is considered, the most
massive ellipticals have the most extended star formation
histories. Too many massive systems are, however, produced
at redshift zero, at odds with observations. Late mergers
and late accretion, which still involve a substantial amount
of gas in this model, cause the formation of luminous and
young bulge stars. An artificial cutoff of the gas condensa-
tion, similar to that employed in previous models, produces
results that are qualitatively similar (see also De Lucia 2004)
to those obtained with the more physically motivated AGN
model introduced by Croton et al. (2005), as is shown in the
bottom panel of Fig. 10. The figure also indicates however,
that the model does not produce a monotonic behaviour as
a function of stellar mass.
This is better seen in Fig. 11 where we show the me-
dian luminosity–weighted ages of model elliptical galaxies
as a function of their stellar mass for the same three mod-
els. Filled circles show the result for the model with AGN
feedback, open circles show the result for the model with-
out AGN feedback and without any artificial cutoff, and
filled triangles show the result for the model with the artifi-
cial cooling cutoff. The lines coincide perfectly up to stellar
masses ≃ 5 × 1010 M⊙. For larger masses, the median age
stays almost constant for the model with AGN feedback,
decreases for the model without suppression of the cooling
flows, and shows a non–monotonic behaviour for the model
with an artificial cooling cutoff. We note, however, that the
differences between this scheme and a model with AGN feed-
back are small. In our analysis, a cooling flow cut-off is hence
able to approximately produce the same result as AGN feed-
back, which is still different from many earlier results.
We note that the earlier semi-analytic results were
based on Monte-Carlo merger trees constructed with the
extended Press-Schechter formalism, and not by measuring
merger trees directly from high-resolution numerical simu-
lations as we have done here. Although there have been sug-
gestions that the extended Press–Schechter theory may not
provide a sufficiently accurate description of the merger trees
(Benson, Kamionkowski & Hassani 2005), it seems unlikely
that this is responsible for reversing the trends found in this
analysis. We believe this reversal to be a combination of the
change in the physical model and in the cosmology. We note
that the work of Kauffmann & Charlot (1998) was carried
out in the framework of a cosmological model with critical
matter density, where massive haloes are formed much later
than in a low-density Universe normalised to the same clus-
ter abundance. In addition, Kauffmann & Charlot (1998)
employed an artificial cooling cutoff corresponding to a crit-
ical velocity equal to 500 kms−1. This leaves room for late
gaseous mergers and gas accretion that can substantially
rejuvenate the stellar population of elliptical galaxies.
Another important difference between our model and
previous ones is that we explicitly follow dark matter sub-
structures within each halo, even after their progenitor ha-
los have been accreted by larger structures. Springel et al.
(2001) have shown that this allows a more faithful tracking
of the orbits of galaxies and an improved modelling of the
Figure 10. Average star formation histories of model elliptical
galaxies split into bins of different stellar mass, normalised to the
total mass of stars formed. In the upper panel, results are shown
for the ‘standard’ model used for our analysis, which employs the
suppression of cooling flows by central galaxy AGN activity, as
introduced by Croton et al. (2005). In the middle panel, results
are shown for a model without AGN feedback and without any
cooling cutoff. Finally, in the bottom panel, results are shown for
a model without AGN feedback but with a cooling cutoff with a
critical velocity equal to 350 km s−1. Different line styles have the
same meaning as in Fig. 1.
actual merging rate in any given halo. Most of the galaxies
we classify as ellipticals are indeed genuine ‘satellite’ galax-
ies with their own self-bound dark matter subhalo. If too
many of these satellite galaxies are assumed to merge on
too short a timescale, excessively bright and blue central
galaxies result.
The short formation time–scales we find for very mas-
sive ellipticals are qualitatively in agreement with those re-
quired by Thomas et al. (2005) in order to reproduce the
observed α-element enhancements. The detailed census of
c© 2005 RAS, MNRAS 000, 1–12

12 G. De Lucia et al.
Figure 11. Median age of model elliptical galaxies as a function
of galaxy stellar mass. Filled circles show results for our default
model. Empty circles are for a model without AGN feedback and
without any cooling cutoff. Filled triangles are for a model with-
out AGN feedback but with a cooling cutoff with a critical velocity
equal to 350 km s−1.
ages and metallicities for stars in our model elliptical galax-
ies depends on details of our feedback model and chemical
enrichment scheme. We plan to come back to these issues in
future work.
Our results demonstrate that an apparent ‘down-sizing’
in the formation of ellipticals is not in contradiction with
the hierarchical paradigm. Modern semi-analytic models of
galaxy formation do predict ‘anti-hierarchical’ star forma-
tion histories for ellipticals in a ΛCDM universe even though
the assembly of these galaxies is indeed hierarchical.
ACKNOWLEDGEMENTS
G. D. L. would like to thank M. Pannella and V. Strazzullo
for intense and provocative discussions on our poor knowl-
edge of galaxy formation and evolution. We thank B. Pog-
gianti and A. Arago´n-Salamanca for useful comments and
stimulating discussions. G. D. L. thanks the Alexander von
Humboldt Foundation, the Federal Ministry of Education
and Research, and the Programme for Investment in the
Future (ZIP) of the German Government for financial sup-
port.
This paper has been typeset from a TEX/ LATEX file prepared
by the author.
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