arXiv:0704.0932v1  [astro-ph]  6 Apr 2007
Mon. Not. R. Astron. Soc. 000, 1–13 (2000) Printed 28 August 2021 (MN LATEX style file v1.4)
On the Origin of the Dichotomy of Early-Type Galaxies:
The Role of Dry Mergers and AGN Feedback
X. Kang1,2⋆, Frank C. van den Bosch1, A. Pasquali1
1Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
2Shanghai Astronomical Observatory; the Partner Group of MPA, Nandan Road 80, Shanghai 200030, China
ABSTRACT
Using a semi-analytical model for galaxy formation, combined with a large N -body
simulation, we investigate the origin of the dichotomy among early-type galaxies. In
qualitative agreement with previous studies and with numerical simulations, we find
that boxy galaxies originate from mergers with a progenitor mass ratio n < 2 and with
a combined cold gas mass fraction Fcold < 0.1. Our model accurately reproduces the
observed fraction of boxy systems as a function of luminosity and halo mass, for both
central galaxies and satellites. After correcting for the stellar mass dependence, the
properties of the last major merger of early-type galaxies are independent of their halo
mass. This provides theoretical support for the conjecture of Pasquali et al. (2007) that
the stellar mass (or luminosity) of an early-type galaxy is the main parameter that
governs its isophotal shape. If wet and dry mergers mainly produce disky and boxy
early-types, respectively, the observed dichotomy of early-type galaxies has a natural
explanation within the hierarchical framework of structure formation. Contrary to
naive expectations, the dichotomy is independent of AGN feedback. Rather, we argue
that it owes to the fact that more massive systems (i) have more massive progenitors,
(ii) assemble later, and (iii) have a larger fraction of early-type progenitors. Each
of these three trends causes the cold gas mass fraction of the progenitors of more
massive early-types to be lower, so that their last major merger involved less cold
gas (was more “dry”). Finally, our model predicts that (i) less than 10 percent of all
early-type galaxies form in major mergers that involve two early-type progenitors, (ii)
more than 95 percent of all boxy early-type galaxies with M∗ <∼ 2 × 10
10h−1 M⊙ are
satellite galaxies, and (iii) about 70 percent of all low mass early-types do not form
a supermassive black hole binary at their last major merger. The latter may help to
explain why low mass early-types have central cusps, while their massive counterparts
have cores.
Key words: dark matter — galaxies: elliptical and lenticular — galaxies: interactions
— galaxies: structure — galaxies: formation
1 INTRODUCTION
Ever since the seminal paper by Davies et al. (1983) it
is clear that early-type galaxies (ellipticals and lenticulars,
hereafter ETGs) can be split in two distinct sub-classes.
Davies et al. showed that bright ETGs typically have lit-
tle rotation, such that their flattening must originate from
anisotropic pressure. This is consistent with bright ellipti-
cals being in general triaxial. Low luminosity ellipticals, on
the other hand, typically have rotation velocities that are
consistent with them being oblate isotropic rotators (see
Emsellem et al. 2007 and Cappellari et al. 2007 for a more
contemporary description). These different kinematic classes
⋆ E-mail:kang@mpia.de
also have different morphologies and different central surface
brightness profiles. In particular, bright, pressure-supported
systems usually have boxy isophotes and luminosity pro-
files that break from steep outer power-laws to shallow in-
ner cusps (often called ‘cores’). The low luminosity, rotation
supported systems, on the other hand, often reveal disky
isophotes and luminosity profiles with a steep central cusp
(e.g., Bender 1988; Nieto et al. 1988; Ferrarese et al. 1994;
Gebhardt et al. 1996; Rest et al. 2001; Lauer et al. 2005,
2006). Finally, the bimodality of ETGs has also been found
to extend to their radio and X-ray properties. Objects which
are radio-loud and/or bright in soft X-ray emission generally
have boxy isophotes, while disky ETGs are mostly radio-
quiet and faint in soft X-rays (Bender et al. 1989; Pellegrini
1999, 2005; Ravindranath et al. 2001).
c© 2000 RAS
http://arxiv.org/abs/0704.0932v1
2 Kang et al.
Recently, Hao et al. (2006) constructed a homoge-
neous samples of 847 ETGs from the SDSS DR4 catalogue
(Adelman-McCarthy et al. 2006), and analyzed their isopho-
tal shapes. This sample was used by Pasquali et al. (2007:
hereafter P07) to investigate the relative fractions of disky
and boxy ETGs as function of luminosity, stellar mass and
environment. They found that the disky fraction decreases
smoothly with increasing (B-band) luminosity, stellar mass,
and halo mass, where the latter is obtained from the SDSS
group catalogue of Weinmann et al. (2006). In addition, the
disky fraction is found to be higher for satellite galaxies than
for central galaxies in a halo of the same mass. These data
provide a powerful benchmark against which to test models
for the formation of ETGs.
Within the framework of hierarchical structure for-
mation, elliptical galaxies are generally assumed to form
through major mergers (e.g., Toomre & Toomre 1972;
Schweizer 1982; Barnes 1988; Hernquist 1992; Kauffmann,
White & Guiderdoni 1993). In this case, it seems logical that
the bimodality in their isophotal and kinematical properties
must somehow be related to the details of their merger his-
tories. Using dissipationless N-body simulations it has been
shown that equal mass mergers of disk galaxies mainly result
in slowly rotating ETGs with boxy (but sometimes disky)
isophotes, while mergers in which the mass ratio between the
progenitor disks is significantly different from unity mainly
yields disky ETGs (Negroponte & White 1983; Barnes 1988;
Hernquist 1992; Bendo & Barnes 2000; Naab & Burkert
2003; Bournaud et al. 2004, 2005; Naab & Trujillo 2006).
However, simulations that also include a dissipative gas com-
ponent and star formation have shown that the presence of
even a relatively small amount of cold gas in the progenitors
results in a merger remnant that resembles a disky ellipti-
cal even when the mass ratio of the progenitors is close to
unity (Barnes & Hernquist 1996; Naab et al. 2006a; Cox
et al. 2006a). This suggests that boxy ETGs can only form
out of dry, major mergers (see also discussion in Faber et
al. 1997). In this paper we test this paradigm using a semi-
analytical model for galaxy formation and the observational
constraints of P07.
Our study is similar to those of Khochfar & Burk-
ert (2005; hereafter KB05) and Naab et al. (2006b; here-
after N06), who also used semi-analytical models to explore
whether the dichotomy of elliptical galaxies can be related to
their merger properties. However, our analysis differs from
theirs on the following grounds.
• We use a numerical N-body simulation to construct the
merger histories of dark matter haloes. The models of KB05
and N06, on the other hand, used merger trees based on
the extended Press-Schechter (EPS) formalism (e.g., Lacey
& Cole 1993). As we will show, this results in significant
differences.
• Because of our use of numerical N-body simulations,
our model more accurately traces the dynamical evolution of
dark matter subhaloes with their associated satellite galax-
ies. In particular, it takes proper account of dynamical fric-
tion, tidal stripping and the merging between subhaloes.
• Contrary to KB05 and N06, we include a prescription
for the feedback from active galactic nuclei (AGN) in our
semi-analytical model.
• Our semi-analytical model is tuned to reproduce the
luminosity function and the color-bimodality of the redshift
zero galaxy population (see Kang et al. 2005). The works of
KB05 and N06 do not mention such a comparison.
• Our criteria for the production of boxy ETGs are dif-
ferent from those used in KB05 and N06.
• We use a much larger, more homogeneous data set to
constrain the models.
This paper is organized as follows. In Section 2 we de-
scribe our N-body simulation and semi-analytical model,
and outline the methodology. The results are described in
Section 3 and discussed in Section 4. We summarize our
findings in Section 5
2 METHODOLOGY
The aim of this paper is to investigate to what extend semi-
analytical models of galaxy formation can reproduce the
ecology of ETGs, in particular the fractions of disky and
boxy systems as function of luminosity and halo mass. Par-
tially motivated by numerical simulations of galaxy mergers,
both with and without gas, we adopt a framework in which
(i) ETGs are red and dominated by a spheroidal compo-
nent, (ii) ETGs are the outcome of major mergers, (iii) the
remnant is boxy if the merger is sufficiently “dry” (i.e., the
progenitors have little or no cold gas) and sufficiently “ma-
jor” (i.e., the progenitors have roughly equal masses) and
(iv) a boxy elliptical becomes a disky elliptical if newly ac-
creted material builds a sufficiently large stellar disk.
2.1 N-body simulation and model descriptions
In order to have accurate merger trees, and to be able
to follow the dynamical evolution of satellite galaxies, we
use a numerical simulation of the evolution of dark mat-
ter which we populate with galaxies using a state-of-the-art
semi-analytical model for galaxy formation. The numerical
simulation has been carried out by Jing & Suto (2002) using
a vectorized-parallel P3M code. It follows the evolution of
5123 particles in a cosmological box of 100h−1 Mpc, assum-
ing a flat ΛCDM ‘concordance’ cosmology with Ωm = 0.3,
σ8 = 0.9, and h = H0/100 kms
−1 Mpc−1 = 0.7. Each parti-
cle has a mass of 6.2 × 108h−1 M⊙. Dark matter haloes are
identified using the friends-of-friends (FOF) algorithm with
a linking length equal to 0.2 times the mean particle sepa-
ration. For each halo thus identified we compute the virial
radius, rvir, defined as the spherical radius centered on the
most bound particle inside of which the average density is
340 times the average density of the Universe (cf. Bryan &
Norman 1998). The virial mass is simply defined as the mass
of all particles that have halocentric radii r ≤ rvir. Since our
FOF haloes have a characteristic overdensity of ∼ 180 (e.g.,
White 2002), the virial mass is typically smaller than the
FOF mass.
Dark matter subhaloes within each FOF (parent) halo
are identified using the SUBFIND routine described in
Springel et al. (2001). In the present study, we use all haloes
and subhaloes with masses down to 6.2 × 109h−1M⊙ (10
particles). Using 60 simulation outputs between z = 15 and
z = 0, equally spaced in log(1 + z), Kang et al. (2005; here-
after K05) constructed the merger history for each (sub)halo
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 3
in the simulation box, which are then used in the semi-
analytical model. In what follows, whenever we refer to a
halo, we mean a virialized object which is not a sub-structure
of a larger virialized object, while subhaloes are virialized ob-
jects that orbit within a halo. In addition, (model) galaxies
associated with haloes and subhaloes are referred to as cen-
tral galaxies and satellites, respectively.
The semi-analytical model used to populate the haloes
and subhaloes with galaxies is described in detail in K05, to
which we refer the reader for details. Briefly, the model as-
sumes that the baryonic material accreted by a dark matter
halo is heated to the virial temperature. The gas then cools
radiatively and settles down into a centrifugally supported
disk, in which the star formation rate is proportional to the
total amount of cold gas, and inversely proportional to the
dynamical time of the disk. The energy feedback from su-
pernova is related to the initial stellar mass function (IMF)
and proportional to the star formation rate. It is assumed
that the gas that is reheated by supernova feedback remains
bound to the host halo so that it can cool back onto the
disk at later stages. When the subhalo associated with a
satellite galaxy is dissolved in the numerical simulation the
satellite galaxy becomes an “orphan” galaxy, which is as-
sumed to merge with the central galaxy of the parent halo
after a dynamical friction time (computed assuming stan-
dard Chandrasekhar dynamical friction). When two galaxies
merge, the outcome is assumed to depend on their mass ratio
n ≡ M1/M2 with M1 ≥ M2. If n ≤ 3 the merger is assumed
to result in the formation of an elliptical galaxy, and we
speak of a “major merger”. Any cold gas available in both
progenitors is turned into stars. This is supported by hy-
drodynamical simulations, which show that major mergers
cause the cold gas to flow to the center where the resulting
high gas density triggers a starburst (e.g., Barnes & Hern-
quist 1991, 1996; Mihos & Hernquist 1996; Springel 2000;
Cox et al. 2006a,b; Di Matteo et al. 2007). A new disk of cold
gas and stars may form around the elliptical if new gas can
cool in the halo of the merger remnant, thus giving rise to
a disk-bulge system. If n > 3 we speak of a “minor merger”
and we simply add the cold gas of the less massive progeni-
tor to that of the disk of the more massive progenitor, while
its stellar mass is added to the bulge of the massive progen-
itor. The semi-analytical model also includes a prescription
for “radio-mode” AGN feedback as described in Kang, Jing
& Silk (2006; see also Section 3.2). This ingredient is es-
sential to prevent significant amounts of star formation in
the brightest galaxies, and thus to ensure that these systems
are predominantly members of the red sequence (e.g., Cat-
taneo et al. 2006; De Lucia et al. 2006; Bower et al. 2006;
Croton et al. 2006). Finally, luminosities for all model galax-
ies are computed using the predicted star formation histo-
ries and the stellar population models of Bruzual & Charlot
(2003). Throughout we assume a Salpeter IMF and we self-
consistently model the metalicities of gas and stars, includ-
ing metal-cooling.
As shown in K05 and Kang et al. (2006) this model ac-
curately fits, among others, the galaxy luminosity function
at z = 0, the color bimodality of the z = 0 galaxy popula-
tion, and the number density of massive, red galaxies out to
z ∼ 3. We emphasize that in this paper we use this model
without changing any of its parameters.
2.2 Predicting Isophotal Shapes
In our model we determine whether an elliptical galaxy is
disky or boxy as follows. Using the output at z = 0 we first
identify the early-type (E/S0) galaxies based on two criteria.
First of all, following Simien & de Vaucouleurs (1986), we
demand that an ETG has a bulge-to-disk ratio in theB-band
of LB,bulge/LB,total ≥ 0.4. In addition, we require the B−V
color of the galaxy to be red. Following Hao et al. (2006) and
P07, we adopt B − V > 0.8. We have verified that none of
our results are sensitive to the exact choice of these selection
criteria.
Having thus identified all ETGs at z = 0, we subse-
quently trace their formation histories back until their last
major merger, and register the mass ratio n of the merger
event, as well as the total cold gas mass fraction at that
epoch, defined as
Fcold ≡
Mcold,i
(Mcold,i +M∗,i)
Here Mcold,i and M∗,i are the cold gas mass and stellar mass
of progenitor i, respectively. We adopt the hypothesis that
the merger results in a boxy elliptical if, and only if, n < ncrit
and Fcold < Fcrit. The main aim of this paper is to use the
data of P07 to constrain the values of ncrit and Fcrit, and to
investigate whether a model can be found that is consistent
with the observed fraction of boxy (disky) ETGs as function
of both galaxy luminosity and halo mass.
The final ingredient for determining whether an ETG
is disky or boxy is the potential regrowth of a stellar disk.
Between its last major merger and the present day, new gas
in the halo of the remnant may cool out to form a new disk.
In addition, the ETG may also accrete new stars and cold
gas via minor mergers (those with n > 3). Any cold gas in
those accreted systems is added to the new disk, where it
is allowed to form new stars. Whenever the stellar disk has
grown sufficiently massive, its presence will reveal itself in
the isophotes, and the system changes from being boxy to
being disky. To take this effect into account, we follow KB05
and we reclassify a boxy system as disky if at z = 0 it has
grown a disk with a stellar mass that contributes more than
a fraction fd,max of the total stellar mass in the galaxy. In
our fiducial model we set fd,max = 0.2. This is motivated by
Rix & White (1990), who have shown that if an embedded
stellar disk contains more than ∼ 20 percent of the total
stellar mass, the isophotes of its host galaxy become disky.
Note that the same value for fd,max has also been used in
the analysis of KB05.
3 RESULTS
In Figure 1 we show the fraction of boxy ETGs, fboxy, as a
function of the luminosity in the B-band (in the AB system).
Open squares with errorbars (reflecting Poisson statistics)
correspond to the data of P07, while the various lines indi-
cate the results obtained from three different models that
we describe in detail below. The (Poisson) errors on these
model predictions are comparable to those on the P07 data
and are not shown for clarity. Each column and row show,
c© 2000 RAS, MNRAS 000, 1–13
4 Kang et al.
Figure 1. The boxy fraction of ETGs as function of their B-band magnitude (in the AB system). The open, red squares with (Poissonian)
errorbars correspond to the data of P07, and are duplicated in each panel. The solid, dotted and dashed lines correspond to the three
models discussed in the text. Different columns and rows correspond to different values for the critical progenitor mass ratio, ncrit, and
the critical cold gas mass fraction, Fcrit, respectively, as indicated.
respectively, the results for different values of ncrit and Fcrit
as indicated.
We start our investigation by setting fd,max = 1, which
implies that the isophotal shape of an elliptical galaxy (disky
or boxy) is assumed to be independent of the amount of mass
accreted since the last major merger. Although we don’t con-
sider this realistic, it is a useful starting point for our investi-
gation, as it clearly separates the effects of ncrit and Fcrit on
the boxy fraction. The results thus obtained from our semi-
analytical model with AGN feedback are shown in Figure 1
as dotted lines. If we assign the isophotal shapes of ETGs
depending only on the progenitor mass ratio n, which cor-
responds to setting Fcrit = 1, we obtain the boxy fractions
shown in the upper panels. In agreement with KB05 (see
their Figure 1) this results in a boxy fraction that is virtually
independent of luminosity, in clear disagreement with the
data. Note that, for a given value of ncrit, our boxy fractions
are significantly higher than in the model of KB05. For ex-
ample, for ncrit = 2 we obtain a boxy fraction of ∼ 0.6, while
KB05 find that fboxy ∼ 0.33. This mainly reflects the differ-
ence in the type of merger trees used. As discussed above, we
use the merger trees extracted from a N-body simulation,
while KB05 use monte-carlo merger trees based on the EPS
formalism. It is well known that EPS merger trees predict
masses for the most massive progenitors that are too large
(e.g., Lacey & Cole 1994; Somerville et al. 2000; van den
Bosch 2002; Benson, Kamionkowski & Hassani 2005). This
implies that the number of mergers with a small progenitor
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 5
Figure 2. The fractions of last major mergers between centrals and satellites (C-S; solid lines) and between two satellites (S-S; dashed
lines) that result in the formation of an ETG as function of its stellar mass at z = 0. Results are shown for all ETGs (left-hand panel) and
for those with Fcold < 0.1 (right-hand panel). Black and red lines correspond to models with and without AGN feedback, respectively.
Low mass ETGs that form in dry mergers, and hence end up being boxy, mainly form out of S-S mergers. At the massive end, the
fraction of ETGs that form out of S-S mergers with Fcold = 0.1 depends strongly on the presence or absence of AGN feedback. See text
for detailed discussion.
mass ratio n will be too small, which explains the difference
between our results and those of KB05. Using cosmological
SPH simulations, Maller et al. (2006) found that the distri-
bution of merger mass ratios scales as dN/dn ∝ n−0.8. This
means that 60 percent of all galaxy mergers with n < 3 have
a progenitor mass ratio n < 2, in excellent agreement with
our results.
The dotted lines in the remaining panels of Figure 1
show the results obtained for three different values of the
maximum cold gas mass fraction, Fcrit = 0.6, 0.3, and 0.1.
Lowering Fcrit has a strong impact on the boxy fraction
of low-luminosity ETGs, while leaving that of bright ETGs
largely unaffected. As we show in §4 this mainly owes to the
fact that Fcold decreases strongly with increasing luminosity.
Consequently, by changing Fcrit we can tune the slope of
the relation between fboxy and luminosity, while ncrit mainly
governs the absolute normalization. We obtain a good match
to the P07 data for ncrit = 2 and Fcrit = 0.1 (third panel in
lowest row). This implies that boxy ETGs only form out of
relatively dry and violent mergers, in good agreement with
numerical simulations.
3.1 The influence of disk regrowth
The analysis above, however, does not consider the impact
of the growth of a new disk around the merger remnant.
Since this may turn boxy systems into disky systems, it can
have a significant impact on the predicted fboxy. We now
take this effect into account by setting fd,max to its fiducial
value of 0.2.
The solid lines in Fig. 1 show the boxy fractions thus
obtained. A comparison with the dotted lines shows that the
newly formed disks only cause a significant decrease of fboxy
at the faint end. At the bright end, AGN feedback prevents
the cooling of hot gas, therewith significantly reducing the
rate at which a new disk can regrow†. However, when Fcrit =
0.1, we obtain the same boxy fractions for fd,max = 0.2 as
for fd,max = 1, even at the faint end. This implies that we
obtain the same conclusions as above: matching the data
of P07 requires ncrit ≃ 2 and Fcrit ≃ 0.1. In other words,
our constraints on ncrit and Fcrit are robust to exactly how
much disk regrowth is allowed before it reveals itself in the
isophotes.
Why do faint ETGs with Fcold < 0.1 not regrow signifi-
cant disks, while does with Fcold > 0.1 do? Note that during
the last major merger, the entire cold gas mass is converted
into stars in a starburst. Therefore, it is somewhat puzzling
that the galaxy’s ability to regrow a disk depends on its cold
gas mass fraction at the last major merger. As it turns out,
this owes to the fact that progenitors with a low cold gas
mass fraction are more likely to be satellite galaxies. Fig. 2
plots the fractions of ETGs with last major mergers be-
tween a central galaxy and a satellite (C-S; solid lines) and
between two satellites (S-S; dashed lines). Note that in our
model, S-S mergers occur whenever their dark matter sub-
haloes in the N-body simulation merge. Results are shown
for all ETGs (left-hand panel), and for only those ETGs
that have Fcold < 0.1 (right-hand panel). In our fiducial
model with AGN feedback (black lines) the most massive
ETGs almost exclusively form out of C-S mergers. Since a
satellite galaxy can never become a central galaxy, this is
† In the absence of cooling, the only way in which a galaxy can
(re)grow a disk is via minor mergers.
c© 2000 RAS, MNRAS 000, 1–13
6 Kang et al.
Figure 3. The progenitor mass ratio, n, (left-hand panel) and the cold gas mass fraction at the last major merger, Fcold, (right-hand
panel) as function of the z = 0 stellar mass, M∗, of ETGs. Solid lines with errorbars indicate the median and the 20
th and 80th percentiles
of the distributions. While the mass ratio of the progenitors of early-type galaxies is independent of its stellar mass, Fcold decreases
strongly with increasing M∗.
consistent with the fact that virtually all massive ETGs at
z = 0 are central galaxies (in massive haloes). Roughly 40
percent of all low mass ETGs have a last major merger be-
tween two satellite galaxies. However, when we only focus on
low mass ETGs with Fcold < 0.1, we find that ∼ 95 percent
of their last major mergers are between two satellite galax-
ies. Since the z = 0 descendents of S-S mergers will also
be satellites, this implies that virtually all boxy ETGs with
M∗ <∼ 2 × 10
10h−1 M⊙ are satellite galaxies. Furthermore,
since satellite galaxies do not have a hot gas reservoir (at
least not in our semi-analytical model) they can not regrow
a new disk by cooling. This explains why for Fcrit = 0.1 the
boxy fractions are independent of the value of fd,max.
3.2 The role of AGN feedback
Our semi-analytical model includes “radio-mode” AGN
feedback, similar to that in Croton et al. (2006), in order to
suppresses the cooling in massive haloes. This in turn shuts
down star formation in the central galaxies in these haloes,
so that they become red. In the absence of AGN feedback,
new gas continues to cool making the central galaxies in
massive haloes overly massive and too blue (e.g., Benson
et al. 2003; Bower et al. 2006; Croton et al. 2006; Kang et
al. 2006). In order to study its impact on fboxy as func-
tion of luminosity, we simply turn off AGN feedback in our
model. Although this results in a semi-analytical model that
no longer fits the galaxy luminosity function at the bright
end, and results in a color-magnitude relation with far too
many bright, blue galaxies, a comparison with the models
discussed above nicely isolates the effects that are directly
due to our prescription for AGN feedback.
The dashed lines in Figure 1 show the predictions of
our model without AGN feedback (and with fd,max = 0.2).
A comparison with our fiducial model (solid lines) shows
that apparently the AGN feedback has no impact on fboxy
for faint ETGs with MB −5 log h >∼ −18. At the bright end,
though, the model without AGN feedback predicts boxy
fractions that are significantly lower (for reasons that will
be discussed in §4.2). Consequently, the luminosity depen-
dence of fboxy is much weaker than in the fiducial case. The
only model that comes close to matching the data of P07
is the one with ncrit = 3 and Fcrit = 0.1. We emphasize,
though, that this model is not realistic. In addition to the
fact that this semi-analytical model does not fit the observed
luminosity function and color magnitude relation, a value of
ncrit = 3 is also very unlikely: numerical simulations have
clearly shown that mergers with a mass ratio near 1:3 almost
invariably result in disky remnants (e.g., Naab & Burkert
2003).
4 DISCUSSION
4.1 The Origin of the ETG Dichotomy
We now examine the physical causes for the various scal-
ings noted above. We start by investigating why our fiducial
model with ncrit = 2 and Fcrit = 0.1 is successful in repro-
ducing the luminosity dependence of fboxy, i.e., why it pre-
dicts that the boxy fraction increases with luminosity. Given
the method used to assign isophotal shapes to the ETGs in
our model, there are three possibilities: (i) brighter ETGs
have smaller progenitor mass ratios, (ii) brighter ETGs have
progenitors with smaller cold gas mass fractions, or (iii)
brighter ETGs have less disk regrowth after their last major
merger.
We can exclude (i) from the fact that the models that
ignore disk regrowth (i.e., with fd,max = 1) and that ignore
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 7
Figure 4. Contour plots for the number density of ETGs as function of their present day stellar mass, M∗, and their cold gas mass
fraction at the last major merger, Fcold. Results are shown both for our fiducial model with AGN feedback (left-hand panel), as well as
for the model without AGN feedback (right-hand panel). In both cases a clear bimodality is apparent: ETGs with large and low masses
formed out of dry and wet mergers, respectively. Note that this bimodality is present independent of the presence of AGN feedback.
the cold gas mass fractions (i.e., with Fcrit = 1) predict
that the boxy fraction is roughly independent of luminosity
(dotted lines in upper panels of Fig. 1). This suggests that
the distribution of n is roughly independent of the (present
day) luminosity of the ETGs. This is demonstrated in the
left-hand panel of Fig. 3, were we plot n as function of,
M∗, the stellar mass at z = 0. Each dot corresponds to an
ETG in our fiducial model, while the solid black line with
the errorbars indicates the median and the 20th and 80th
percentiles of the distribution: clearly the progenitor mass
ratio is independent of M∗.
The boxy fraction of our best-fit model with ncrit = 2
and Fcrit = 0.1 is also independent of the regrowth of
disks, which is evident from the fact that the models with
fd,max = 1 (dotted lines) and fd,max = 0.2 (solid lines) pre-
dict boxy fractions that are indistinguishable. Therefore op-
tion (iii) can also be excluded, and the luminosity depen-
dence of fboxy thus has to indicate that the progenitors of
more luminous ETGs have a lower gas mass fraction. That
this is indeed the case can be seen from the right-hand panel
of Fig. 3 which shows Fcold as function of M∗. Once again,
the solid black line with the errorbars indicates the median
and the 20th and 80th percentiles of the distribution. Note
that Fcold decreases strongly with increasing stellar mass;
the most massive ETGs form almost exclusively from dry
mergers with Fcold < 0.1.
The left-hand panel of Fig. 4 shows a different rendi-
tion of the relation between Fcold and M∗. Contours indicate
the number density, φ(Fcold,M∗), of ETGs in the Fcold-M∗
plane, normalized by the total number of ETGs at each given
M∗-bin, i.e.,
φ(Fcold,M∗) dFcold = 1 (2)
Note that φ(Fcold,M∗) is clearly bimodal: low mass ETGs
with M∗ <∼ 3 × 10
9h−1 M⊙ have high Fcold, while the pro-
genitors of massive ETGs have low cold gas mass fractions.
Clearly, if wet and dry mergers produce disky and boxy el-
lipticals, respectively, this bimodality is directly responsible
for the ETG dichotomy.
What is the physical origin of this bimodality? It is
tempting to expect that it owes to AGN feedback. After all,
in our model AGN feedback is more efficient in more massive
galaxies. Since more massive ETGs have more massive pro-
genitors, one could imagine that their cold gas mass fractions
are lower because of the AGN feedback. However, the right-
hand panel of Fig. 4 shows that this is not the case. Here
we show φ(Fcold,M∗) for the model without AGN feedback.
Somewhat surprisingly, this model predicts almost exactly
the same bimodality as the model with AGN feedback. Their
are subtle differences, which have a non-negligible effect on
the boxy fractions and which will be discussed in §4.2 be-
low. However, it should be clear from Fig. 4 that the overall
bimodality in φ(Fcold,M∗) is not due to AGN feedback.
In order to explore alternative explanations for the bi-
modality, Fig. 5 shows some relevant statistics. Upper and
lower panels correspond to the models with and without
AGN feedback, respectively. Here we focus on our fiducial
model with AGN feedback; the results for the model without
AGN feedback will be discussed in §4.2. The upper left-hand
panel shows the average cold gas mass fraction of individ-
ual galaxies, 〈fcold〉, as function of lookback time. Note that
here we use fcold to distinguish it from Fcold, which indi-
cates the cold gas mass fraction of the combined progeni-
tors taking part in a major merger, as defined in eq. (1).
Results are shown for galaxies of two different (instanta-
neous) stellar masses, M∗ = 3× 109h−1 M⊙ (red lines) and
M∗ = 3× 1010h−1 M⊙ (black lines), and for two (instanta-
neous) types: early-types (dotted lines) and late-types (solid
lines). Following N06, here we define early-types as systems
with a bulge-to-total stellar mass ratio of 0.6 or larger; con-
trary to our z = 0 selection criteria described in §2.1, we do
not include a color selection, simply because the overall color
of the galaxy population evolves as function of time. First
of all, note that 〈fcold〉 of galaxies of given type and given
mass decreases with increasing time (i.e., with decreasing
lookback time). This is simply due to the consumption by
star formation. Secondly, at a given time, early-type galax-
ies have lower gas mass fractions than late-type galaxies.
This mainly owes to the fact that at a major merger, which
creates an early-type, all the available cold gas is consumed
in a starburst. Consequently, each early-type starts its life
c© 2000 RAS, MNRAS 000, 1–13
8 Kang et al.
Figure 5. Various statistics of our semi-analytical models. Upper and lower panels refer to our models with and without AGN feedback,
respectively. Left-hand panels: The average cold gas mass fraction of individual galaxies as function of lookback time t. Results are shown
for galaxies of two different (instantaneous) stellar masses, M∗ = 3 × 10
9h−1 M⊙ (red lines) and M∗ = 3 × 10
10h−1 M⊙ (black lines),
and for two (instantaneous) types: early-types (dotted lines) and late-types (solid lines). Middle panels: The fractions of late-late (L-L;
solid lines) , early-late (E-L; dotted lines) and early-early (E-E; dashes lines) type mergers as function of the z = 0 stellar mass of the
resulting ETG. Right-hand panels: The average lookback time to the last major merger of z = 0 ETGs as function of their z = 0 stellar
mass. Results are shown separately for L-L mergers (solid line), E-L mergers (dotted line), and E-E mergers (dashed line). The errorbars
indicate the 20th and 80th percentiles of the distribution of the E-L mergers. For clarity, we do not show these percentiles for the L-L
and E-E mergers, though they are very similar. See text for detailed discussion.
with fcold = 0. Finally, massive galaxies have lower gas
mass fractions than their less massive counterparts. This
owes to the fact that more massive galaxies live, on average,
in more massive haloes, which tend to form (not assem-
ble!) earlier thus allowing star formation to commence at
an earlier epoch (see Neistein et al. 2006). In addition, the
star formation efficiency used in the semi-analytical model
is proportional to the mass of the cold gas times M0.73vir . As
discussed in K05, this scaling with the halo virial mass is re-
quired in order to match the observed 〈fcold〉(M∗) at z = 0
(see also Cole et al. 1994, 2000; De Lucia et al. 2004).
The middle panel in the upper row of Fig. 5 shows what
kind of galaxy types are involved in the last major mergers
of present-day ETGs. Solid, dotted and dashed curves show
the fractions of L-L, E-L and E-E mergers, where ‘L’ and ‘E’
refer to late-types and early-types, respectively. As above,
these types are based solely on the bulge-to-total mass ratio
of the galaxy and not on its color. In our semi-analytical
model, the lowest mass ETGs almost exclusively form via
L-L mergers. With increasing M∗, however, there is a pro-
nounced decrease of the fraction of L-L mergers, which are
mainly replaced by E-L mergers. The fraction of E-E merg-
ers increases very weakly with increasing stellar mass but
never exceeds 10 percent. Thus, although boxy ellipticals
form out of dry mergers, these are not necessarily mergers
between early-type galaxies. In fact, our model predicts that
the vast majority of all dry mergers involve at least one late-
type galaxy (though with a low cold gas mass fraction). This
is in good agreement with the SPH simulation of Maller et
al. (2006), who also find that E-E mergers are fairly rare.
However, it is in stark contrast to the predictions of the
semi-analytical model of N06, how find that more than 50
percent of the last major mergers of massive ellipticals are E-
E mergers. We suspect that the main reason for this strong
discrepancy is the fact that N06 used merger trees based on
the EPS formalism.
Finally, the upper right-hand panel of Fig. 5 plots the
average lookback time to the last major merger of ETGs as
function of their present day stellar mass. Results are shown
separately for L-L mergers (solid line), E-L mergers (dotted
line), and E-E mergers (dashed line). Clearly, more massive
ETGs assemble later (at lower lookback times). This mainly
owes to the fact that more massive galaxies live in more
massive haloes, which themselves assemble later (cf. Lacey
& Cole 1993; Wechsler et al. 2002; van den Bosch 2002;
Neistein et al. 2006; De Lucia et al. 2006). In addition, it is
clear that at fixed stellar mass, E-E mergers occur later than
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 9
L-L mergers, with E-L mergers in between. This difference,
however, is small compared to the scatter.
If we combine all this information, we infer that the
bimodality in φ(Fcold,M∗) owes to the following three facts:
• More massive ETGs have more massive progenitors
(this follows from the fact that n is independent of M∗).
Since at a given time more massive galaxies of a given type
have lower cold gas mass fractions, 〈Fcold〉 decreases with
increasing M∗.
• More massive ETGs assemble later (at lower redshifts).
Galaxies of given mass and given type have lower 〈fcold〉 at
later times. Consequently, 〈Fcold〉 decreases with increasing
• More massive ETGs have a larger fraction of early-type
progenitors. ETGs of a given mass have a lower cold gas
mass fraction than late type galaxies of the same mass, at
any redshift. In addition, E-L mergers occur at later times
than L-L mergers. Both these effects also contribute to the
fact that 〈Fcold〉 decreases with increasing M∗.
4.2 Is AGN feedback relevant?
A comparison of the upper and lower panels in Fig. 5
shows that the three effects mentioned above, and thus
the bimodality in φ(Fcold,M∗), are present independent of
whether or not the model includes feedback from active
galactic nuclei. There are only two small differences: with-
out AGN feedback massive ETGs (i) are more likely to result
from L-L mergers, and (ii) have a higher 〈fcold〉 (cf. black
dotted curves in the left-hand panels of Fig. 5). Both ef-
fects reflect that AGN feedback prevents the cooling of hot
gas around massive galaxies, therewith removing an impor-
tant channel for building a new disk. As is evident from
Fig. 4, these two effects only have a very mild impact on
φ(Fcold,M∗). We therefore conclude that the bimodality of
ETGs is not due to AGN feedback.
This does not imply, however, that AGN feedback does
not have an impact on the boxy fractions. As is evident from
Fig. 1, the models with and without AGN feedback clearly
predict different fboxy at the bright end. To understand the
origin of these differences, first focus on Fig. 4. Although
both panels look very similar, upon closer examination one
can notice that at M∗ >∼ 10
11h−1 M⊙ the number density of
ETGs with 0.1 <∼ Fcold <∼ 0.25 is significantly larger in the
model without AGN feedback. In the model with AGN feed-
back these systems all have Fcold < 0.1. This explains why
the model without AGN feedback predicts a lower boxy frac-
tion for bright galaxies when Fcrit = 0.1. However, this does
not explain why fboxy is also different when Fcrit ≥ 0.3.
After all, for those models it should not matter whether
Fcold = 0.05 or Fcold = 0.25, for example. It turns out that
in these cases the differences between the models with and
without AGN feedback are due to the regrowth of a new
disk; since AGN feedback suppresses the cooling of hot gas
around massive galaxies, it strongly suppresses the regrowth
of a new disk, thus resulting in higher boxy fractions.
Note however, that in ETGs with Fcold < 0.1, disk re-
growth is always negligible. In the presence of AGN feedback
this is due to the suppression of cooling in massive haloes.
In the absence of AGN feedback it owes to the fact that only
a very small fraction of ETGs are central galaxies. As can
Figure 6. The boxy fraction of ETGs as function of halo (group)
mass. Red triangles (for satellite galaxies) and blue circles (for
central galaxies) are taken from P07, and have been obtained us-
ing the galaxy group catalogue of Weinmann et al. (2006). Dashed
and solid lines correspond to the predictions from our fiducial
model.
be seen from the right-hand panel of Fig. 2, more than 90
percent of the ETGs have last major mergers between two
satellite galaxies (with AGN feedback this fraction is smaller
than 20 percent). Since satellite galaxies do not have hot gas
reservoirs, no significant disks can regrow around these sys-
tems.
4.3 Environment dependence
Using the SDSS galaxy group catalogue of Weinmann et
al. (2006), which has been constructed using the halo-based
group finder developed by Yang et al. (2005), P07 inves-
tigated how fboxy scales with group mass. They also split
their sample in ‘central’ galaxies (defined as the brightest
group members) and ‘satellites’. The open circles and trian-
gles in Fig. 6 show their results for centrals and satellites,
respectively. Although there are only two data points for the
satellites, it is clear that central galaxies are more likely to
be boxy than a satellite galaxy in a group (halo) of the same
mass.
We now investigate whether our fiducial semi-analytic
model that fits the luminosity dependence of the boxy frac-
tion (i.e., the one with ncrit = 2 and Fcrit = 0.1) can also
reproduce these trends. The model predictions for the cen-
trals and satellites are shown in Fig. 6 as solid and dashed
lines, respectively. Here we have associated the halo virial
mass with the group mass, and an ETG is said to be a cen-
tral galaxy if it is the brightest galaxy in its halo. The model
accurately reproduces the boxy fraction of both central and
satellite galaxies. In particular, it reproduces the fact that
fboxy of central galaxies is higher than that of satellites in
groups (haloes) of the same mass.
As shown in P07, the boxy fraction as function of group
c© 2000 RAS, MNRAS 000, 1–13
10 Kang et al.
Figure 7. The residuals of the relations between n and M∗ (left panel) and Fcold and M∗ (right panel) as functions of the virial mass of
the halo in which the ETGs reside at z = 0. As in Fig. 3 the solid lines with errorbars indicate the mean and the 20th and 80th percentiles
of the distributions. These show that after one corrects for the stellar mass dependence, the properties of the last major mergers of ETGs
are independent of their halo mass.
mass, for both centrals and satellites, is perfectly consistent
with the null-hypothesis that the isophotal shape of an ETG
depends only on its luminosity; the fact that centrals have a
higher boxy fraction than satellites in the same group, sim-
ply owes to the fact that the centrals are brighter. Also, the
increase of fboxy with increasing group mass simply reflects
that more massive haloes host brighter galaxies. It there-
fore may not come as a surprise that our semi-analytical
model that fits the luminosity dependence of fboxy also fits
the group mass dependencies shown in Fig. 6. It does mean,
though, that in our model the merger histories of ETGs of
a given luminosity do not strongly depend on the halo mass
in which the galaxy resides.
To test this we proceed as follows. For each ETG in
our model we compute 〈n〉 and 〈Fcold〉, where the average
is over all ETGs with stellar masses similar to that of the
galaxy in question. Fig. 7 plots the residuals n − 〈n〉 and
Fcold − 〈Fcold〉 as function of the virial mass, Mvir, of the
halo in which they reside. This clearly shows that after one
corrects for the stellar mass dependence, the properties of
the last major merger of ETGs are indeed independent of
their halo mass‡. This provides theoretical support for the
conclusion of P07 that the stellar mass (or luminosity) of an
ETG is the main parameter that determines whether it will
be disky or boxy.
4.4 The Origin of Cusps and Cores
As discussed in §1, the dichotomy of ETGs is not only re-
stricted to their isophotal shapes. One other important as-
pect of the dichotomy regards the central density distribu-
‡ The fact that the distribution of the progenitor mass ratio n is
independent of halo mass was also found by KB05
tion of ETGs; while disky systems typically have cuspy pro-
files, the bright and boxy ellipticals generally reveal density
profiles with a pronounced core. Here we briefly discuss how
the formation of cusps and cores fits in the picture sketched
above.
In the paradigm adopted here, low luminosity ETGs
form mainly via wet mergers. Due to the fluctuating poten-
tial of the merging galaxies and the onset of bar instabilities,
the gas experiences strong torques which causes a significant
fraction of the gas to sink towards the center of the po-
tential well where it undergoes a starburst (e.g., Shlosman,
Frank & Begelman 1989; Barnes & Hernquist 1991; Mihos
& Hernquist 1996). Detailed hydrodynamical simulations of
gas-rich mergers (e.g., Springel & Hernquist 2005; Cox et
al. 2006b) result in the formation of remnants with surface
brightness profiles that are reminiscent of cuspy ETGs (John
Kormendy, private communication). Hence, cusps seem a
natural by-product of the dissipative processes associated
with a wet merger.
Boxy ETGs, however, are thought to form via dry merg-
ers. As can be seen from Fig. 5 roughly 35 percent of all mas-
sive ETGs originate from a last major merger that involves
an early-type progenitor. If this progenitor contains a cusp,
this will survive the merger, as most clearly demonstrated by
Dehnen (2005). The only mergers that are believed to result
directly in a remnant with a core, are mergers between pure
stellar disks with a negligible fcold (e.g., Cox et al. 2006a).
Fig. 8 shows the cumulative distributions of the bulge-to-
total stellar mass ratios of the progenitors of present day
ETGs. Results are shown for ETGs in three mass ranges,
as indicated. The probability that a progenitor of a massive
ETGs (with M∗ > 10
11h−1 M⊙) has a negligible bulge com-
ponent (M∗,bulge < 0.01M∗) is only about 3 percent. Hence,
we expect that only about 1 out of every 1000 major merg-
ers that result in a massive ETG will have a remnant with
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 11
a core. And this is most likely an overestimate, since we
did not take the cold gas mass fractions into consideration.
Since the cusp accounts for only about one percent of the
total stellar mass (e.g., Faber et al. 1997; Milosavljević et
al. 2002), cold gas mass fractions of a few percent are prob-
ably enough to create a cusp via dissipational processes.
Therefore, an additional mechanism is required in order
to create a core (i.e., destroy a cusp). Arguably the most
promising mechanism is the orbital decay of a supermas-
sive black hole (SMBH) binary, which can scour a core by
exchanging angular momentum with the cusp stars (e.g.,
Begelman et al. 1980; Ebisuzaki et al. 1991; Quinlan 1996;
Faber et al. 1997; Milosavljević et al. 2002; Merritt 2006a).
Since virtually all spheroids contain a SMBH at their cen-
ter, with a mass that is tightly correlated with the mass of
the spheroid (e.g., Kormendy & Richstone 1995; Ferrarese &
Merritt 2000; Gebhardt et al. 2000; Marconi & Hunt 2003;
Häring & Rix 2004), it is generally expected that such bina-
ries are common in merger remnants (but see below).
While offering an attractive explanation for the pres-
ence of cores in massive, boxy ETGs, this picture simulta-
neously poses a potential problem for the presence of cusps
in disky ETGs. After all, if the progenitors of disky ETGs
also harbor SMBHs, the same process could create a core
in these systems as well. There are two possible ways out
of this paradox: (i) low mass ETGs do not form a SMBH
binary, or (ii) a cusp is regenerated after the two SMBHs
have coalesced. We now discuss these two options in turn.
In order for a SMBH binary to form, dynamical friction
must first deliver the two SMBHs from the two progenitors
to the center of the newly formed merger remnant. This
process will only be efficient if the spheroidal hosts of the
SMBHs are sufficiently massive. Consider a (small) bulge
that was part of a late-type progenitor which is now orbiting
the remnant of its merger with another galaxy. Assume for
simplicity that both the bulge and the merger remnant are
purely stellar singular isothermal spheres (ρ ∝ r−2) with
velocity dispersions equal to σb and σg, respectively. Then,
assuming that the bulge is on a circular orbit, with an initial
radius ri, Chandrasekhar’s (1943) formula gives an infall
time for the bulge of
tinfall ≈ 3.3
≈ 4.7× 108 yr
(Merritt 2006b). Here we have used that ri/σg ≃
2 tcross
with tcross ∼ 108 yr the galaxy crossing time. If the galaxy
is the remnant of an equal mass merger, so that Mb ∼
(∆/2)Mg , with ∆ the bulge-to-total stellar mass ratio of
the late-type progenitor, we find that tinfall is equal to the
Hubble time (1.3 × 1010 yr) for ∆ ≃ 0.07. As can be seen
from Fig. 8, about 70 percent of the low mass ETGs (with
109h−1M⊙ < M∗ < 10
10h−1M⊙) have at least one progeni-
tor with a stellar bulge-to-total mass ratio ∆ < 0.07. There-
fore, we expect that a similar fraction will form without a
SMBH binary, and thus will not form a core. For compari-
son, for massive ETGs (with M∗ > 10
11h−1M⊙) only about
20 percent of the progenitors will have a sufficiently small
bulge to prevent the formation of a SMBH binary.
An alternative explanation for the presence of cusps in
low mass ETGs is that the cusp is regenerated by star for-
mation from gas present at the last major merger. However,
as emphasized by Faber et al. (1997), this results in a serious
Figure 8. The cumulative probability that a progenitor of a
z = 0 ETG has a stellar bulge-to-total mass ratio less then
M∗,bulge/M∗. Results are shown for the progenitors of ETGs in
three stellar mass ranges, as indicated (masses are in h−1 M⊙).
Note that the progenitors of more massive ETGs have signifi-
cantly higher M∗,bulge/M∗. As discussed in the text, this may
help to explain why low mass ETGs have cusps, while massive
ones have cores.
timing problem, as it requires that the new stars must form
after the SMBH binary has coalesced. Another potential
problem with this picture, is that the cusp would be younger
than the main body of the ETG which may lead to observ-
able effects (i.e., cusp could be bluer than main body). How-
ever, in light of the results presented here, we believe that
neither of these two issues causes a serious problem. First of
all, the cold gas mass fractions involved with the last major
merger, and hence the mass fraction that is turned into stars
in the resulting starburst, is extremely large: 〈Fcold〉 ∼ 0.8
(see Fig. 4). As mentioned above, a significant fraction of
this gas is transported to the center, where it will function
as an important energy sink for the SMBH binary, greatly
speeding up its coalescence (Escala et al. 2004, 2005) and
therewith reducing the timing problem mentioned above. In
fact, the gas may well be the dominant energy sink, so that
the pre-existing cusps of the progenitors are only mildly af-
fected. But even if the cusps were destroyed, there clearly
should be enough gas left to build a new cusp. In fact, if,
as envisioned in our semi-analytical model, all the cold gas
present at the last major merger is consumed in a starburst,
a very significant fraction of the stars in the main body
would also be formed in this starburst (not only the cusp).
This would help to diminish potential population differences
between the cusp and the main body of the ETG. In addi-
tion, as can be seen from the right-hand panels of Fig. 5,
the last major merger of low luminosity ETGs occurred on
average ∼ 9.5 Gyr ago. Hence, the stars made in this burst
are not easily distinguished observationally from the ones
that were already present before the last major merger.
To summarize, our semi-analytical model predicts that
c© 2000 RAS, MNRAS 000, 1–13
12 Kang et al.
the progenitors of ETGs have cold gas mass fractions and
bulge-to-total mass ratios that offer a relatively natural ex-
planation for the observed dichotomy between cusps and
cores.
5 CONCLUSIONS
Using a semi-analytical model for galaxy formation, com-
bined with a large N-body simulation, we have investigated
the origin of the dichotomy among ETGs. In order to assign
isophotal shapes to the ETGs in our model we use three cri-
teria: an ETG is said to be boxy if (i) the progenitor mass
ratio at the last major merger is n < ncrit, (ii) the total
cold gas mass fraction of the sum of the two progenitors
at the last major merger is Fcold < Fcrit, and (iii) after its
last major merger the ETG is not allowed to regrow a new
disk with a stellar mass that exceeds 20 percent of the total
stellar mass.
In agreement with KB05, we find that we can not repro-
duce the observed luminosity (or, equivalently, stellar mass)
dependence of fboxy if we assign isophotal shapes based only
on the progenitor mass ratio. This owes to the fact that
the distribution of n is virtually independent of the stellar
mass, M∗, of the ETG at z = 0. Rather, to obtain a boxy
fraction that increases with increasing luminosity one also
needs to consider the cold gas mass fraction at the last ma-
jor merger. In fact, we can accurately match the data of P07
with ncrit = 2 and Fcrit = 0.1. This implies that boxy galax-
ies originate from relatively violent and dry mergers with
roughly equal mass progenitors and with less than 10 per-
cent cold gas, in good agreement with numerical simulations
(e.g., Naab et al. 2006a; Cox et al. 2006a). Our model also
nicely reproduces the observed boxy fraction as function of
halo mass, for both central galaxies and satellites. We have
demonstrated that this owes to the fact that after one cor-
rects for the stellar mass dependence, the properties of the
last major merger of ETGs are independent of their halo
mass. This provides theoretical support for the conjecture
of P07 that the stellar mass (or luminosity) of an ETG is
the main parameter that determines whether it will be disky
or boxy.
Our model predicts a number density distribution,
φ(Fcold,M∗), of ETGs in the Fcold-M∗ plane that is clearly
bimodal: low mass ETGs with M∗ <∼ 3 × 10
9h−1 M⊙ have
high Fcold, while the progenitors of massive ETGs have low
cold gas mass fractions. Clearly, if wet and dry mergers pro-
duce disky and boxy ellipticals, respectively, this bimodal-
ity is directly responsible for the ETG dichotomy. Contrary
to naive expectations, we find that this bimodality is in-
dependent of the inclusion of AGN feedback in the model.
Although AGN feedback is essential for regulating the lumi-
nosities and colors of the brightest galaxies (which end up
as ETGs with AGN feedback, but as blue disk-dominated
systems without AGN feedback), it does not explain the
bimodality among ETGs. Rather, this bimodality is due to
the fact that more massive ETGs (i) have more massive pro-
genitors, (ii) assemble later, and (iii) have a larger fraction
of early-type progenitors. Each of these three trends causes
the cold gas mass fraction of the progenitors of more mas-
sive ETGs to be lower, and thus its last major merger to
be dryer. In conclusion, the dichotomy among ETGs has a
very natural explanation within the hierarchical framework
of structure formation and does not require AGN feedback.
We also examined the morphological properties of the
progenitors of present day ETGs (at the epoch of the last
major merger). Indicating early- and late-type galaxies with
‘E’ and ‘L’, respectively, we find that the lowest mass ETGs
almost exclusively form via L-L mergers. With increasing
M∗, however, there is a pronounced decrease of the fraction
of L-L mergers, which are mainly replaced by E-L mergers.
The E-E mergers, however, never contribute more than 10
percent, in good agreement with the SPH simulations of
Maller et al. (2006). Thus, although boxy ellipticals form
out of dry mergers, these only rarely involve two early-type
systems.
Since satellite galaxies do not have a hot corona from
which new gas cools down, they typically have lower cold gas
mass fractions than central galaxies of the same mass. Con-
sequently, dry mergers are preferentially mergers between
two satellite galaxies. In fact, since a satellite galaxy can
not become a central galaxy, our model predicts that more
than 95 percent of all boxy ETGs with M∗ <∼ 2×10
10h−1M⊙
are satellites.
We also find that the progenitors of less massive ETGs
typically have lower bulge-to-total mass ratios. In fact,
for ETGs with present day stellar masses in the range
109h−1 M⊙ < M∗ < 10
10h−1 M⊙ we find that almost half
of the progenitors at the last major merger have bulges
that do not contribute more than one percent to the to-
tal stellar mass. This may have important implications for
the observed dichotomy between cusps and cores in ETGs.
Cores are believed to form via the scouring effect of a SMBH
binary, that arises when the SMBHs associated with the
spheroidal components of the progenitor galaxies form a
bound pair. This requires both spheroids to sink to the cen-
ter of the potential well of the merger remnant via dynamical
friction. However, if the time scale for this infall exceeds the
Hubble time, no SMBH binary will form, thus preventing
the creation of a core. Using our prediction for the bulge-to-
total mass ratios of progenitor galaxies, and a simple esti-
mate based on Chandrasekhar’s dynamical friction formula,
we have estimated that ∼ 70 percent of low mass ETGs
in the aforementioned mass range will not form a SMBH
binary. For massive ETGs with M∗ > 10
11h−1M⊙ this frac-
tion is only ∼ 20 percent. This may help to explain why
low mass ETGs have steep cusps, while massive ETGs have
cores.
Finally, in those low mass systems that do form a SMBH
binary, the large cold gas mass fraction at its last major
merger (〈Fcold〉 ≃ 0.8) provides more than enough raw ma-
terial for the regeneration of a new cusp. In addition, a large
fraction of the cold gas will sink to the center due to angular
momentum transfer where it will function as an important
energy sink for the SMBH binary. As shown by Escala et
al. (2004, 2005), this can cause a tremendous acceleration of
the coalescence of the SMBHs, largely removing the timing
problem interjected by Faber et al. (1997).
6 ACKNOWLEDGEMENTS
We are grateful to Eric Bell, Eric Emsellem, John Kormendy,
Thorsten Naab, Hans-Walter Rix, and the entire Galaxies-
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 13
Cosmology-Theory group at the MPIA for enlightening dis-
cussions.
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c© 2000 RAS, MNRAS 000, 1–13

  Using a semi-analytical model for galaxy formation, combined with a large
N-body simulation, we investigate the origin of the dichotomy among early-type
galaxies. We find that boxy galaxies originate from mergers with a progenitor
mass ratio $n < 2$ and with a combined cold gas mass fraction $F_{\rm cold} <
0.1$. Our model accurately reproduces the observed fraction of boxy systems as
a function of luminosity and halo mass, for both central galaxies and
satellites. After correcting for the stellar mass dependence, the properties of
the last major merger of early-type galaxies are independent of their halo
mass. This provides theoretical support for the conjecture of Pasquali et al
(2007) that the stellar mass of an early-type galaxy is the main parameter that
governs its isophotal shape. We argue that the observed dichotomy of early-type
galaxies has a natural explanation within hierarchical structure formation, and
does not require AGN feedback. Rather, we argue that it owes to the fact that
more massive systems (i) have more massive progenitors, (ii) assemble later,
and (iii) have a larger fraction of early-type progenitors. Each of these three
trends causes the cold gas mass fraction of the progenitors of more massive
early-types to be lower, so that their last major merger was dryer. Finally,
our model predicts that (i) less than 10 percent of all early-type galaxies
form in major mergers that involve two early-type progenitors, (ii) more than
95 percent of all boxy early-type galaxies with $M_* < 2 \times 10^{10} h^{-1}
\Msun$ are satellite galaxies, and (iii) about 70 percent of all low mass
early-types do not form a supermassive black hole binary at their last major
merger. The latter may help to explain why low mass early-types have central
cusps, while their massive counterparts have cores.

arXiv:0704.0932v1  [astro-ph]  6 Apr 2007
Mon. Not. R. Astron. Soc. 000, 1–13 (2000) Printed 28 August 2021 (MN LATEX style file v1.4)
On the Origin of the Dichotomy of Early-Type Galaxies:
The Role of Dry Mergers and AGN Feedback
X. Kang1,2⋆, Frank C. van den Bosch1, A. Pasquali1
1Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
2Shanghai Astronomical Observatory; the Partner Group of MPA, Nandan Road 80, Shanghai 200030, China
ABSTRACT
Using a semi-analytical model for galaxy formation, combined with a large N -body
simulation, we investigate the origin of the dichotomy among early-type galaxies. In
qualitative agreement with previous studies and with numerical simulations, we find
that boxy galaxies originate from mergers with a progenitor mass ratio n < 2 and with
a combined cold gas mass fraction Fcold < 0.1. Our model accurately reproduces the
observed fraction of boxy systems as a function of luminosity and halo mass, for both
central galaxies and satellites. After correcting for the stellar mass dependence, the
properties of the last major merger of early-type galaxies are independent of their halo
mass. This provides theoretical support for the conjecture of Pasquali et al. (2007) that
the stellar mass (or luminosity) of an early-type galaxy is the main parameter that
governs its isophotal shape. If wet and dry mergers mainly produce disky and boxy
early-types, respectively, the observed dichotomy of early-type galaxies has a natural
explanation within the hierarchical framework of structure formation. Contrary to
naive expectations, the dichotomy is independent of AGN feedback. Rather, we argue
that it owes to the fact that more massive systems (i) have more massive progenitors,
(ii) assemble later, and (iii) have a larger fraction of early-type progenitors. Each
of these three trends causes the cold gas mass fraction of the progenitors of more
massive early-types to be lower, so that their last major merger involved less cold
gas (was more “dry”). Finally, our model predicts that (i) less than 10 percent of all
early-type galaxies form in major mergers that involve two early-type progenitors, (ii)
more than 95 percent of all boxy early-type galaxies with M∗ <∼ 2 × 10
10h−1 M⊙ are
satellite galaxies, and (iii) about 70 percent of all low mass early-types do not form
a supermassive black hole binary at their last major merger. The latter may help to
explain why low mass early-types have central cusps, while their massive counterparts
have cores.
Key words: dark matter — galaxies: elliptical and lenticular — galaxies: interactions
— galaxies: structure — galaxies: formation
1 INTRODUCTION
Ever since the seminal paper by Davies et al. (1983) it
is clear that early-type galaxies (ellipticals and lenticulars,
hereafter ETGs) can be split in two distinct sub-classes.
Davies et al. showed that bright ETGs typically have lit-
tle rotation, such that their flattening must originate from
anisotropic pressure. This is consistent with bright ellipti-
cals being in general triaxial. Low luminosity ellipticals, on
the other hand, typically have rotation velocities that are
consistent with them being oblate isotropic rotators (see
Emsellem et al. 2007 and Cappellari et al. 2007 for a more
contemporary description). These different kinematic classes
⋆ E-mail:kang@mpia.de
also have different morphologies and different central surface
brightness profiles. In particular, bright, pressure-supported
systems usually have boxy isophotes and luminosity pro-
files that break from steep outer power-laws to shallow in-
ner cusps (often called ‘cores’). The low luminosity, rotation
supported systems, on the other hand, often reveal disky
isophotes and luminosity profiles with a steep central cusp
(e.g., Bender 1988; Nieto et al. 1988; Ferrarese et al. 1994;
Gebhardt et al. 1996; Rest et al. 2001; Lauer et al. 2005,
2006). Finally, the bimodality of ETGs has also been found
to extend to their radio and X-ray properties. Objects which
are radio-loud and/or bright in soft X-ray emission generally
have boxy isophotes, while disky ETGs are mostly radio-
quiet and faint in soft X-rays (Bender et al. 1989; Pellegrini
1999, 2005; Ravindranath et al. 2001).
c© 2000 RAS
http://arxiv.org/abs/0704.0932v1
2 Kang et al.
Recently, Hao et al. (2006) constructed a homoge-
neous samples of 847 ETGs from the SDSS DR4 catalogue
(Adelman-McCarthy et al. 2006), and analyzed their isopho-
tal shapes. This sample was used by Pasquali et al. (2007:
hereafter P07) to investigate the relative fractions of disky
and boxy ETGs as function of luminosity, stellar mass and
environment. They found that the disky fraction decreases
smoothly with increasing (B-band) luminosity, stellar mass,
and halo mass, where the latter is obtained from the SDSS
group catalogue of Weinmann et al. (2006). In addition, the
disky fraction is found to be higher for satellite galaxies than
for central galaxies in a halo of the same mass. These data
provide a powerful benchmark against which to test models
for the formation of ETGs.
Within the framework of hierarchical structure for-
mation, elliptical galaxies are generally assumed to form
through major mergers (e.g., Toomre & Toomre 1972;
Schweizer 1982; Barnes 1988; Hernquist 1992; Kauffmann,
White & Guiderdoni 1993). In this case, it seems logical that
the bimodality in their isophotal and kinematical properties
must somehow be related to the details of their merger his-
tories. Using dissipationless N-body simulations it has been
shown that equal mass mergers of disk galaxies mainly result
in slowly rotating ETGs with boxy (but sometimes disky)
isophotes, while mergers in which the mass ratio between the
progenitor disks is significantly different from unity mainly
yields disky ETGs (Negroponte & White 1983; Barnes 1988;
Hernquist 1992; Bendo & Barnes 2000; Naab & Burkert
2003; Bournaud et al. 2004, 2005; Naab & Trujillo 2006).
However, simulations that also include a dissipative gas com-
ponent and star formation have shown that the presence of
even a relatively small amount of cold gas in the progenitors
results in a merger remnant that resembles a disky ellipti-
cal even when the mass ratio of the progenitors is close to
unity (Barnes & Hernquist 1996; Naab et al. 2006a; Cox
et al. 2006a). This suggests that boxy ETGs can only form
out of dry, major mergers (see also discussion in Faber et
al. 1997). In this paper we test this paradigm using a semi-
analytical model for galaxy formation and the observational
constraints of P07.
Our study is similar to those of Khochfar & Burk-
ert (2005; hereafter KB05) and Naab et al. (2006b; here-
after N06), who also used semi-analytical models to explore
whether the dichotomy of elliptical galaxies can be related to
their merger properties. However, our analysis differs from
theirs on the following grounds.
• We use a numerical N-body simulation to construct the
merger histories of dark matter haloes. The models of KB05
and N06, on the other hand, used merger trees based on
the extended Press-Schechter (EPS) formalism (e.g., Lacey
& Cole 1993). As we will show, this results in significant
differences.
• Because of our use of numerical N-body simulations,
our model more accurately traces the dynamical evolution of
dark matter subhaloes with their associated satellite galax-
ies. In particular, it takes proper account of dynamical fric-
tion, tidal stripping and the merging between subhaloes.
• Contrary to KB05 and N06, we include a prescription
for the feedback from active galactic nuclei (AGN) in our
semi-analytical model.
• Our semi-analytical model is tuned to reproduce the
luminosity function and the color-bimodality of the redshift
zero galaxy population (see Kang et al. 2005). The works of
KB05 and N06 do not mention such a comparison.
• Our criteria for the production of boxy ETGs are dif-
ferent from those used in KB05 and N06.
• We use a much larger, more homogeneous data set to
constrain the models.
This paper is organized as follows. In Section 2 we de-
scribe our N-body simulation and semi-analytical model,
and outline the methodology. The results are described in
Section 3 and discussed in Section 4. We summarize our
findings in Section 5
2 METHODOLOGY
The aim of this paper is to investigate to what extend semi-
analytical models of galaxy formation can reproduce the
ecology of ETGs, in particular the fractions of disky and
boxy systems as function of luminosity and halo mass. Par-
tially motivated by numerical simulations of galaxy mergers,
both with and without gas, we adopt a framework in which
(i) ETGs are red and dominated by a spheroidal compo-
nent, (ii) ETGs are the outcome of major mergers, (iii) the
remnant is boxy if the merger is sufficiently “dry” (i.e., the
progenitors have little or no cold gas) and sufficiently “ma-
jor” (i.e., the progenitors have roughly equal masses) and
(iv) a boxy elliptical becomes a disky elliptical if newly ac-
creted material builds a sufficiently large stellar disk.
2.1 N-body simulation and model descriptions
In order to have accurate merger trees, and to be able
to follow the dynamical evolution of satellite galaxies, we
use a numerical simulation of the evolution of dark mat-
ter which we populate with galaxies using a state-of-the-art
semi-analytical model for galaxy formation. The numerical
simulation has been carried out by Jing & Suto (2002) using
a vectorized-parallel P3M code. It follows the evolution of
5123 particles in a cosmological box of 100h−1 Mpc, assum-
ing a flat ΛCDM ‘concordance’ cosmology with Ωm = 0.3,
σ8 = 0.9, and h = H0/100 kms
−1 Mpc−1 = 0.7. Each parti-
cle has a mass of 6.2 × 108h−1 M⊙. Dark matter haloes are
identified using the friends-of-friends (FOF) algorithm with
a linking length equal to 0.2 times the mean particle sepa-
ration. For each halo thus identified we compute the virial
radius, rvir, defined as the spherical radius centered on the
most bound particle inside of which the average density is
340 times the average density of the Universe (cf. Bryan &
Norman 1998). The virial mass is simply defined as the mass
of all particles that have halocentric radii r ≤ rvir. Since our
FOF haloes have a characteristic overdensity of ∼ 180 (e.g.,
White 2002), the virial mass is typically smaller than the
FOF mass.
Dark matter subhaloes within each FOF (parent) halo
are identified using the SUBFIND routine described in
Springel et al. (2001). In the present study, we use all haloes
and subhaloes with masses down to 6.2 × 109h−1M⊙ (10
particles). Using 60 simulation outputs between z = 15 and
z = 0, equally spaced in log(1 + z), Kang et al. (2005; here-
after K05) constructed the merger history for each (sub)halo
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 3
in the simulation box, which are then used in the semi-
analytical model. In what follows, whenever we refer to a
halo, we mean a virialized object which is not a sub-structure
of a larger virialized object, while subhaloes are virialized ob-
jects that orbit within a halo. In addition, (model) galaxies
associated with haloes and subhaloes are referred to as cen-
tral galaxies and satellites, respectively.
The semi-analytical model used to populate the haloes
and subhaloes with galaxies is described in detail in K05, to
which we refer the reader for details. Briefly, the model as-
sumes that the baryonic material accreted by a dark matter
halo is heated to the virial temperature. The gas then cools
radiatively and settles down into a centrifugally supported
disk, in which the star formation rate is proportional to the
total amount of cold gas, and inversely proportional to the
dynamical time of the disk. The energy feedback from su-
pernova is related to the initial stellar mass function (IMF)
and proportional to the star formation rate. It is assumed
that the gas that is reheated by supernova feedback remains
bound to the host halo so that it can cool back onto the
disk at later stages. When the subhalo associated with a
satellite galaxy is dissolved in the numerical simulation the
satellite galaxy becomes an “orphan” galaxy, which is as-
sumed to merge with the central galaxy of the parent halo
after a dynamical friction time (computed assuming stan-
dard Chandrasekhar dynamical friction). When two galaxies
merge, the outcome is assumed to depend on their mass ratio
n ≡ M1/M2 with M1 ≥ M2. If n ≤ 3 the merger is assumed
to result in the formation of an elliptical galaxy, and we
speak of a “major merger”. Any cold gas available in both
progenitors is turned into stars. This is supported by hy-
drodynamical simulations, which show that major mergers
cause the cold gas to flow to the center where the resulting
high gas density triggers a starburst (e.g., Barnes & Hern-
quist 1991, 1996; Mihos & Hernquist 1996; Springel 2000;
Cox et al. 2006a,b; Di Matteo et al. 2007). A new disk of cold
gas and stars may form around the elliptical if new gas can
cool in the halo of the merger remnant, thus giving rise to
a disk-bulge system. If n > 3 we speak of a “minor merger”
and we simply add the cold gas of the less massive progeni-
tor to that of the disk of the more massive progenitor, while
its stellar mass is added to the bulge of the massive progen-
itor. The semi-analytical model also includes a prescription
for “radio-mode” AGN feedback as described in Kang, Jing
& Silk (2006; see also Section 3.2). This ingredient is es-
sential to prevent significant amounts of star formation in
the brightest galaxies, and thus to ensure that these systems
are predominantly members of the red sequence (e.g., Cat-
taneo et al. 2006; De Lucia et al. 2006; Bower et al. 2006;
Croton et al. 2006). Finally, luminosities for all model galax-
ies are computed using the predicted star formation histo-
ries and the stellar population models of Bruzual & Charlot
(2003). Throughout we assume a Salpeter IMF and we self-
consistently model the metalicities of gas and stars, includ-
ing metal-cooling.
As shown in K05 and Kang et al. (2006) this model ac-
curately fits, among others, the galaxy luminosity function
at z = 0, the color bimodality of the z = 0 galaxy popula-
tion, and the number density of massive, red galaxies out to
z ∼ 3. We emphasize that in this paper we use this model
without changing any of its parameters.
2.2 Predicting Isophotal Shapes
In our model we determine whether an elliptical galaxy is
disky or boxy as follows. Using the output at z = 0 we first
identify the early-type (E/S0) galaxies based on two criteria.
First of all, following Simien & de Vaucouleurs (1986), we
demand that an ETG has a bulge-to-disk ratio in theB-band
of LB,bulge/LB,total ≥ 0.4. In addition, we require the B−V
color of the galaxy to be red. Following Hao et al. (2006) and
P07, we adopt B − V > 0.8. We have verified that none of
our results are sensitive to the exact choice of these selection
criteria.
Having thus identified all ETGs at z = 0, we subse-
quently trace their formation histories back until their last
major merger, and register the mass ratio n of the merger
event, as well as the total cold gas mass fraction at that
epoch, defined as
Fcold ≡
Mcold,i
(Mcold,i +M∗,i)
Here Mcold,i and M∗,i are the cold gas mass and stellar mass
of progenitor i, respectively. We adopt the hypothesis that
the merger results in a boxy elliptical if, and only if, n < ncrit
and Fcold < Fcrit. The main aim of this paper is to use the
data of P07 to constrain the values of ncrit and Fcrit, and to
investigate whether a model can be found that is consistent
with the observed fraction of boxy (disky) ETGs as function
of both galaxy luminosity and halo mass.
The final ingredient for determining whether an ETG
is disky or boxy is the potential regrowth of a stellar disk.
Between its last major merger and the present day, new gas
in the halo of the remnant may cool out to form a new disk.
In addition, the ETG may also accrete new stars and cold
gas via minor mergers (those with n > 3). Any cold gas in
those accreted systems is added to the new disk, where it
is allowed to form new stars. Whenever the stellar disk has
grown sufficiently massive, its presence will reveal itself in
the isophotes, and the system changes from being boxy to
being disky. To take this effect into account, we follow KB05
and we reclassify a boxy system as disky if at z = 0 it has
grown a disk with a stellar mass that contributes more than
a fraction fd,max of the total stellar mass in the galaxy. In
our fiducial model we set fd,max = 0.2. This is motivated by
Rix & White (1990), who have shown that if an embedded
stellar disk contains more than ∼ 20 percent of the total
stellar mass, the isophotes of its host galaxy become disky.
Note that the same value for fd,max has also been used in
the analysis of KB05.
3 RESULTS
In Figure 1 we show the fraction of boxy ETGs, fboxy, as a
function of the luminosity in the B-band (in the AB system).
Open squares with errorbars (reflecting Poisson statistics)
correspond to the data of P07, while the various lines indi-
cate the results obtained from three different models that
we describe in detail below. The (Poisson) errors on these
model predictions are comparable to those on the P07 data
and are not shown for clarity. Each column and row show,
c© 2000 RAS, MNRAS 000, 1–13
4 Kang et al.
Figure 1. The boxy fraction of ETGs as function of their B-band magnitude (in the AB system). The open, red squares with (Poissonian)
errorbars correspond to the data of P07, and are duplicated in each panel. The solid, dotted and dashed lines correspond to the three
models discussed in the text. Different columns and rows correspond to different values for the critical progenitor mass ratio, ncrit, and
the critical cold gas mass fraction, Fcrit, respectively, as indicated.
respectively, the results for different values of ncrit and Fcrit
as indicated.
We start our investigation by setting fd,max = 1, which
implies that the isophotal shape of an elliptical galaxy (disky
or boxy) is assumed to be independent of the amount of mass
accreted since the last major merger. Although we don’t con-
sider this realistic, it is a useful starting point for our investi-
gation, as it clearly separates the effects of ncrit and Fcrit on
the boxy fraction. The results thus obtained from our semi-
analytical model with AGN feedback are shown in Figure 1
as dotted lines. If we assign the isophotal shapes of ETGs
depending only on the progenitor mass ratio n, which cor-
responds to setting Fcrit = 1, we obtain the boxy fractions
shown in the upper panels. In agreement with KB05 (see
their Figure 1) this results in a boxy fraction that is virtually
independent of luminosity, in clear disagreement with the
data. Note that, for a given value of ncrit, our boxy fractions
are significantly higher than in the model of KB05. For ex-
ample, for ncrit = 2 we obtain a boxy fraction of ∼ 0.6, while
KB05 find that fboxy ∼ 0.33. This mainly reflects the differ-
ence in the type of merger trees used. As discussed above, we
use the merger trees extracted from a N-body simulation,
while KB05 use monte-carlo merger trees based on the EPS
formalism. It is well known that EPS merger trees predict
masses for the most massive progenitors that are too large
(e.g., Lacey & Cole 1994; Somerville et al. 2000; van den
Bosch 2002; Benson, Kamionkowski & Hassani 2005). This
implies that the number of mergers with a small progenitor
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 5
Figure 2. The fractions of last major mergers between centrals and satellites (C-S; solid lines) and between two satellites (S-S; dashed
lines) that result in the formation of an ETG as function of its stellar mass at z = 0. Results are shown for all ETGs (left-hand panel) and
for those with Fcold < 0.1 (right-hand panel). Black and red lines correspond to models with and without AGN feedback, respectively.
Low mass ETGs that form in dry mergers, and hence end up being boxy, mainly form out of S-S mergers. At the massive end, the
fraction of ETGs that form out of S-S mergers with Fcold = 0.1 depends strongly on the presence or absence of AGN feedback. See text
for detailed discussion.
mass ratio n will be too small, which explains the difference
between our results and those of KB05. Using cosmological
SPH simulations, Maller et al. (2006) found that the distri-
bution of merger mass ratios scales as dN/dn ∝ n−0.8. This
means that 60 percent of all galaxy mergers with n < 3 have
a progenitor mass ratio n < 2, in excellent agreement with
our results.
The dotted lines in the remaining panels of Figure 1
show the results obtained for three different values of the
maximum cold gas mass fraction, Fcrit = 0.6, 0.3, and 0.1.
Lowering Fcrit has a strong impact on the boxy fraction
of low-luminosity ETGs, while leaving that of bright ETGs
largely unaffected. As we show in §4 this mainly owes to the
fact that Fcold decreases strongly with increasing luminosity.
Consequently, by changing Fcrit we can tune the slope of
the relation between fboxy and luminosity, while ncrit mainly
governs the absolute normalization. We obtain a good match
to the P07 data for ncrit = 2 and Fcrit = 0.1 (third panel in
lowest row). This implies that boxy ETGs only form out of
relatively dry and violent mergers, in good agreement with
numerical simulations.
3.1 The influence of disk regrowth
The analysis above, however, does not consider the impact
of the growth of a new disk around the merger remnant.
Since this may turn boxy systems into disky systems, it can
have a significant impact on the predicted fboxy. We now
take this effect into account by setting fd,max to its fiducial
value of 0.2.
The solid lines in Fig. 1 show the boxy fractions thus
obtained. A comparison with the dotted lines shows that the
newly formed disks only cause a significant decrease of fboxy
at the faint end. At the bright end, AGN feedback prevents
the cooling of hot gas, therewith significantly reducing the
rate at which a new disk can regrow†. However, when Fcrit =
0.1, we obtain the same boxy fractions for fd,max = 0.2 as
for fd,max = 1, even at the faint end. This implies that we
obtain the same conclusions as above: matching the data
of P07 requires ncrit ≃ 2 and Fcrit ≃ 0.1. In other words,
our constraints on ncrit and Fcrit are robust to exactly how
much disk regrowth is allowed before it reveals itself in the
isophotes.
Why do faint ETGs with Fcold < 0.1 not regrow signifi-
cant disks, while does with Fcold > 0.1 do? Note that during
the last major merger, the entire cold gas mass is converted
into stars in a starburst. Therefore, it is somewhat puzzling
that the galaxy’s ability to regrow a disk depends on its cold
gas mass fraction at the last major merger. As it turns out,
this owes to the fact that progenitors with a low cold gas
mass fraction are more likely to be satellite galaxies. Fig. 2
plots the fractions of ETGs with last major mergers be-
tween a central galaxy and a satellite (C-S; solid lines) and
between two satellites (S-S; dashed lines). Note that in our
model, S-S mergers occur whenever their dark matter sub-
haloes in the N-body simulation merge. Results are shown
for all ETGs (left-hand panel), and for only those ETGs
that have Fcold < 0.1 (right-hand panel). In our fiducial
model with AGN feedback (black lines) the most massive
ETGs almost exclusively form out of C-S mergers. Since a
satellite galaxy can never become a central galaxy, this is
† In the absence of cooling, the only way in which a galaxy can
(re)grow a disk is via minor mergers.
c© 2000 RAS, MNRAS 000, 1–13
6 Kang et al.
Figure 3. The progenitor mass ratio, n, (left-hand panel) and the cold gas mass fraction at the last major merger, Fcold, (right-hand
panel) as function of the z = 0 stellar mass, M∗, of ETGs. Solid lines with errorbars indicate the median and the 20
th and 80th percentiles
of the distributions. While the mass ratio of the progenitors of early-type galaxies is independent of its stellar mass, Fcold decreases
strongly with increasing M∗.
consistent with the fact that virtually all massive ETGs at
z = 0 are central galaxies (in massive haloes). Roughly 40
percent of all low mass ETGs have a last major merger be-
tween two satellite galaxies. However, when we only focus on
low mass ETGs with Fcold < 0.1, we find that ∼ 95 percent
of their last major mergers are between two satellite galax-
ies. Since the z = 0 descendents of S-S mergers will also
be satellites, this implies that virtually all boxy ETGs with
M∗ <∼ 2 × 10
10h−1 M⊙ are satellite galaxies. Furthermore,
since satellite galaxies do not have a hot gas reservoir (at
least not in our semi-analytical model) they can not regrow
a new disk by cooling. This explains why for Fcrit = 0.1 the
boxy fractions are independent of the value of fd,max.
3.2 The role of AGN feedback
Our semi-analytical model includes “radio-mode” AGN
feedback, similar to that in Croton et al. (2006), in order to
suppresses the cooling in massive haloes. This in turn shuts
down star formation in the central galaxies in these haloes,
so that they become red. In the absence of AGN feedback,
new gas continues to cool making the central galaxies in
massive haloes overly massive and too blue (e.g., Benson
et al. 2003; Bower et al. 2006; Croton et al. 2006; Kang et
al. 2006). In order to study its impact on fboxy as func-
tion of luminosity, we simply turn off AGN feedback in our
model. Although this results in a semi-analytical model that
no longer fits the galaxy luminosity function at the bright
end, and results in a color-magnitude relation with far too
many bright, blue galaxies, a comparison with the models
discussed above nicely isolates the effects that are directly
due to our prescription for AGN feedback.
The dashed lines in Figure 1 show the predictions of
our model without AGN feedback (and with fd,max = 0.2).
A comparison with our fiducial model (solid lines) shows
that apparently the AGN feedback has no impact on fboxy
for faint ETGs with MB −5 log h >∼ −18. At the bright end,
though, the model without AGN feedback predicts boxy
fractions that are significantly lower (for reasons that will
be discussed in §4.2). Consequently, the luminosity depen-
dence of fboxy is much weaker than in the fiducial case. The
only model that comes close to matching the data of P07
is the one with ncrit = 3 and Fcrit = 0.1. We emphasize,
though, that this model is not realistic. In addition to the
fact that this semi-analytical model does not fit the observed
luminosity function and color magnitude relation, a value of
ncrit = 3 is also very unlikely: numerical simulations have
clearly shown that mergers with a mass ratio near 1:3 almost
invariably result in disky remnants (e.g., Naab & Burkert
2003).
4 DISCUSSION
4.1 The Origin of the ETG Dichotomy
We now examine the physical causes for the various scal-
ings noted above. We start by investigating why our fiducial
model with ncrit = 2 and Fcrit = 0.1 is successful in repro-
ducing the luminosity dependence of fboxy, i.e., why it pre-
dicts that the boxy fraction increases with luminosity. Given
the method used to assign isophotal shapes to the ETGs in
our model, there are three possibilities: (i) brighter ETGs
have smaller progenitor mass ratios, (ii) brighter ETGs have
progenitors with smaller cold gas mass fractions, or (iii)
brighter ETGs have less disk regrowth after their last major
merger.
We can exclude (i) from the fact that the models that
ignore disk regrowth (i.e., with fd,max = 1) and that ignore
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 7
Figure 4. Contour plots for the number density of ETGs as function of their present day stellar mass, M∗, and their cold gas mass
fraction at the last major merger, Fcold. Results are shown both for our fiducial model with AGN feedback (left-hand panel), as well as
for the model without AGN feedback (right-hand panel). In both cases a clear bimodality is apparent: ETGs with large and low masses
formed out of dry and wet mergers, respectively. Note that this bimodality is present independent of the presence of AGN feedback.
the cold gas mass fractions (i.e., with Fcrit = 1) predict
that the boxy fraction is roughly independent of luminosity
(dotted lines in upper panels of Fig. 1). This suggests that
the distribution of n is roughly independent of the (present
day) luminosity of the ETGs. This is demonstrated in the
left-hand panel of Fig. 3, were we plot n as function of,
M∗, the stellar mass at z = 0. Each dot corresponds to an
ETG in our fiducial model, while the solid black line with
the errorbars indicates the median and the 20th and 80th
percentiles of the distribution: clearly the progenitor mass
ratio is independent of M∗.
The boxy fraction of our best-fit model with ncrit = 2
and Fcrit = 0.1 is also independent of the regrowth of
disks, which is evident from the fact that the models with
fd,max = 1 (dotted lines) and fd,max = 0.2 (solid lines) pre-
dict boxy fractions that are indistinguishable. Therefore op-
tion (iii) can also be excluded, and the luminosity depen-
dence of fboxy thus has to indicate that the progenitors of
more luminous ETGs have a lower gas mass fraction. That
this is indeed the case can be seen from the right-hand panel
of Fig. 3 which shows Fcold as function of M∗. Once again,
the solid black line with the errorbars indicates the median
and the 20th and 80th percentiles of the distribution. Note
that Fcold decreases strongly with increasing stellar mass;
the most massive ETGs form almost exclusively from dry
mergers with Fcold < 0.1.
The left-hand panel of Fig. 4 shows a different rendi-
tion of the relation between Fcold and M∗. Contours indicate
the number density, φ(Fcold,M∗), of ETGs in the Fcold-M∗
plane, normalized by the total number of ETGs at each given
M∗-bin, i.e.,
φ(Fcold,M∗) dFcold = 1 (2)
Note that φ(Fcold,M∗) is clearly bimodal: low mass ETGs
with M∗ <∼ 3 × 10
9h−1 M⊙ have high Fcold, while the pro-
genitors of massive ETGs have low cold gas mass fractions.
Clearly, if wet and dry mergers produce disky and boxy el-
lipticals, respectively, this bimodality is directly responsible
for the ETG dichotomy.
What is the physical origin of this bimodality? It is
tempting to expect that it owes to AGN feedback. After all,
in our model AGN feedback is more efficient in more massive
galaxies. Since more massive ETGs have more massive pro-
genitors, one could imagine that their cold gas mass fractions
are lower because of the AGN feedback. However, the right-
hand panel of Fig. 4 shows that this is not the case. Here
we show φ(Fcold,M∗) for the model without AGN feedback.
Somewhat surprisingly, this model predicts almost exactly
the same bimodality as the model with AGN feedback. Their
are subtle differences, which have a non-negligible effect on
the boxy fractions and which will be discussed in §4.2 be-
low. However, it should be clear from Fig. 4 that the overall
bimodality in φ(Fcold,M∗) is not due to AGN feedback.
In order to explore alternative explanations for the bi-
modality, Fig. 5 shows some relevant statistics. Upper and
lower panels correspond to the models with and without
AGN feedback, respectively. Here we focus on our fiducial
model with AGN feedback; the results for the model without
AGN feedback will be discussed in §4.2. The upper left-hand
panel shows the average cold gas mass fraction of individ-
ual galaxies, 〈fcold〉, as function of lookback time. Note that
here we use fcold to distinguish it from Fcold, which indi-
cates the cold gas mass fraction of the combined progeni-
tors taking part in a major merger, as defined in eq. (1).
Results are shown for galaxies of two different (instanta-
neous) stellar masses, M∗ = 3× 109h−1 M⊙ (red lines) and
M∗ = 3× 1010h−1 M⊙ (black lines), and for two (instanta-
neous) types: early-types (dotted lines) and late-types (solid
lines). Following N06, here we define early-types as systems
with a bulge-to-total stellar mass ratio of 0.6 or larger; con-
trary to our z = 0 selection criteria described in §2.1, we do
not include a color selection, simply because the overall color
of the galaxy population evolves as function of time. First
of all, note that 〈fcold〉 of galaxies of given type and given
mass decreases with increasing time (i.e., with decreasing
lookback time). This is simply due to the consumption by
star formation. Secondly, at a given time, early-type galax-
ies have lower gas mass fractions than late-type galaxies.
This mainly owes to the fact that at a major merger, which
creates an early-type, all the available cold gas is consumed
in a starburst. Consequently, each early-type starts its life
c© 2000 RAS, MNRAS 000, 1–13
8 Kang et al.
Figure 5. Various statistics of our semi-analytical models. Upper and lower panels refer to our models with and without AGN feedback,
respectively. Left-hand panels: The average cold gas mass fraction of individual galaxies as function of lookback time t. Results are shown
for galaxies of two different (instantaneous) stellar masses, M∗ = 3 × 10
9h−1 M⊙ (red lines) and M∗ = 3 × 10
10h−1 M⊙ (black lines),
and for two (instantaneous) types: early-types (dotted lines) and late-types (solid lines). Middle panels: The fractions of late-late (L-L;
solid lines) , early-late (E-L; dotted lines) and early-early (E-E; dashes lines) type mergers as function of the z = 0 stellar mass of the
resulting ETG. Right-hand panels: The average lookback time to the last major merger of z = 0 ETGs as function of their z = 0 stellar
mass. Results are shown separately for L-L mergers (solid line), E-L mergers (dotted line), and E-E mergers (dashed line). The errorbars
indicate the 20th and 80th percentiles of the distribution of the E-L mergers. For clarity, we do not show these percentiles for the L-L
and E-E mergers, though they are very similar. See text for detailed discussion.
with fcold = 0. Finally, massive galaxies have lower gas
mass fractions than their less massive counterparts. This
owes to the fact that more massive galaxies live, on average,
in more massive haloes, which tend to form (not assem-
ble!) earlier thus allowing star formation to commence at
an earlier epoch (see Neistein et al. 2006). In addition, the
star formation efficiency used in the semi-analytical model
is proportional to the mass of the cold gas times M0.73vir . As
discussed in K05, this scaling with the halo virial mass is re-
quired in order to match the observed 〈fcold〉(M∗) at z = 0
(see also Cole et al. 1994, 2000; De Lucia et al. 2004).
The middle panel in the upper row of Fig. 5 shows what
kind of galaxy types are involved in the last major mergers
of present-day ETGs. Solid, dotted and dashed curves show
the fractions of L-L, E-L and E-E mergers, where ‘L’ and ‘E’
refer to late-types and early-types, respectively. As above,
these types are based solely on the bulge-to-total mass ratio
of the galaxy and not on its color. In our semi-analytical
model, the lowest mass ETGs almost exclusively form via
L-L mergers. With increasing M∗, however, there is a pro-
nounced decrease of the fraction of L-L mergers, which are
mainly replaced by E-L mergers. The fraction of E-E merg-
ers increases very weakly with increasing stellar mass but
never exceeds 10 percent. Thus, although boxy ellipticals
form out of dry mergers, these are not necessarily mergers
between early-type galaxies. In fact, our model predicts that
the vast majority of all dry mergers involve at least one late-
type galaxy (though with a low cold gas mass fraction). This
is in good agreement with the SPH simulation of Maller et
al. (2006), who also find that E-E mergers are fairly rare.
However, it is in stark contrast to the predictions of the
semi-analytical model of N06, how find that more than 50
percent of the last major mergers of massive ellipticals are E-
E mergers. We suspect that the main reason for this strong
discrepancy is the fact that N06 used merger trees based on
the EPS formalism.
Finally, the upper right-hand panel of Fig. 5 plots the
average lookback time to the last major merger of ETGs as
function of their present day stellar mass. Results are shown
separately for L-L mergers (solid line), E-L mergers (dotted
line), and E-E mergers (dashed line). Clearly, more massive
ETGs assemble later (at lower lookback times). This mainly
owes to the fact that more massive galaxies live in more
massive haloes, which themselves assemble later (cf. Lacey
& Cole 1993; Wechsler et al. 2002; van den Bosch 2002;
Neistein et al. 2006; De Lucia et al. 2006). In addition, it is
clear that at fixed stellar mass, E-E mergers occur later than
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 9
L-L mergers, with E-L mergers in between. This difference,
however, is small compared to the scatter.
If we combine all this information, we infer that the
bimodality in φ(Fcold,M∗) owes to the following three facts:
• More massive ETGs have more massive progenitors
(this follows from the fact that n is independent of M∗).
Since at a given time more massive galaxies of a given type
have lower cold gas mass fractions, 〈Fcold〉 decreases with
increasing M∗.
• More massive ETGs assemble later (at lower redshifts).
Galaxies of given mass and given type have lower 〈fcold〉 at
later times. Consequently, 〈Fcold〉 decreases with increasing
• More massive ETGs have a larger fraction of early-type
progenitors. ETGs of a given mass have a lower cold gas
mass fraction than late type galaxies of the same mass, at
any redshift. In addition, E-L mergers occur at later times
than L-L mergers. Both these effects also contribute to the
fact that 〈Fcold〉 decreases with increasing M∗.
4.2 Is AGN feedback relevant?
A comparison of the upper and lower panels in Fig. 5
shows that the three effects mentioned above, and thus
the bimodality in φ(Fcold,M∗), are present independent of
whether or not the model includes feedback from active
galactic nuclei. There are only two small differences: with-
out AGN feedback massive ETGs (i) are more likely to result
from L-L mergers, and (ii) have a higher 〈fcold〉 (cf. black
dotted curves in the left-hand panels of Fig. 5). Both ef-
fects reflect that AGN feedback prevents the cooling of hot
gas around massive galaxies, therewith removing an impor-
tant channel for building a new disk. As is evident from
Fig. 4, these two effects only have a very mild impact on
φ(Fcold,M∗). We therefore conclude that the bimodality of
ETGs is not due to AGN feedback.
This does not imply, however, that AGN feedback does
not have an impact on the boxy fractions. As is evident from
Fig. 1, the models with and without AGN feedback clearly
predict different fboxy at the bright end. To understand the
origin of these differences, first focus on Fig. 4. Although
both panels look very similar, upon closer examination one
can notice that at M∗ >∼ 10
11h−1 M⊙ the number density of
ETGs with 0.1 <∼ Fcold <∼ 0.25 is significantly larger in the
model without AGN feedback. In the model with AGN feed-
back these systems all have Fcold < 0.1. This explains why
the model without AGN feedback predicts a lower boxy frac-
tion for bright galaxies when Fcrit = 0.1. However, this does
not explain why fboxy is also different when Fcrit ≥ 0.3.
After all, for those models it should not matter whether
Fcold = 0.05 or Fcold = 0.25, for example. It turns out that
in these cases the differences between the models with and
without AGN feedback are due to the regrowth of a new
disk; since AGN feedback suppresses the cooling of hot gas
around massive galaxies, it strongly suppresses the regrowth
of a new disk, thus resulting in higher boxy fractions.
Note however, that in ETGs with Fcold < 0.1, disk re-
growth is always negligible. In the presence of AGN feedback
this is due to the suppression of cooling in massive haloes.
In the absence of AGN feedback it owes to the fact that only
a very small fraction of ETGs are central galaxies. As can
Figure 6. The boxy fraction of ETGs as function of halo (group)
mass. Red triangles (for satellite galaxies) and blue circles (for
central galaxies) are taken from P07, and have been obtained us-
ing the galaxy group catalogue of Weinmann et al. (2006). Dashed
and solid lines correspond to the predictions from our fiducial
model.
be seen from the right-hand panel of Fig. 2, more than 90
percent of the ETGs have last major mergers between two
satellite galaxies (with AGN feedback this fraction is smaller
than 20 percent). Since satellite galaxies do not have hot gas
reservoirs, no significant disks can regrow around these sys-
tems.
4.3 Environment dependence
Using the SDSS galaxy group catalogue of Weinmann et
al. (2006), which has been constructed using the halo-based
group finder developed by Yang et al. (2005), P07 inves-
tigated how fboxy scales with group mass. They also split
their sample in ‘central’ galaxies (defined as the brightest
group members) and ‘satellites’. The open circles and trian-
gles in Fig. 6 show their results for centrals and satellites,
respectively. Although there are only two data points for the
satellites, it is clear that central galaxies are more likely to
be boxy than a satellite galaxy in a group (halo) of the same
mass.
We now investigate whether our fiducial semi-analytic
model that fits the luminosity dependence of the boxy frac-
tion (i.e., the one with ncrit = 2 and Fcrit = 0.1) can also
reproduce these trends. The model predictions for the cen-
trals and satellites are shown in Fig. 6 as solid and dashed
lines, respectively. Here we have associated the halo virial
mass with the group mass, and an ETG is said to be a cen-
tral galaxy if it is the brightest galaxy in its halo. The model
accurately reproduces the boxy fraction of both central and
satellite galaxies. In particular, it reproduces the fact that
fboxy of central galaxies is higher than that of satellites in
groups (haloes) of the same mass.
As shown in P07, the boxy fraction as function of group
c© 2000 RAS, MNRAS 000, 1–13
10 Kang et al.
Figure 7. The residuals of the relations between n and M∗ (left panel) and Fcold and M∗ (right panel) as functions of the virial mass of
the halo in which the ETGs reside at z = 0. As in Fig. 3 the solid lines with errorbars indicate the mean and the 20th and 80th percentiles
of the distributions. These show that after one corrects for the stellar mass dependence, the properties of the last major mergers of ETGs
are independent of their halo mass.
mass, for both centrals and satellites, is perfectly consistent
with the null-hypothesis that the isophotal shape of an ETG
depends only on its luminosity; the fact that centrals have a
higher boxy fraction than satellites in the same group, sim-
ply owes to the fact that the centrals are brighter. Also, the
increase of fboxy with increasing group mass simply reflects
that more massive haloes host brighter galaxies. It there-
fore may not come as a surprise that our semi-analytical
model that fits the luminosity dependence of fboxy also fits
the group mass dependencies shown in Fig. 6. It does mean,
though, that in our model the merger histories of ETGs of
a given luminosity do not strongly depend on the halo mass
in which the galaxy resides.
To test this we proceed as follows. For each ETG in
our model we compute 〈n〉 and 〈Fcold〉, where the average
is over all ETGs with stellar masses similar to that of the
galaxy in question. Fig. 7 plots the residuals n − 〈n〉 and
Fcold − 〈Fcold〉 as function of the virial mass, Mvir, of the
halo in which they reside. This clearly shows that after one
corrects for the stellar mass dependence, the properties of
the last major merger of ETGs are indeed independent of
their halo mass‡. This provides theoretical support for the
conclusion of P07 that the stellar mass (or luminosity) of an
ETG is the main parameter that determines whether it will
be disky or boxy.
4.4 The Origin of Cusps and Cores
As discussed in §1, the dichotomy of ETGs is not only re-
stricted to their isophotal shapes. One other important as-
pect of the dichotomy regards the central density distribu-
‡ The fact that the distribution of the progenitor mass ratio n is
independent of halo mass was also found by KB05
tion of ETGs; while disky systems typically have cuspy pro-
files, the bright and boxy ellipticals generally reveal density
profiles with a pronounced core. Here we briefly discuss how
the formation of cusps and cores fits in the picture sketched
above.
In the paradigm adopted here, low luminosity ETGs
form mainly via wet mergers. Due to the fluctuating poten-
tial of the merging galaxies and the onset of bar instabilities,
the gas experiences strong torques which causes a significant
fraction of the gas to sink towards the center of the po-
tential well where it undergoes a starburst (e.g., Shlosman,
Frank & Begelman 1989; Barnes & Hernquist 1991; Mihos
& Hernquist 1996). Detailed hydrodynamical simulations of
gas-rich mergers (e.g., Springel & Hernquist 2005; Cox et
al. 2006b) result in the formation of remnants with surface
brightness profiles that are reminiscent of cuspy ETGs (John
Kormendy, private communication). Hence, cusps seem a
natural by-product of the dissipative processes associated
with a wet merger.
Boxy ETGs, however, are thought to form via dry merg-
ers. As can be seen from Fig. 5 roughly 35 percent of all mas-
sive ETGs originate from a last major merger that involves
an early-type progenitor. If this progenitor contains a cusp,
this will survive the merger, as most clearly demonstrated by
Dehnen (2005). The only mergers that are believed to result
directly in a remnant with a core, are mergers between pure
stellar disks with a negligible fcold (e.g., Cox et al. 2006a).
Fig. 8 shows the cumulative distributions of the bulge-to-
total stellar mass ratios of the progenitors of present day
ETGs. Results are shown for ETGs in three mass ranges,
as indicated. The probability that a progenitor of a massive
ETGs (with M∗ > 10
11h−1 M⊙) has a negligible bulge com-
ponent (M∗,bulge < 0.01M∗) is only about 3 percent. Hence,
we expect that only about 1 out of every 1000 major merg-
ers that result in a massive ETG will have a remnant with
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 11
a core. And this is most likely an overestimate, since we
did not take the cold gas mass fractions into consideration.
Since the cusp accounts for only about one percent of the
total stellar mass (e.g., Faber et al. 1997; Milosavljević et
al. 2002), cold gas mass fractions of a few percent are prob-
ably enough to create a cusp via dissipational processes.
Therefore, an additional mechanism is required in order
to create a core (i.e., destroy a cusp). Arguably the most
promising mechanism is the orbital decay of a supermas-
sive black hole (SMBH) binary, which can scour a core by
exchanging angular momentum with the cusp stars (e.g.,
Begelman et al. 1980; Ebisuzaki et al. 1991; Quinlan 1996;
Faber et al. 1997; Milosavljević et al. 2002; Merritt 2006a).
Since virtually all spheroids contain a SMBH at their cen-
ter, with a mass that is tightly correlated with the mass of
the spheroid (e.g., Kormendy & Richstone 1995; Ferrarese &
Merritt 2000; Gebhardt et al. 2000; Marconi & Hunt 2003;
Häring & Rix 2004), it is generally expected that such bina-
ries are common in merger remnants (but see below).
While offering an attractive explanation for the pres-
ence of cores in massive, boxy ETGs, this picture simulta-
neously poses a potential problem for the presence of cusps
in disky ETGs. After all, if the progenitors of disky ETGs
also harbor SMBHs, the same process could create a core
in these systems as well. There are two possible ways out
of this paradox: (i) low mass ETGs do not form a SMBH
binary, or (ii) a cusp is regenerated after the two SMBHs
have coalesced. We now discuss these two options in turn.
In order for a SMBH binary to form, dynamical friction
must first deliver the two SMBHs from the two progenitors
to the center of the newly formed merger remnant. This
process will only be efficient if the spheroidal hosts of the
SMBHs are sufficiently massive. Consider a (small) bulge
that was part of a late-type progenitor which is now orbiting
the remnant of its merger with another galaxy. Assume for
simplicity that both the bulge and the merger remnant are
purely stellar singular isothermal spheres (ρ ∝ r−2) with
velocity dispersions equal to σb and σg, respectively. Then,
assuming that the bulge is on a circular orbit, with an initial
radius ri, Chandrasekhar’s (1943) formula gives an infall
time for the bulge of
tinfall ≈ 3.3
≈ 4.7× 108 yr
(Merritt 2006b). Here we have used that ri/σg ≃
2 tcross
with tcross ∼ 108 yr the galaxy crossing time. If the galaxy
is the remnant of an equal mass merger, so that Mb ∼
(∆/2)Mg , with ∆ the bulge-to-total stellar mass ratio of
the late-type progenitor, we find that tinfall is equal to the
Hubble time (1.3 × 1010 yr) for ∆ ≃ 0.07. As can be seen
from Fig. 8, about 70 percent of the low mass ETGs (with
109h−1M⊙ < M∗ < 10
10h−1M⊙) have at least one progeni-
tor with a stellar bulge-to-total mass ratio ∆ < 0.07. There-
fore, we expect that a similar fraction will form without a
SMBH binary, and thus will not form a core. For compari-
son, for massive ETGs (with M∗ > 10
11h−1M⊙) only about
20 percent of the progenitors will have a sufficiently small
bulge to prevent the formation of a SMBH binary.
An alternative explanation for the presence of cusps in
low mass ETGs is that the cusp is regenerated by star for-
mation from gas present at the last major merger. However,
as emphasized by Faber et al. (1997), this results in a serious
Figure 8. The cumulative probability that a progenitor of a
z = 0 ETG has a stellar bulge-to-total mass ratio less then
M∗,bulge/M∗. Results are shown for the progenitors of ETGs in
three stellar mass ranges, as indicated (masses are in h−1 M⊙).
Note that the progenitors of more massive ETGs have signifi-
cantly higher M∗,bulge/M∗. As discussed in the text, this may
help to explain why low mass ETGs have cusps, while massive
ones have cores.
timing problem, as it requires that the new stars must form
after the SMBH binary has coalesced. Another potential
problem with this picture, is that the cusp would be younger
than the main body of the ETG which may lead to observ-
able effects (i.e., cusp could be bluer than main body). How-
ever, in light of the results presented here, we believe that
neither of these two issues causes a serious problem. First of
all, the cold gas mass fractions involved with the last major
merger, and hence the mass fraction that is turned into stars
in the resulting starburst, is extremely large: 〈Fcold〉 ∼ 0.8
(see Fig. 4). As mentioned above, a significant fraction of
this gas is transported to the center, where it will function
as an important energy sink for the SMBH binary, greatly
speeding up its coalescence (Escala et al. 2004, 2005) and
therewith reducing the timing problem mentioned above. In
fact, the gas may well be the dominant energy sink, so that
the pre-existing cusps of the progenitors are only mildly af-
fected. But even if the cusps were destroyed, there clearly
should be enough gas left to build a new cusp. In fact, if,
as envisioned in our semi-analytical model, all the cold gas
present at the last major merger is consumed in a starburst,
a very significant fraction of the stars in the main body
would also be formed in this starburst (not only the cusp).
This would help to diminish potential population differences
between the cusp and the main body of the ETG. In addi-
tion, as can be seen from the right-hand panels of Fig. 5,
the last major merger of low luminosity ETGs occurred on
average ∼ 9.5 Gyr ago. Hence, the stars made in this burst
are not easily distinguished observationally from the ones
that were already present before the last major merger.
To summarize, our semi-analytical model predicts that
c© 2000 RAS, MNRAS 000, 1–13
12 Kang et al.
the progenitors of ETGs have cold gas mass fractions and
bulge-to-total mass ratios that offer a relatively natural ex-
planation for the observed dichotomy between cusps and
cores.
5 CONCLUSIONS
Using a semi-analytical model for galaxy formation, com-
bined with a large N-body simulation, we have investigated
the origin of the dichotomy among ETGs. In order to assign
isophotal shapes to the ETGs in our model we use three cri-
teria: an ETG is said to be boxy if (i) the progenitor mass
ratio at the last major merger is n < ncrit, (ii) the total
cold gas mass fraction of the sum of the two progenitors
at the last major merger is Fcold < Fcrit, and (iii) after its
last major merger the ETG is not allowed to regrow a new
disk with a stellar mass that exceeds 20 percent of the total
stellar mass.
In agreement with KB05, we find that we can not repro-
duce the observed luminosity (or, equivalently, stellar mass)
dependence of fboxy if we assign isophotal shapes based only
on the progenitor mass ratio. This owes to the fact that
the distribution of n is virtually independent of the stellar
mass, M∗, of the ETG at z = 0. Rather, to obtain a boxy
fraction that increases with increasing luminosity one also
needs to consider the cold gas mass fraction at the last ma-
jor merger. In fact, we can accurately match the data of P07
with ncrit = 2 and Fcrit = 0.1. This implies that boxy galax-
ies originate from relatively violent and dry mergers with
roughly equal mass progenitors and with less than 10 per-
cent cold gas, in good agreement with numerical simulations
(e.g., Naab et al. 2006a; Cox et al. 2006a). Our model also
nicely reproduces the observed boxy fraction as function of
halo mass, for both central galaxies and satellites. We have
demonstrated that this owes to the fact that after one cor-
rects for the stellar mass dependence, the properties of the
last major merger of ETGs are independent of their halo
mass. This provides theoretical support for the conjecture
of P07 that the stellar mass (or luminosity) of an ETG is
the main parameter that determines whether it will be disky
or boxy.
Our model predicts a number density distribution,
φ(Fcold,M∗), of ETGs in the Fcold-M∗ plane that is clearly
bimodal: low mass ETGs with M∗ <∼ 3 × 10
9h−1 M⊙ have
high Fcold, while the progenitors of massive ETGs have low
cold gas mass fractions. Clearly, if wet and dry mergers pro-
duce disky and boxy ellipticals, respectively, this bimodal-
ity is directly responsible for the ETG dichotomy. Contrary
to naive expectations, we find that this bimodality is in-
dependent of the inclusion of AGN feedback in the model.
Although AGN feedback is essential for regulating the lumi-
nosities and colors of the brightest galaxies (which end up
as ETGs with AGN feedback, but as blue disk-dominated
systems without AGN feedback), it does not explain the
bimodality among ETGs. Rather, this bimodality is due to
the fact that more massive ETGs (i) have more massive pro-
genitors, (ii) assemble later, and (iii) have a larger fraction
of early-type progenitors. Each of these three trends causes
the cold gas mass fraction of the progenitors of more mas-
sive ETGs to be lower, and thus its last major merger to
be dryer. In conclusion, the dichotomy among ETGs has a
very natural explanation within the hierarchical framework
of structure formation and does not require AGN feedback.
We also examined the morphological properties of the
progenitors of present day ETGs (at the epoch of the last
major merger). Indicating early- and late-type galaxies with
‘E’ and ‘L’, respectively, we find that the lowest mass ETGs
almost exclusively form via L-L mergers. With increasing
M∗, however, there is a pronounced decrease of the fraction
of L-L mergers, which are mainly replaced by E-L mergers.
The E-E mergers, however, never contribute more than 10
percent, in good agreement with the SPH simulations of
Maller et al. (2006). Thus, although boxy ellipticals form
out of dry mergers, these only rarely involve two early-type
systems.
Since satellite galaxies do not have a hot corona from
which new gas cools down, they typically have lower cold gas
mass fractions than central galaxies of the same mass. Con-
sequently, dry mergers are preferentially mergers between
two satellite galaxies. In fact, since a satellite galaxy can
not become a central galaxy, our model predicts that more
than 95 percent of all boxy ETGs with M∗ <∼ 2×10
10h−1M⊙
are satellites.
We also find that the progenitors of less massive ETGs
typically have lower bulge-to-total mass ratios. In fact,
for ETGs with present day stellar masses in the range
109h−1 M⊙ < M∗ < 10
10h−1 M⊙ we find that almost half
of the progenitors at the last major merger have bulges
that do not contribute more than one percent to the to-
tal stellar mass. This may have important implications for
the observed dichotomy between cusps and cores in ETGs.
Cores are believed to form via the scouring effect of a SMBH
binary, that arises when the SMBHs associated with the
spheroidal components of the progenitor galaxies form a
bound pair. This requires both spheroids to sink to the cen-
ter of the potential well of the merger remnant via dynamical
friction. However, if the time scale for this infall exceeds the
Hubble time, no SMBH binary will form, thus preventing
the creation of a core. Using our prediction for the bulge-to-
total mass ratios of progenitor galaxies, and a simple esti-
mate based on Chandrasekhar’s dynamical friction formula,
we have estimated that ∼ 70 percent of low mass ETGs
in the aforementioned mass range will not form a SMBH
binary. For massive ETGs with M∗ > 10
11h−1M⊙ this frac-
tion is only ∼ 20 percent. This may help to explain why
low mass ETGs have steep cusps, while massive ETGs have
cores.
Finally, in those low mass systems that do form a SMBH
binary, the large cold gas mass fraction at its last major
merger (〈Fcold〉 ≃ 0.8) provides more than enough raw ma-
terial for the regeneration of a new cusp. In addition, a large
fraction of the cold gas will sink to the center due to angular
momentum transfer where it will function as an important
energy sink for the SMBH binary. As shown by Escala et
al. (2004, 2005), this can cause a tremendous acceleration of
the coalescence of the SMBHs, largely removing the timing
problem interjected by Faber et al. (1997).
6 ACKNOWLEDGEMENTS
We are grateful to Eric Bell, Eric Emsellem, John Kormendy,
Thorsten Naab, Hans-Walter Rix, and the entire Galaxies-
c© 2000 RAS, MNRAS 000, 1–13
On the Origin of the Dichotomy of Early-Type Galaxies 13
Cosmology-Theory group at the MPIA for enlightening dis-
cussions.
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