to be published in ApJ
The Formation of Globular Cluster Systems in Massive Elliptical
Galaxies: Globular Cluster Multimodality from Radial Variation
of Stellar Populations
Antonio Pipino1,3, Thomas H. Puzia2,4, & Francesca Matteucci3
ABSTRACT
The most massive elliptical galaxies show a prominent multi-modality in their
globular cluster system color distributions. Understanding the mechanisms which
lead to multiple globular cluster sub-populations is essential for a complete pic-
ture of massive galaxy formation. By assuming that globular cluster formation
traces the total star formation and taking into account the radial variations in
the composite stellar populations predicted by the Pipino & Matteucci (2004)
multi-zone photo-chemical evolution code, we compute the distribution of glob-
ular cluster properties as a function of galactocentric radius. We compare our
results to the spectroscopic measurements of globular clusters in nearby early-
type galaxies by Puzia et al. (2006) and show that the observed multi-modality
in globular cluster systems of massive ellipticals can be, at least partly, ascribed
to the radial variation in the mix of stellar populations. Our model predicts the
presence of a super-metal-rich population of globular clusters in the most massive
elliptical galaxies, which is in very good agreement with the spectroscopic obser-
vations. The size of this high-metallicity population scales with galaxy mass, in
the sense that more massive galaxies host larger such cluster populations. We
predict an increase of mean metallicity of the globular cluster systems with host
galaxy mass, and forecast that those clusters that were formed within the initial
1Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, U.K.
email: axp@astro.ox.ac.uk.
2Herzberg Institute of Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada, email:
puziat@nrc.ca.
3Dipartimento di Astronomia, Università di Trieste, Via G.B. Tiepolo 11, 34100 Trieste, Italy, email:
matteucci@ts.astro.it.
4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA.
http://arxiv.org/abs/0704.0535v1
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galaxy halo closely follow an age-metallicity and α/Fe-metallicity relation, where
older clusters exhibit lower metallicities and higher α/Fe ratios. Furthermore, we
investigate the impact of other non-linear mechanisms that shape the metallicity
distribution of globular cluster systems, in particular the role of merger-induced
globular cluster formation and a non-linear color-metallicity transformation, and
discuss their influence in the context of our model. We find that a non-linear
color-metallicity relation may be partly responsible for a color multi-modality.
On the other hand, the formation of globular clusters from subsequently ac-
creted gas, either with primordial abundances or solar metallicity, delivers model
predictions which are at variance with the observations, and suggests that a sig-
nificant fraction of metal-poor globular clusters is accreted from satellite halos
which formed their globular clusters independently.
Subject headings: galaxies: elliptical and lenticular, cD — galaxies: formation —
galaxies: star cluster — globular clusters: general — galaxies: structure
1. Introduction
1.1. The Multimodality of Globular Cluster Systems
One of the most significant developments in the study of extragalactic globular cluster
systems (GCSs) was the discovery of bimodality in their color distributions (see Ashman & Zepf
1998; Harris 2001; West et al. 2004 and references therein). Today, we generally refer to glob-
ular clusters (GCs) belonging to the blue peak of the color distribution as metal-poor GCs
and to the red-peak members as the metal-rich sub-population. It is generally considered
that the presence of multiple modes implies multiple distinct GC formation epochs and/or
mechanisms and ties those directly into formation scenarios that have to describe the par-
allel assembly histories of GCSs and the diffuse stellar populations in their host galaxies. In
massive early-type galaxies the current GCS assembly paradigms view the origin of the two
color peaks from the perspective of either episodic star-cluster formation bursts triggered by
gas-rich galaxy mergers (e.g. Ashman & Zepf 1992), temporarily interrupted cluster forma-
tion (so-called in-situ formation, e.g. Forbes et al. 1997; Harris et al. 1998), and star-cluster
accretion as a result of the hierarchical assembly of galaxies (e.g. Côté et al. 1998).
While the majority of GCSs in early-type galaxies show clearly bimodal color distri-
butions, the general picture is much more complex, ranging from purely blue to purely
red color distributions (e.g. Gebhardt & Kissler-Patig 1999; Kundu & Whitmore 2001a,b;
Larsen et al. 2001; Peng et al. 2006). This complexity is exacerbated by the fact that color
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bimodality is a function of galaxy mass and morphology, as less massive and later-type
galaxies tend to have single-mode blue (i.e. metal-poor) GC populations (e.g. Lotz et al.
2004; Sharina et al. 2005; Peng et al. 2006). Furthermore, color bimodality is also a func-
tion of galactocentric distance and is mainly due to the more extended spatial distribution
of the metal-poor sub-population relative to metal-rich clusters (e.g. Harris & Harris 2002;
Rhode & Zepf 2004; Dirsch et al. 2003, 2005).
1.2. Numerical Models of Globular Cluster System Formation
The aspect of GCS formation and assembly entered recently the domain of numerical
simulations of galaxy formation due to the increasing spatial resolution of these computa-
tions. For instance, Li et al. (2004) model GC formation by identifying absorbing sink parti-
cles in their smoothed particle hydrodynamics (SPH) high-resolution simulation of isolated
gaseous disks and their mergers. They find a bimodal globular-cluster metallicity distribution
in their merger remnant under the assumption of a particular age-metallicity relation. A key
finding of their merger simulation is a more concentrated spatial distribution of metal-rich
GCs with respect to the metal-poor sub-population in good agreement with observations.
Since their models of isolated galaxies produce a smooth age distribution (implying a smooth
metallicity and color distribution), Li et al. conclude that mergers are required to produce
a bimodal metallicity (i.e. color) distribution.
In a more detailed adaptive-grid cosmological simulation, Kravtsov & Gnedin (2005)
followed the formation of a star-cluster system during the early evolution of a Milky Way-size
disk galaxy to redshift z=3. Their model could reproduce the extended spatial distribution of
metal-poor halo globular clusters as observed in M31 and the Milky Way. However, because
their simulation does not follow the later evolution at z < 3 it is unclear whether it would
produce a metallicity bimodality and any significant age-metallicity relation.
An alternative, more statistical approach to modeling GCS assembly is to directly link
the mode of GC formation to the star-formation rate in semi-analytic models. Beasley et al.
(2002) were the first to explore this path by assuming that metal-poor GCs form in gaseous
proto-galactic disks while metal-rich GCs are created during gaseous merger events. Their
study showed that the observed globular-cluster color bimodality can only be reproduced by
artificially stopping the formation of metal-poor GCs at redshifts z & 5. By construction,
no spatial information on metal-rich and/or metal-poor GCs is provided in these models.
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1.3. A Spatially Resolved Chemical Evolution Model for Spheroid Galaxies
Recently, Pipino & Matteucci (2004, hereafter PM04) presented a spatially resolved
chemical evolution model for the formation of spheroids, which successfully reproduces a large
number of photo-chemical properties that could be inferred from either the optical or from
the X-ray spectra of the light coming from ellipticals. The model includes an initial gas infall
and a subsequent galactic wind; it takes into account detailed nucleosynthesis prescriptions
of both type-II and Ia supernovae as well as low and intermediate-mass stars. It has been
extensively tested against the main photo-chemical properties of nearby ellipticals, including
the observed increase of the α-enhancement in their stellar populations with galaxy mass (e.g.
Worthey et al. 1992; Weiss et al. 1995). This is at variance with standard models based on
the hierarchical merging paradigm, which do not reproduce this trend (Thomas et al. 2002).
Since the PM04 model provides full radial information on the composite nature of
stellar populations that make up elliptical galaxies, the observation of different GC sub-
populations is, therefore, a new sanity check for the validity of this model. Moreover, we
recall that PM04 and, more recently, Pipino et al. (2006, hereafter PMC06) suggested that
elliptical galaxies should form outside-in, namely the outermost regions form faster as well
as develop an earlier galactic wind with respect to the central parts (see also Martinelli et al.
1998). This mechanism implies that the stars in massive spheroids form a Composite Stellar
Population (CSP), whose chemical properties, in particular their metallicity distribution,
changes with galactocentric distance.
Starting with the assumption that GC sub-populations trace the components of CSPs,
we will show how the observed multi-modality in GCSs can be ascribed to the radial vari-
ation in the underlying stellar populations. In particular, the observed GCSs are a linear
combination of GC sub-populations inhabiting a given projected galactocentric radius.
The paper is organized as follows: in Section 2 we briefly describe the adopted theo-
retical model; in Section 3 we compare the predictions with observations and discuss the
implications, while Section 4 presents the final conclusions.
2. The model
2.1. The Chemical Evolution Code
The chemical evolution code for elliptical galaxies adopted here is described in PM04,
where we refer the reader for more details. In this work, we present the results for a
galaxy with Mlum ∼ 10
11M⊙, taken from PM04’s Model IIb. This model is characterized
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by a Salpeter (1955) IMF, Thielemann et al. (1996) yields for massive stars, Nomoto et al.
(1997) yields for Type-Ia SNe, and van den Hoek & Groenewegen (1997) yields for low- and
intermediate-mass stars.
An important feature of the PM04 model is its multi-zone nature, namely the model
galaxy is divided into several non-interacting spherical shells of radius ri, which facilitate a
detailed study of the radial variation of the photo-chemical properties of the GCS and its
host galaxy. In each zone i, the equations for the chemical evolution of 21 chemical elements
are solved (see PM04, Matteucci 2001).
The model assumes that the galaxy assembles by merging of gaseous lumps on short
timescales. The chemical composition of the lumps is assumed to be primordial. In fact, our
model assumes that the accretion of primordial gas from the surroundings1 is more efficient
in more massive systems, given their higher cross section per unit mass (see PM04). The
model galaxy suffers a strong starburst which injects a large amount of energy into the
interstellar medium, able to trigger a galactic wind, occurring at different times at different
radii, mainly due to the radial variation of the potential well, which is shallower in the
galactic outskirts. After the onset of wind activity the star formation is assumed to stop
and the galaxy evolves passively with continuous mass loss. In order to correctly evaluate
the amount of energy driving the wind, a detailed treatment of stellar feedback is included
in the code (that takes into account the stellar lifetimes). In particular, the energy restored
to the interstellar medium by both Type-Ia and Type-II supernovae has been calculated
in a self-consistent manner according to the time of explosion of each supernova and the
characteristics of the ambient medium (see PM04 for details). The potential well that keeps
the gas bound to the galaxy is assumed to be dominated by a diffuse and massive halo of
Dark Matter surrounding the galaxy.
In the following we adopt the standard star formation rate ψ∗(t, ri) = ν · ρgas(ri, t)
before the onset of the galactic wind (tgw), where ρgas is the gas density, ν the star-formation
efficiency; otherwise we assume that ψ∗(t > tgw, ri) = 0. We recall here that the adopted
star-formation efficiency is ν = 10Gyr−1, while the infall timescale is τ = 0.4Gyr in the
galactic core and τ = 0.01Gyr at one effective radius (of the diffuse light, Reff), respectively.
These values were chosen by PM04 in order to reproduce the majority of the chemical and
photometric properties of ellipticals such as: the 〈[Mg/Fe]〉−σ (e.g. Faber et al. 1992), the
Color-Magnitude (e.g. Bower et al. 1992), the Mass-Metallicity relation (e.g. Gallazzi et al.
2005) as well as the observed gradients in metallicity (e.g. Carollo et al. 1993), 〈[Mg/Fe]〉
1Since we lack a cosmological framework we cannot further specify the properties of the infalling primordial
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(e.g. Mendez et al. 2005), and color (e.g. Peletier et al. 1990). Pipino et al. (2005) recently
extended this model to explain also the properties of hot X-ray emitting halos surrounding
more massive spheroids.
2.2. Globular Cluster Formation
The formation rate of GCs, ψGC , in the i-th shell is assumed to be directly linked to its
star formation rate ψ∗(t, ri, Zi) via a suitable function of time t, radius ri, and metallicity
Z, which represents some scaling law between star formation rate ψ∗ and the star cluster
formation ψGC and can be regarded as a GC formation efficiency. A similar relation be-
tween the average star formation rate per surface area and the star cluster formation was
recently found by Larsen & Richtler (2000) to hold in nearby spiral galaxies. In addition,
the efficiency of cluster formation in massive ellipticals appears to be constant, where the
mass ratio between the mass in star clusters and the baryons locked in field stars+gas is
ǫGC≈ 0.25% (McLaughlin 1999). Here we extend this surface density relation to 3-D space.
Moreover, PMC06 showed that at a given galactocentric radius model galaxies are made
of a CSP, namely a mixture of several simple stellar populations (SSPs) each with a single age
and chemical composition. The CSP reflects the chemical enrichment history of the entire
system, weighted by the star formation rate. We define the stellar metallicity distribution
Υ∗ as the distribution of stars belonging to a given CSP as a function of [Z/H].
We can then write the globular-cluster metallicity distribution ΥGC at a given radius ri
and time t as:
ΥGC(t, ri, Z) = f(t, ri, Z) ·Υ∗(t, ri, Z) , (1)
where f includes all the information pertaining to the connection between ψGC and ψ∗.
It is not trivial, and beyond the scope of the paper, to find an explicit definition for
f(t, ri, Zi), which basically carries the information on the internal physics of gas clouds where
GCs are expected to form. In the following we will show that, for a few and sensible choices
of f , the observed multi-modality in the color distribution of globular clusters may be driven
by the radial variations in the stellar population mix of ellipticals. We will first adopt a
constant function f (see Sec. 3.1) and then allow f to mildly vary with Z (see Sec. 3.2). No
absolute values for f will be given, since our formalism deals with normalized distributions.
In particular, the total ΥGC summed over all radial shells can be written as:
ΥGC,tot(t, Z) =
f(t, ri, Z) ·Υ∗(t, ri, Z) . (2)
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Similar equations hold for other GC distributions as a function of either [Mg/Fe] or [Fe/H].
At this stage it is useful to recall that Υ∗(t, ri, Z) can be represented in two following
ways: i) as the fraction of mass of a CSP which is locked in stars at any given metallicity
(Pagel & Patchett 1975; Matteucci 2001). In the following we refer to this stellar metal-
licity distribution as Υ∗,m (MSMD: mass-weighted stellar metallicity distribution); ii) as a
fraction of luminosity of the CSP in each metallicity bin. This definition is closer to the
measurement as it can be directly compared to the luminosity-weighted mean Υ∗,l (LSMD:
luminosity-weighted stellar metallicity distribution) at a given radius (see Arimoto & Yoshii
1987; Gibson 1996). This classification is important since PMC06 showed that the Υ∗,m and
Υ∗,l might differ, especially at large radii, even for old stellar populations. The advantage
of GCSs, for which accurate ages are known, is that they directly probe the mass-weighted
distributions.
At this point it is useful to recall that our the adopted chemical evolution model divides
the galaxy in several non-interacting shells. In each shell the time at which the galactic wind
occurs is self-consistently evaluated from the local condition. In particular, we follow Mar-
tinelli et al. (1998) suggestion that gradients can arise as a consequence of a more prolonged
SF, and thus stronger chemical enrichment, in the inner zones. In the galactic core, in fact,
the potential well is deeper and the supernovae (SNe) driven wind develops later relative to
the most external regions. This particular formation scenario leaves a characteristic imprint
on the shape of both Υ∗,m and Υ∗,l and here we give some general considerations. In partic-
ular, we can explain the slow rise in the low metallicity tail of the distributions as the effect
of the initially infalling gas, whereas the onset of the galactic wind sets the maximum metal-
licity of the Υ∗,m and Υ∗,l. In general, the suggested outside-in formation process reflects in
a more asymmetric stellar metallicity distribution at larger radii, where the galactic wind
occurs earlier (i.e. closer to the peak of the star formation rate), with respect to the galactic
center. The qualitative agreement between these model predictions and the observed stellar
metallicity distributions derived at different radii by Harris & Harris (2002, see their Fig. 18)
for the stars in the elliptical galaxy NGC 5128 is remarkable. If confirmed from observations
in other ellipticals, the expected sharp truncation of Υ∗,m at large radii might be the first
direct evidence of a sudden and strong wind which stopped the star formation earlier in the
galactic outskirts (see PMC06 and Pipino, D’Ercole, & Matteucci, in preparation).
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3. Results and discussion
3.1. The Multi-Modality of Globular Cluster Systems in Elliptical Galaxies
The general presence of multi-modal GCSs implies that their host galaxies did not form
in a single, isolated monolithic event, but experienced spatially and/or temporally separated
star-formation bursts. In the recent past, both semi-analytic and hydrodynamic simula-
tions of galaxy formation attempted to follow the process of GC formation (Beasley et al.
2002; Kravtsov & Gnedin 2005), but neither could produce a clearly bimodal MDF in their
simulated GCSs.
In this section we will show how to obtain a bimodal metallicity distribution function for
GCs ΥGC,tot starting from single-mode stellar metallicity distribution functions Υ∗(t, ri, Z)
(commonly known as G-dwarf-like diagrams) for the CSP inhabiting different radii of a
prototypical elliptical galaxy according to Equation 2.
3.1.1. The Comparison Sample
As stressed in the introduction, the multi-modality in GCSs varies as a function of host
galaxy properties (e.g. mass, morphological type, etc.). Here we try to match the distri-
butions resulting from the recent compilation of spectroscopic data by Puzia et al. (2006,
hereafter P06), which samples the typical bimodal color distribution of GCs in nearby galax-
ies (see also Puzia et al. 2004, 2005). This is illustrated in Figure 1, where we plot the
(V−I)0 color distribution of the P06 sample of GCs in elliptical galaxies (top panel) together
with those of GCs in NGC 4472 and the Milky Way (middle and bottom panel). NGC 4472
is the most luminous elliptical in the Virgo galaxy cluster and hosts a GC system with a
prototypical color bimodality (e.g. Puzia et al. 1999). To allow direct comparison with the
P06 sample, we use GCs in NGC 4472 that are brighter than V ≃ 22.5 since the P06 sample
includes only the brightest GCs in nearby early-type galaxies in order to maximize the S/N
of their spectra. The resulting color distribution is remarkably similar to the one of the P06
sample, which assures that the P06 sample includes a representative sampling of the GC
color bimodality in massive elliptical galaxies.
However, the comparison with the Milky Way GCs shows that the P06 sample covers
few of the most metal-poor GCs. Therefore, the bimodality which we refer to in the fol-
lowing may not be the same as the one observed in spirals or in some elliptical galaxies,
where a substantial population of metal-poor clusters with [Z/H] . −1.5 is present (e.g.
Gebhardt & Kissler-Patig 1999).
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We do not include the dynamical evolution of GCs in our model, since we are considering
only the brightest (most massive, i.e. > 105.5M⊙, see also Puzia et al. 2004, A&A 415, 123)
clusters in nearby galaxies as comparison sample. The comparison sample includes GCs much
brighter than the typical turnover magnitude of the globular cluster luminosity function and
we, therefore, do not expect significant differential dynamical evolution for these massive
systems (see Gnedin & Ostriker 1997, for details). In fact, it has been shown (e.g. Fall
& Zhang, 2001) that the timescales for both evaporation by two body relaxation and tidal
stripping of star clusters is longer than a Hubble time for GCs more massive than ∼ 105.5M⊙.
In our model, the number of clusters formed in a star-formation burst of a given strength
is adjusted to match the observations. Hence, the absolute scaling of GC numbers is arbi-
trary, i.e., within physical limitations of the star formation rate any number of GCs can be
reproduced by adjusting the function f in Equation 2.
If, however, metal-poor and metal-rich GCs are on systematically different orbits and
experience significantly different dynamical evolutions the effect of tidal disruption might
be slowly changing relative GC numbers with time. Another complication is the variation
of the initial star-cluster mass function, in particular as a function of metallicity. Modeling
these effects requires detailed knowledge of the orbital characteristics and chemo-dynamical
processes that lead to star cluster formation, and goes far beyond the scope of this work.
We keep these potential systematics in mind, but expect negligible impact on our analysis.
3.1.2. A Simple Model
In order to make a first-order comparison between our model predictions and the ob-
served ΥGC,tot at t=13 Gyr, we first focus on the simple case in which:
ΥGC,tot(Z) = fred ·Υ∗(t = 13Gyr, r1, Z) +
fblue ·Υ∗(t = 13Gyr, r2, Z) , (3)
with fred , fblue = const and r1 = 0.1Reff , r2 ≥ 1Reff . The first term (red) corresponds
to a population typical of the galaxy core (well inside r < 1Reff). The second term (blue)
represents Υ∗ in the outer regions. In order to take into account the different amounts of
stars formed in each galactic region, we point out that the stellar metallicity distributions
entering Equation 2 were not normalized.
As a first step, we take several values for the weights fred , fblue in order to mimic
different mixtures of the two GC populations. In particular, we used the relative numbers of
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the red (here identified as the metal-rich core population) and the blue globular clusters (the
halo metal-poor population) as a function of galactocentric radius for the elliptical galaxy
NGC 1399 (Dirsch et al. 2003). Our particular choice is driven by observationally motivated
values for the weights, although we realize that NGC 1399 is a quite peculiar, massive cD
elliptical and might not be representative of less massive
systems. In the context of this first step, the weights might reflect the effects of the
projection on the sky of a three-dimensional structure. However, we show below that the
results do not strongly depend on the weights. Therefore they might be interpreted as mean
values and could be changed if one decides to model a particular galaxy, with a different
ellipticity, inclination, and luminosity profile.
In Figure 2 we show the globular-cluster metallicity distribution ΥGC by mass (compu-
tation based on Υ∗,m) in two radial bins for three particular choices of weights. In particular
in the following we will use the ratios fred = 0.77,fblue = 0.23, fred = 0.60,fblue = 0.40 and
fred= fblue = 0.50 in order to define the theoretical innermost, intermediate and outermost
sub-sample of the GCS, respectively. These ΥGC will be compared against subsamples of
the P06 data, obtained by selecting GCs with either r < 1Reff (in the case of the innermost
population) or r ≥ 1Reff (for the intermediate and the outemost cases, respectively), unless
otherwise stated.
3.1.3. Globular Cluster Metallicity Distribution
In order to plot the different cases on the same scale we normalize each ΥGC by its
maximum value. In the left panel of Figure 2 the shaded histogram represents the innermost
population. Our predictions match the data very well, especially in the metal-rich slope
and the mean of the distribution. The same happens for the pure core populations, which
shows how the GCS might be used to probe the CSP in ellipticals. It should be remarked
that a second peak centered at super-solar metallicity appears in the distribution predicted
by our models, although not evident in the data of the particular radial sub-sample. The
right panel of Figure 2 illustrates model predictions which are more representative of the
galaxy as a whole (either at 1Reff , i.e. the intermediate population, or at several effective
radii, the outermost population), and we consider them as the fiducial case. These two
cases look quite similar to each other and have clear signs of bimodality in remarkable
agreement with the spectroscopic data (solid empty histogram, sub-sample of the P06 data
with r ≥ Reff). A Kolmogorov-Smirnov test returns > 99% probability that both model
predictions and observations are drawn from the same parent distribution in the left panel of
Figure 2. The right panel statistics gives a lower likelihood of 98.4% that both distributions
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have the same origin, which is mainly due to the observed excess of metal-poor GCs at
large galactocentric radii compared to the model predictions. The prediction of a super-
solar metallicity globular cluster sub-population is entirely new and a result of the radially
varying and violent formation of the parent galaxy. Moving to the low-metallicity tail, we
predict slightly fewer low metallicity objects than expected from observations. But we recall
the systematics mentioned in Section 3.1.1.
In Figure 3 (left panel) we show the results for a pure core GCs, namely one in which we
adopt fred :fblue = 1:0. In this quite extreme case the observed GCs have been selected with
radius r < 0.5Reff . The histogram reflects the shape of a G-dwarf-like diagram expected for
a typical CSP inhabiting the galactic core. This finding is particularly important, because it
might offer the opportunity to resolve the SSPs in ellipticals, at variance with data coming
from the integrated spectra which deal with luminosity-weighted quantities. Whereas in
Figure 3 (right panel), the intermediate population is compared to a sub-sample of P06 GCs
with 0.5 < r < 0.5Reff . This is to show that the multimodality is not an artifact due to the
particular radial binning adopted in this paper.
Figure 4 shows the V -band luminosity-weighted ΥGC for which the computation is based
on Υ∗,l. This metallicity distribution has been obtained by converting the mass in each [Z/H]
bin of the previous figure into LV , by means of theM/LV ratio computed by Maraston (2005)
as a function of [Z/H] for 13 Gyr old SSPs. Due to the well-known increase of the M/LV
in the high metallicity tail of the distribution2, we notice in Figure 4 that now the second
peak has a smaller intensity in all the cases. The corresponding diffuse-light population goes
undetected in integrated-light studies. In any case, the conclusions reached by analyzing
Figure 2 are not significantly altered. We conclude that our analysis is not significantly
biased by some metallicity effect which may alter the shape of the observed ΥGC,tot by
luminosity. We stress the power of GCSs in disentangling stellar sub-populations in massive
ellipticals, due to their nature as simple stellar populations that can be directly compared
to SSP model predictions, unlike diffuse light measurements.
Even with this simple parametrization, where f in Equation 3 does not depend on
metallicity, we suggest that the bimodality for the metal-rich GCs is the result of different
shapes of Υ∗,m (and the Υ∗,l) at different galactocentric radii.
2See PMC06 for a comparison between G-dwarf like diagrams for Υ∗,m and Υ∗,l predicted for the same
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3.1.4. Globular Cluster [Mg/Fe] Distributions
Finally, in Figure 5 we show the [Mg/Fe] distributions for GCs divided in radial bins as in
Figure 2. According to PMC06, these [Mg/Fe] distributions are narrower, more symmetric,
and exhibit a smaller radial variation with respect to the [Z/H] distributions. In any case, a
small degree of bimodality is still present. We point out the impressive agreement with the
spectroscopic observations by P06. There is a rather large discrepancy between data and
models at the high-[Mg/Fe] end. Hence, the corresponding Kolmogorov-Smirnov likelihood
tests return a probaility of 1% (for inner sample) and 95% (for the outer ones). If we limit
the model predictions to [Mg/Fe] < 0.8 dex, the agreement slightly improves, reaching a 10%
probablity in the inner region. However, the inner field data still does not reach the extreme
[Mg/Fe] values of the models. In fact, due to the monotonic decrease of the [Mg/Fe] as a
function of either metallicity or time (see PM04), the lack of low-metallicity GCs, evident
from Figure 2, translates into a lack of α-enhanced clusters.
The [Mg/Fe] bimodality of our model predictions and the match with the spectroscopic
measurements strongly imply that globular clusters in massive elliptical galaxies form on two
different timescales. Their chemical compositions are consistent with an early mode with a
duration of ∆t . 100 Myr and a normal formation that lasted for ∆t . 500 Myr. In fact,
according to the time-delay model (see Matteucci, 2001) and given the typical star formation
history of our model ellipticals, the [Mg/Fe] ratio in the gas - out of which the GCs form -
is quickly and continuously decreasing with time. We predict that the [Mg/Fe] ratio can be
higher than 0.65 dex (i.e. in the bins in which our predictions exhibit a deficit of GCs with
respect to the observed distribution) only in the first ∼ 100 Myr (see also Fig.3 in P06 and
related discussion). In fact, such a high value for the [Mg/Fe] can be attained only if very
massive type II SNe contribute to the chemical evolution, without any contribution from
either lower-mass type II or type Ia SNe. The normal formation, instead, is the one already
plotted in Fig. 5 and forms on a typical timescale of 0.5 − 0.7 Gyr. More quantitatively,
our initial theoretical GCMD predicts that only ∼ 4% of the GCS forms at [Mg/Fe] larger
than 0.65 dex. In order to improve the agreement with observations we require that the
above fraction should be increased to ∼ 12− 15%. Since star and globular cluster formation
are expected to be closely linked (e.g. Chandar et al. 2006) the same must be true for the
diffuse stellar population of such galaxies. We therefore foresee the presence of a similar
[Mg/Fe] bimodality in the diffuse light of massive elliptical galaxies. Unfortunately, there
are not direct observations confirming our suggestions, until the metallicity distributions for
the diffuse stellar component in ellipticals will become available for a number of galaxies.
Indeed, the detection of bimodality in the [Mg/Fe]-distribution might be a benchmark test
for our predictions.
– 13 –
We will still refer to multiple GC sub-populations. However, their differences ought
to be ascribed only to the fact that they are created during an extended (and intense) star
formation event during which the variation in chemical evolution is not negligible. The
radial differences originate from the fact that the galactic wind epoch is tightly linked to the
potential, occurring later in the innermost regions (e.g. Carollo et al. 1993; Martinelli et al.
1998). Moreover, PM04 and PMC06 found that also the infall timescale is linked to the
galactocentric radius. In particular, it lasts longer in the more internal regions, owing to the
continuous gas flows in the center of the galactic potential well. In particular, we recall that
in our model the core experiences a longer (∼ 0.7 Gyr) star-formation history with respect
to the outskirts where the typical star-formation timescale is ∼0.2 Gyr.
According to our models the metal-rich population of GCs in massive elliptical galaxies
may consist of multiple sub-populations which basically play the same role as the CSPs
populating each galactocentric shell in our framework of the global galaxy evolution. At the
same time, we point out the lack of our models to produce a significant fraction of metal-
poor GCs similar to the halo GC population in the Milky Way, with the caveat that the star
formation histories are very different. This, in turn, suggests that GCSs in giant elliptical
galaxies were assembled by accretion of a significant number of metal-poor GCs.
3.2. Metallicity Dependent Globular Cluster Formation
In this section we explore the approach outlined in Equation 2, by introducing the effect
of metallicity in the function f. In particular, we start by assuming that
f(t, ri, [Z/H]<−1)
f(t, ri, [Z/H]>−1)
= 2 , (4)
roughly following what was found for the GCS of the most nearby giant elliptical galaxy
NGC 5128 (Centaurus A) by Harris & Harris (2002, hereafter HH02) for their “inner field”,
regardless of the radius of the i-th shell. Since the final distributions are normalized, the
actual zeropoint of the function f is not relevant. Our model predictions are plotted in
Figure 6. We notice a modest increase of the low-metalliticy tail of the distribution with
respect to the simple picture sketched in Section 3.1 without metallicity dependence, as
well as a lower fraction of globular clusters populating the high-metallicity peak. Including
the metallicity dependence leads to an ambiguous change in agreement with the general
observed trend. Hence, no firm conclusions on the real need for a metallicity dependence
can be drawn. Similar results are obtained in the more realistic case in which f is a linearly
decreasing function of [Z/H].
– 14 –
At variance with HH02, we chose to adopt the same scaling irrespective of galacto-
centric radius, for the following reason. Despite the fact that the HH02 stellar metallicity
distributions Υ∗ as functions of [Z/H] confirm both the shape and the radial behavior of
our model predictions for the mass-weighted stellar metallicity distribution Υ∗,m (compare
their Fig. 7 with PMC06 Fig. 4), care should be taken when comparing their results for
Υ∗ as a function of [Fe/H]. The latter, in fact, had been obtained by assuming a particular
trend in the [α/Fe] as a function of galactocentric radius which disagrees with the results
of our detailed chemical evolution model. In particular, we find an offset of at least 0.2
dex in the sense that [Fe/H] HH02 ∼ 0.2+ [Fe/H] PM04 at a given metallicity ([Z/H]). This
disagreement becomes larger either at very low metallicity or at larger galactocentric radii,
where we expect a stronger α-enhancement. Once the PM04 value for [Fe/H] is adopted in
Fig. 18 of HH02, we find that: i) for the inner halo, the stellar Υ∗,m should be shifted by
∼ 0.2 dex toward lower metallicities, removing any metallicity effect, and ii) for the outer
halo the discrepancy between the stellar Υ∗,m and the ΥGC,tot should be reduced.
Nevertheless, we believe that some decrease with time of the function f could be mo-
tivated by theoretical arguments. In fact, recent work (e.g. Elmegreen & Efremov 1997;
Elmegreen 2004) shows that GCs of all ages preferentially form in turbulent high-pressure
regions. If we interpret the decrease in the efficiency of star formation (inside the gas clouds
that form GCs), as a function of the ambient pressure (Elmegreen & Efremov 1997) as a
proxy for the temporal behaviour of our function f, we find again a reduction of a factor
∼2−3 from the early high-pressure epochs to a late, more quiescent evolutionary phase.
3.2.1. The Ratio of Metal-poor to Metal-rich Globular Clusters
For our fiducial model we predict a ratio of metal-poor (namely with [Z/H] ≤ −1) to
metal-rich GCs of ∼0.2. Previous photometric surveys found that the typical value for GC
systems in elliptical galaxies is close to unity (Gebhardt & Kissler-Patig 1999; Kundu & Whitmore
2001a). Provided a linear color-metallicity transformation (see also Section 3.5), a possible
explanation for the discrepancy between our models and the observations might be obtained
by boosting the metal-poor population by a factor of f(t, ri, [Z/H]<−1)/f(t, ri, [Z/H]>−1) ≥
Another way to solve the discrepancy is to assume that all the missing globular clusters
have been accreted from the surroundings, e.g. from dwarf satellites (e.g. Côté et al. 1998).
We estimate the amount of the accreted metal-poor GCs, needed to achieve a ratio close to
1, as a factor of ∼4 of the number of globular clusters initially formed inside the galaxy.
– 15 –
3.3. The Role of the Host Galaxy Mass
A natural consequence of the scenario depicted in Sections 3.1 and 3.2 is that, at a
given galactocentric radius, the mean metallicity and [α/Fe] ratios of a GCS coincide with
the mass-weighted [〈Z/H〉∗] and [〈α/Fe〉∗] of the underlying stellar population, because the
GC quantities are calculated either from Υ∗,m or the Υ∗,l (see Eqs. 1 and 2 of PMC06),
unless the scaling function f is allowed to strongly vary with time. We expect this to happen
at least in the innermost GC sub-populations, in which the effects of the accretion of GCs
from the environment can be reasonably neglected. In particular, PM04 predict that more
massive galaxies should show higher [〈α/Fe〉∗] and [〈Z/H〉∗]. If accretion plays a negligible
role, we expect the same correlations for the total GC population with host galaxy mass for
the most massive systems, in agreement with current observations (e.g. van den Bergh 1975;
Brodie & Huchra 1991; Peng et al. 2006).
In fact, if we perform the same study of the above sections for a 1012M⊙ galaxy (see
Table 2 of PM04 for its properties), both peaks in ΥGC,tot shift their positions by about 0.2
dex to higher [Z/H]. This is in good agreement with the results of (Peng et al. 2006, see their
Figure 13 and 14). This trend holds for smaller objects as well. If we apply the procedure
to a 1010M⊙ galaxy (Model IIb of PM04), we find that the metal-rich peak shifts towards a
lower metallicity by 0.3 dex (with respect to our fiducial model with Mlum = 10
11M⊙), while
the other peak is now centered around [Z/H] = −0.8 dex. In particular, we find a faster
decrease in the mean metalliticy of the metal-poor GCs than for the metal-rich ones, again
in agreement with the Peng et al. results.
Interestingly, the ratio of metal-poor to metal-rich cluster increases up to ∼ 0.5 for
less massive halos. We recall that in the PM04 scenario, the low-mass galaxies are those
forming on a longer timescales and with a slower infall rate. Therefore, we suggest that
the combination of these factors is likely to at least partly explain the change of the GC
distributions in different galaxy morphologies. This is especially the case in dwarf galaxies,
where star formation is slow and still on-going, together with the fact that the probability
for a substantial change in the pressure of the interstellar medium relative to its initial values
is higher than in ellipticals, thus implying a much stronger variation of f with time.
3.4. Merger-Induced Globular Cluster Formation
It has been suggested that GC populations are produced during major merger events
which would lead to present-day ellipticals and their rich GCSs (e.g. Schweizer 1987; Ashman & Zepf
1992). Subsequent studies (e.g. Forbes et al. 1997; Kissler-Patig et al. 1998b) challenged this
– 16 –
view by pointing out the much higher SN and more metal-rich GCSs in early-type galaxies
compared to those of spiral and irregular galaxies, which are thought to represent the early
building blocks of massive ellipticals.
In the following, we study the impact of the merger hypothesis on the predictions of
our simulations. In order to do that, we extended the procedure sketched in the previous
sections to the merger models presented by Pipino & Matteucci (2006, hereafter PM06). In
this paper, the effects of late gas accretion episodes and subsequent merger-induced starbursts
on the photo-chemical evolution of elliptical galaxies have been studied and compared to the
picture of galaxy formation emerging from PM04; in particular the PM04 best model is
taken here as a reference. By means of the comparison with the colour-magnitude relations
and the [〈Mg/Fe〉V ]-σ relation observed in ellipticals (e.g. Renzini 2006), PM06 showed that
either bursts involving a gas mass comparable to the mass already transformed into stars
during the first episode of star formation and occurring at any redshift (major mergers), or
bursts occurring at low redshift (i.e. z ≤ 0.2) and with a large range of accreted mass (minor
mergers), are ruled out. The reason lies in the fact that the chemical abundances in the ISM
after the galactic wind (and before the occurrence of the merger) are dominated by Type
Ia SN explosions, which continuously enrich the gas with their ejecta (mainly Fe). When
the merger-induced starburst occurs, most stars form out of this enriched gas (thus, e.g.,
lowering the total [〈Mg/Fe〉]); at the same time, we expect the metallicities of GCs formed
out of this gas to be on average higher and their [Mg/Fe] ratios to be lower than those of
the bulk of stars and GCs formed in the initial starburst.
In this work we present the case in which the galaxy accretes a gas mass Macc = Mlum
at tacc = 2 Gyr (i.e. ∼1 Gyr after the onset of the galactic wind). We make this choice for
several reasons: i This model is quite similar to the PM06 models b and g, which were among
those in good agreement with observations of the diffuse galaxy light properties. ii) The
formation epoch of the bulk of these second generation GCs cannot occur &2 Gyr later than
tgw, because the majority of GCs in the most massive elliptical galaxies studied today appear
old within the age resolution of current photometric (∆t/t ≈ 0.4−0.5) and spectroscopic
studies (∆t/t ≈ 0.2−0.3). Finally, the composition of the newly accreted gas is assumed to
be primordial (see PM06 for a detailed discussion), but we remark that we reach roughly the
same conclusion in the case of solar composition, in order to mimic some pre-enrichment for
the newly accreted gas. We point out that, lacking dynamics, PM06 presented their results
for one-zone models. Therefore, in this section we are considering Equation 2 limited to only
one shell. In this way we can check whether the single merger hypothesis alone is enough to
produce some bimodality in the total globular-cluster metallicity distribution ΥGC,tot, and if
it is consistent with the predictions based on our fiducial model described in Section 3.2.
– 17 –
We show our results in Figure 7 and 8. We notice a clear change in the overall shape of
the metallicity distribution ΥGC,tot with respect to the cases shown in the previous sections, in
the sense that now ΥGC,tot is narrower and dominated by objects with super-solar metallicity
(and sub-solar [Mg/Fe] ratios) with a dominant population at [Z/H] ≈ 0.1, which is not
prominent in the observations of P06. The high-metallicity globular cluster populations
dominate the metallicity distribution which is at variance with both the results from previous
sections and the observations.
Our merger model does not include the accretion of globular clusters that were already
formed within the accreted satellite galaxies. The inclusion of this effect could remedy the
match between models and observations at low metallicities, as the typical GC in a dwarf
galaxy is metal-poor (e.g. Lotz et al. 2004; Sharina et al. 2005) and their addition to the
initial GC population would enhance the total number of metal-poor GCs and improve the
fit to the data. However, these clusters need to be α-enhanced to match the observations.
The impact of GC accretion on our post-merger model predictions will be studied in detail
in a future paper. Here, we remark that the time at which the purely gaseous subsequent
merger event can occur (which does not import already formed GCs), is limited by the
onset of the galactic wind, after which the type-Ia SNe dominates the nucleosynthesis, and
needs to be completed at tmrg . 1 − 2 Gyr after the first starburst. However, this time
constraint implies that such merger events would overlap with the initial starburst and be
mostly indistinguishable from each other. Such a scenario closely resembles the Searle-Zinn
scenario (Searle & Zinn 1978), in which galaxy halos are formed from the agglomeration of
gaseous protogalactic fragments. Later merger events are excluded in our models, as they
would produce GCs with sub-solar [Mg/Fe] ratios which is at variance with the observations.
Note also that the fraction of GCs at [Z/H]< −1 can be recovered in our models only
if the cluster formation at low metallicity is enhanced (e.g. using a value of 10 instead of 2
in eq.4). However, even in the case in which we adopt some f(Z) strongly declining with
total metallicity, which may alter the shape of ΥGC,tot enhancing the low-metallicity tail and
thus improving the agreement with observations, the position of both super-solar metallicity
peaks will not change, remaining at variance with the data.
3.5. Other Mechanisms responsible for Multimodality
The picture emerging from our analysis is far from being the general solution to ex-
plaining the complexity of GC color distributions, and it suggests only a scheme in which
multiple mechanisms could be at work together, either broadening or adding features to the
observed distributions.
– 18 –
For instance, Yoon et al. (2006) suggested that the color bimodality could arise from the
presence of hot horizontal-branch stars (so far not accounted for in SSP model predictions)
that results in a non-linear color-metallicity transformation producing two color peaks from
an originally single-peak metallicity distribution. We tested this scenario on our fiducial
model GC metallicity distribution, by applying to each SSP the following transformation
from [Fe/H] to the (g − z) color:
(g − z) = α + β [Fe/H] + γ [Fe/H]
+δ [Fe/H]3 + ǫ [Fe/H]
The numerical values of the coefficients are given in Table 1 and the relation was adopted from
Yoon et al. (2006) and is consistent with the best-fit relation presented in their Figure 1b.
We show our results in Figure 9.
Since we start from symmetric metallicity distributions, the non-linear transformation
seems to work and produce a color bimodality for the CSP inhabiting the < 10Reff shell
(Figure 9, solid line), although the bimodality is slightly exaggerated compared to real data
(see Figure 1). In fact, a look at the color distribution which we obtained for the sole
0.1Reff shell reveals that it still has one peak and is roughly symmetric (Figure 9, dashed
line). Obviously, since the (g − z)− [Fe/H] relationship is meant to explain the GCs color
bimodality without invoking any other effect, we did not combine the two histograms, either
according to Eq.2 or to Eq. 3 in our models, as we are comparing metallicity distributions
to spectroscopic measurements.
It is of great importance to investigate this transformation with large and homoge-
neous data sets that cover a wide enough metallicity range to allow a robust analysis of
the non-linear inflection point in the color-metallicity transformation. However, as a re-
sult of Figure 9, we point out that the color bimodality typically found for GCSs in massive
early-type galaxies might be only partly due to a non-linear color-metallicity transformation.
Another effect put forward by, e.g.,Recchi & Danziger (2005) is the claim that GCs
might have undergone a self-enrichment phase at the early stages of their formation, and
Table 1. Numerical values of coefficients used in Equation 6.
coefficient numerical value
α 1.5033
β 0.172774
γ −0.623522
δ −0.453331
ǫ −0.089038
– 19 –
therefore some GCs could have experienced a boost in metallicity which would be not rep-
resentative of the metallicity of their parent gas cloud. Finally, as already mentioned above
in Section 3.4, some GCs residing in the outermost regions of the galaxies (e.g. Lee et al.
2006) could have experienced entirely different chemical enrichment histories at the time
of their formation and later been added to a more massive system through accretion (e.g.
Côté et al. 1998). The inclusion of these effects goes far beyond the scope of this work, but
we remind the reader that all the aforementioned effects might influence the interpretation
of any globular cluster color and metallicity distribution.
4. Conclusions
By means of the comparison between PM04’s best model predictions for the radial
changes in the CSP chemical properties and the recent spectroscopic data on the metallicity
distributions of extragalactic GCSs from Puzia et al. (2006), we are able to derive some
conclusions on the GC metallicity distributions in massive elliptical galaxies. In particular,
we focused on the main drivers of the multi-modality that is observed in the majority of
GCSs in massive elliptical galaxies. Our main conclusions are:
• We show that the observed multi-modality in the GC metallicity distributions can be
ascribed to the radial variation in the underlying stellar populations in giant elliptical
galaxies. In particular, the observed GCSs are consistent with a linear combination of
the GC sub-populations inhabiting different galactocentric radii projected on the sky.
• A new prediction of our models, which is in astonishing agreement with the spectro-
scopic observations, is the presence of a super-solar metallicity mode that seems to
emerge in the most massive elliptical galaxies. In smaller objects, instead, this mode
disappears quickly with decreasing stellar mass of the host galaxy.
• Our models successfully reproduce the observed [Mg/Fe] bimodality in GCSs of mas-
sive elliptical galaxies. This, in turn, suggests a bimodality in formation timescales
during the early formation epochs of GCs in massive galaxy halos. The two modes are
consistent with an early (initial) and later (triggered) formation mode.
• Since the GC populations trace the properties of galactic CSPs in our scenario, we
predict an increase of the mean metallicity of the cluster system with the host galaxy
mass, which closely follows the mass-metallicity relation for ellipticals. Moreover, we
expect that a major fraction of the GCs (i.e. those born inside the galaxy) follows an
age-metalliticity relationship, in the sense that the older ones are also more α-enhanced
and more metal-poor.
– 20 –
• The role of host galaxy metallicity in shaping the observed GC metallicity distribution
is non-negligible, although its effects have been estimated to change the function f ≃
ψGC/ψ∗ by a factor of ∼ 2 − 5, in order to match the sample of Puzia et al. (2006).
Either a non-linear color-metallicity transformation, or a stronger metallicity effect,
and/or accretion of GCs from the surrounding environment is needed to explain a
ratio of metal-poor to metal-rich GCs close to unity, as reported for ellipticals based
on results from photometric surveys.
• Merger models which include the later accretion of primordial and/or solar-metallicity
gas predict a shape for the GC metallicity distribution which is at variance with the
spectroscopic observations.
We thank the referee for a careful reading of the paper. A.P. warmly thanks S.Recchi
for useful discussions. A.P. acknowledges support by the Italian Ministry for University
under the COFIN03 prot. 2003028039 scheme. T.H.P. acknowledges support by NASA
through grants GO-10129 and GO-10515 from the Space Telescope Science Institute, which
is operated by AURA, Inc., under NASA Contract NAS5-26555, and the support in form of
a Plaskett Research Fellowship at the Herzberg Institute of Astrophysics.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 24 –
Fig. 1.— Color distributions of GCs in nearby, massive elliptical galaxies (Puzia et al. 2006,
top panel), in NGC 4472 (Puzia et al. 1999, middle panel), and the Milky Way, taken from the
February 2003 update of the McMaster catalog (Harris 1996, bottom panel). In order to allow
a robust comparison between the P06 and NGC 4472 sample, only GCs in NGC 4472 with
with luminosities brighter than V ≃ 22.5 mag are shown. The solid lines are Epanechnikov-
kernel probability density estimates with their bootstrapped 90% confidence limits.
– 25 –
Fig. 2.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for three different radial compositions (i.e. fred/fblue). The left panel shows both
model predictions and observations related to the central part of an elliptical galaxy. The
right panel shows the same quantities for cluster populations residing at r ≥ Reff . Solid empty
histograms: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel.
– 26 –
Fig. 3.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for two different projected galactocentric radii. The left panel shows both model
predictions and observations related to the pure core of an elliptical galaxy (namely fred :
fblue = 1 : 0). The right panel shows the same quantities for cluster populations residing
either at 0.5Reff < r < 1.5Reff . Solid empty histograms: observational data taken as sub-
samples of the P06 compilation, according to the galactic regions presented in each panel.
– 27 –
Fig. 4.— Predicted globular-cluster metallicity distribution ΥGC,tot by luminosity at three
different projected galactocentric radii. Solid: innermost region; dotted: average galactic
(intermediate population); dashed: outermost part.
– 28 –
Fig. 5.— Shaded histogram: Predicted distribution of globular-cluster [Mg/Fe] values at
two different projected galactocentric radii (innermost and outermost regions). Solid empty
histogram: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel (see text).
– 29 –
Fig. 6.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for three different radial compositions (i.e. different fred/fblue). In this case, the
function f has an explicit dependence on [Z/H] (see text). The left panel shows both model
predictions and observations related to the central part of an elliptical galaxy. The right
panel shows the same quantities for cluster populations residing at r ≥ Reff . Solid empty
histograms: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel.
– 30 –
Fig. 7.— Shaded histogram: predicted total GC metallicity distribution ΥGC,tot by mass
for the < 1Reff shell, for a case in which a second episode of star formation, induced by
a gaseous merger, is taken into account (see text). Solid histogram: observations from
Puzia et al. (2006), their entire sample.
– 31 –
Fig. 8.— Shaded histogram: predicted total GC [Mg/Fe] distribution by mass for the < 1Reff
shell, for a case in which a second episode of star formation, induced by a gaseous merger,
is taken into account (see text). Solid histogram: observations by Puzia et al. (2006), their
entire sample.
– 32 –
Fig. 9.— Predicted globular-cluster metallicity distribution by mass as a function of the
(g−z) colour at two different projected galactocentric radii. Dashed: galactic core. Solid:
galactic halo out to 10 Reff .
	Introduction
	The Multimodality of Globular Cluster Systems
	Numerical Models of Globular Cluster System Formation
	A Spatially Resolved Chemical Evolution Model for Spheroid Galaxies
	The model
	The Chemical Evolution Code
	Globular Cluster Formation
	Results and discussion
	The Multi-Modality of Globular Cluster Systems in Elliptical Galaxies
	The Comparison Sample
	A Simple Model
	Globular Cluster Metallicity Distribution
	Globular Cluster [Mg/Fe] Distributions
	Metallicity Dependent Globular Cluster Formation
	The Ratio of Metal-poor to Metal-rich Globular Clusters
	The Role of the Host Galaxy Mass
	Merger-Induced Globular Cluster Formation
	Other Mechanisms responsible for Multimodality
	Conclusions

  The most massive elliptical galaxies show a prominent multi-modality in their
globular cluster system color distributions. Understanding the mechanisms which
lead to multiple globular cluster sub-populations is essential for a complete
picture of massive galaxy formation. By assuming that globular cluster
formation traces the total star formation and taking into account the radial
variations in the composite stellar populations predicted by the Pipino &
Matteucci (2004) multi-zone photo-chemical evolution code, we compute the
distribution of globular cluster properties as a function of galactocentric
radius. We compare our results to the spectroscopic measurements of globular
clusters in nearby early-type galaxies by Puzia et al. (2006) and show that the
observed multi-modality in globular cluster systems of massive ellipticals can
be, at least partly, ascribed to the radial variation in the mix of stellar
populations. Our model predicts the presence of a super-metal-rich population
of globular clusters in the most massive elliptical galaxies, which is in very
good agreement with the spectroscopic observations. Furthermore, we investigate
the impact of other non-linear mechanisms that shape the metallicity
distribution of globular cluster systems, in particular the role of
merger-induced globular cluster formation and a non-linear color-metallicity
transformation, and discuss their influence in the context of our model
(abridged)

Introduction
1.1. The Multimodality of Globular Cluster Systems
One of the most significant developments in the study of extragalactic globular cluster
systems (GCSs) was the discovery of bimodality in their color distributions (see Ashman & Zepf
1998; Harris 2001; West et al. 2004 and references therein). Today, we generally refer to glob-
ular clusters (GCs) belonging to the blue peak of the color distribution as metal-poor GCs
and to the red-peak members as the metal-rich sub-population. It is generally considered
that the presence of multiple modes implies multiple distinct GC formation epochs and/or
mechanisms and ties those directly into formation scenarios that have to describe the par-
allel assembly histories of GCSs and the diffuse stellar populations in their host galaxies. In
massive early-type galaxies the current GCS assembly paradigms view the origin of the two
color peaks from the perspective of either episodic star-cluster formation bursts triggered by
gas-rich galaxy mergers (e.g. Ashman & Zepf 1992), temporarily interrupted cluster forma-
tion (so-called in-situ formation, e.g. Forbes et al. 1997; Harris et al. 1998), and star-cluster
accretion as a result of the hierarchical assembly of galaxies (e.g. Côté et al. 1998).
While the majority of GCSs in early-type galaxies show clearly bimodal color distri-
butions, the general picture is much more complex, ranging from purely blue to purely
red color distributions (e.g. Gebhardt & Kissler-Patig 1999; Kundu & Whitmore 2001a,b;
Larsen et al. 2001; Peng et al. 2006). This complexity is exacerbated by the fact that color
– 3 –
bimodality is a function of galaxy mass and morphology, as less massive and later-type
galaxies tend to have single-mode blue (i.e. metal-poor) GC populations (e.g. Lotz et al.
2004; Sharina et al. 2005; Peng et al. 2006). Furthermore, color bimodality is also a func-
tion of galactocentric distance and is mainly due to the more extended spatial distribution
of the metal-poor sub-population relative to metal-rich clusters (e.g. Harris & Harris 2002;
Rhode & Zepf 2004; Dirsch et al. 2003, 2005).
1.2. Numerical Models of Globular Cluster System Formation
The aspect of GCS formation and assembly entered recently the domain of numerical
simulations of galaxy formation due to the increasing spatial resolution of these computa-
tions. For instance, Li et al. (2004) model GC formation by identifying absorbing sink parti-
cles in their smoothed particle hydrodynamics (SPH) high-resolution simulation of isolated
gaseous disks and their mergers. They find a bimodal globular-cluster metallicity distribution
in their merger remnant under the assumption of a particular age-metallicity relation. A key
finding of their merger simulation is a more concentrated spatial distribution of metal-rich
GCs with respect to the metal-poor sub-population in good agreement with observations.
Since their models of isolated galaxies produce a smooth age distribution (implying a smooth
metallicity and color distribution), Li et al. conclude that mergers are required to produce
a bimodal metallicity (i.e. color) distribution.
In a more detailed adaptive-grid cosmological simulation, Kravtsov & Gnedin (2005)
followed the formation of a star-cluster system during the early evolution of a Milky Way-size
disk galaxy to redshift z=3. Their model could reproduce the extended spatial distribution of
metal-poor halo globular clusters as observed in M31 and the Milky Way. However, because
their simulation does not follow the later evolution at z < 3 it is unclear whether it would
produce a metallicity bimodality and any significant age-metallicity relation.
An alternative, more statistical approach to modeling GCS assembly is to directly link
the mode of GC formation to the star-formation rate in semi-analytic models. Beasley et al.
(2002) were the first to explore this path by assuming that metal-poor GCs form in gaseous
proto-galactic disks while metal-rich GCs are created during gaseous merger events. Their
study showed that the observed globular-cluster color bimodality can only be reproduced by
artificially stopping the formation of metal-poor GCs at redshifts z & 5. By construction,
no spatial information on metal-rich and/or metal-poor GCs is provided in these models.
– 4 –
1.3. A Spatially Resolved Chemical Evolution Model for Spheroid Galaxies
Recently, Pipino & Matteucci (2004, hereafter PM04) presented a spatially resolved
chemical evolution model for the formation of spheroids, which successfully reproduces a large
number of photo-chemical properties that could be inferred from either the optical or from
the X-ray spectra of the light coming from ellipticals. The model includes an initial gas infall
and a subsequent galactic wind; it takes into account detailed nucleosynthesis prescriptions
of both type-II and Ia supernovae as well as low and intermediate-mass stars. It has been
extensively tested against the main photo-chemical properties of nearby ellipticals, including
the observed increase of the α-enhancement in their stellar populations with galaxy mass (e.g.
Worthey et al. 1992; Weiss et al. 1995). This is at variance with standard models based on
the hierarchical merging paradigm, which do not reproduce this trend (Thomas et al. 2002).
Since the PM04 model provides full radial information on the composite nature of
stellar populations that make up elliptical galaxies, the observation of different GC sub-
populations is, therefore, a new sanity check for the validity of this model. Moreover, we
recall that PM04 and, more recently, Pipino et al. (2006, hereafter PMC06) suggested that
elliptical galaxies should form outside-in, namely the outermost regions form faster as well
as develop an earlier galactic wind with respect to the central parts (see also Martinelli et al.
1998). This mechanism implies that the stars in massive spheroids form a Composite Stellar
Population (CSP), whose chemical properties, in particular their metallicity distribution,
changes with galactocentric distance.
Starting with the assumption that GC sub-populations trace the components of CSPs,
we will show how the observed multi-modality in GCSs can be ascribed to the radial vari-
ation in the underlying stellar populations. In particular, the observed GCSs are a linear
combination of GC sub-populations inhabiting a given projected galactocentric radius.
The paper is organized as follows: in Section 2 we briefly describe the adopted theo-
retical model; in Section 3 we compare the predictions with observations and discuss the
implications, while Section 4 presents the final conclusions.
2. The model
2.1. The Chemical Evolution Code
The chemical evolution code for elliptical galaxies adopted here is described in PM04,
where we refer the reader for more details. In this work, we present the results for a
galaxy with Mlum ∼ 10
11M⊙, taken from PM04’s Model IIb. This model is characterized
– 5 –
by a Salpeter (1955) IMF, Thielemann et al. (1996) yields for massive stars, Nomoto et al.
(1997) yields for Type-Ia SNe, and van den Hoek & Groenewegen (1997) yields for low- and
intermediate-mass stars.
An important feature of the PM04 model is its multi-zone nature, namely the model
galaxy is divided into several non-interacting spherical shells of radius ri, which facilitate a
detailed study of the radial variation of the photo-chemical properties of the GCS and its
host galaxy. In each zone i, the equations for the chemical evolution of 21 chemical elements
are solved (see PM04, Matteucci 2001).
The model assumes that the galaxy assembles by merging of gaseous lumps on short
timescales. The chemical composition of the lumps is assumed to be primordial. In fact, our
model assumes that the accretion of primordial gas from the surroundings1 is more efficient
in more massive systems, given their higher cross section per unit mass (see PM04). The
model galaxy suffers a strong starburst which injects a large amount of energy into the
interstellar medium, able to trigger a galactic wind, occurring at different times at different
radii, mainly due to the radial variation of the potential well, which is shallower in the
galactic outskirts. After the onset of wind activity the star formation is assumed to stop
and the galaxy evolves passively with continuous mass loss. In order to correctly evaluate
the amount of energy driving the wind, a detailed treatment of stellar feedback is included
in the code (that takes into account the stellar lifetimes). In particular, the energy restored
to the interstellar medium by both Type-Ia and Type-II supernovae has been calculated
in a self-consistent manner according to the time of explosion of each supernova and the
characteristics of the ambient medium (see PM04 for details). The potential well that keeps
the gas bound to the galaxy is assumed to be dominated by a diffuse and massive halo of
Dark Matter surrounding the galaxy.
In the following we adopt the standard star formation rate ψ∗(t, ri) = ν · ρgas(ri, t)
before the onset of the galactic wind (tgw), where ρgas is the gas density, ν the star-formation
efficiency; otherwise we assume that ψ∗(t > tgw, ri) = 0. We recall here that the adopted
star-formation efficiency is ν = 10Gyr−1, while the infall timescale is τ = 0.4Gyr in the
galactic core and τ = 0.01Gyr at one effective radius (of the diffuse light, Reff), respectively.
These values were chosen by PM04 in order to reproduce the majority of the chemical and
photometric properties of ellipticals such as: the 〈[Mg/Fe]〉−σ (e.g. Faber et al. 1992), the
Color-Magnitude (e.g. Bower et al. 1992), the Mass-Metallicity relation (e.g. Gallazzi et al.
2005) as well as the observed gradients in metallicity (e.g. Carollo et al. 1993), 〈[Mg/Fe]〉
1Since we lack a cosmological framework we cannot further specify the properties of the infalling primordial
– 6 –
(e.g. Mendez et al. 2005), and color (e.g. Peletier et al. 1990). Pipino et al. (2005) recently
extended this model to explain also the properties of hot X-ray emitting halos surrounding
more massive spheroids.
2.2. Globular Cluster Formation
The formation rate of GCs, ψGC , in the i-th shell is assumed to be directly linked to its
star formation rate ψ∗(t, ri, Zi) via a suitable function of time t, radius ri, and metallicity
Z, which represents some scaling law between star formation rate ψ∗ and the star cluster
formation ψGC and can be regarded as a GC formation efficiency. A similar relation be-
tween the average star formation rate per surface area and the star cluster formation was
recently found by Larsen & Richtler (2000) to hold in nearby spiral galaxies. In addition,
the efficiency of cluster formation in massive ellipticals appears to be constant, where the
mass ratio between the mass in star clusters and the baryons locked in field stars+gas is
ǫGC≈ 0.25% (McLaughlin 1999). Here we extend this surface density relation to 3-D space.
Moreover, PMC06 showed that at a given galactocentric radius model galaxies are made
of a CSP, namely a mixture of several simple stellar populations (SSPs) each with a single age
and chemical composition. The CSP reflects the chemical enrichment history of the entire
system, weighted by the star formation rate. We define the stellar metallicity distribution
Υ∗ as the distribution of stars belonging to a given CSP as a function of [Z/H].
We can then write the globular-cluster metallicity distribution ΥGC at a given radius ri
and time t as:
ΥGC(t, ri, Z) = f(t, ri, Z) ·Υ∗(t, ri, Z) , (1)
where f includes all the information pertaining to the connection between ψGC and ψ∗.
It is not trivial, and beyond the scope of the paper, to find an explicit definition for
f(t, ri, Zi), which basically carries the information on the internal physics of gas clouds where
GCs are expected to form. In the following we will show that, for a few and sensible choices
of f , the observed multi-modality in the color distribution of globular clusters may be driven
by the radial variations in the stellar population mix of ellipticals. We will first adopt a
constant function f (see Sec. 3.1) and then allow f to mildly vary with Z (see Sec. 3.2). No
absolute values for f will be given, since our formalism deals with normalized distributions.
In particular, the total ΥGC summed over all radial shells can be written as:
ΥGC,tot(t, Z) =
f(t, ri, Z) ·Υ∗(t, ri, Z) . (2)
– 7 –
Similar equations hold for other GC distributions as a function of either [Mg/Fe] or [Fe/H].
At this stage it is useful to recall that Υ∗(t, ri, Z) can be represented in two following
ways: i) as the fraction of mass of a CSP which is locked in stars at any given metallicity
(Pagel & Patchett 1975; Matteucci 2001). In the following we refer to this stellar metal-
licity distribution as Υ∗,m (MSMD: mass-weighted stellar metallicity distribution); ii) as a
fraction of luminosity of the CSP in each metallicity bin. This definition is closer to the
measurement as it can be directly compared to the luminosity-weighted mean Υ∗,l (LSMD:
luminosity-weighted stellar metallicity distribution) at a given radius (see Arimoto & Yoshii
1987; Gibson 1996). This classification is important since PMC06 showed that the Υ∗,m and
Υ∗,l might differ, especially at large radii, even for old stellar populations. The advantage
of GCSs, for which accurate ages are known, is that they directly probe the mass-weighted
distributions.
At this point it is useful to recall that our the adopted chemical evolution model divides
the galaxy in several non-interacting shells. In each shell the time at which the galactic wind
occurs is self-consistently evaluated from the local condition. In particular, we follow Mar-
tinelli et al. (1998) suggestion that gradients can arise as a consequence of a more prolonged
SF, and thus stronger chemical enrichment, in the inner zones. In the galactic core, in fact,
the potential well is deeper and the supernovae (SNe) driven wind develops later relative to
the most external regions. This particular formation scenario leaves a characteristic imprint
on the shape of both Υ∗,m and Υ∗,l and here we give some general considerations. In partic-
ular, we can explain the slow rise in the low metallicity tail of the distributions as the effect
of the initially infalling gas, whereas the onset of the galactic wind sets the maximum metal-
licity of the Υ∗,m and Υ∗,l. In general, the suggested outside-in formation process reflects in
a more asymmetric stellar metallicity distribution at larger radii, where the galactic wind
occurs earlier (i.e. closer to the peak of the star formation rate), with respect to the galactic
center. The qualitative agreement between these model predictions and the observed stellar
metallicity distributions derived at different radii by Harris & Harris (2002, see their Fig. 18)
for the stars in the elliptical galaxy NGC 5128 is remarkable. If confirmed from observations
in other ellipticals, the expected sharp truncation of Υ∗,m at large radii might be the first
direct evidence of a sudden and strong wind which stopped the star formation earlier in the
galactic outskirts (see PMC06 and Pipino, D’Ercole, & Matteucci, in preparation).
– 8 –
3. Results and discussion
3.1. The Multi-Modality of Globular Cluster Systems in Elliptical Galaxies
The general presence of multi-modal GCSs implies that their host galaxies did not form
in a single, isolated monolithic event, but experienced spatially and/or temporally separated
star-formation bursts. In the recent past, both semi-analytic and hydrodynamic simula-
tions of galaxy formation attempted to follow the process of GC formation (Beasley et al.
2002; Kravtsov & Gnedin 2005), but neither could produce a clearly bimodal MDF in their
simulated GCSs.
In this section we will show how to obtain a bimodal metallicity distribution function for
GCs ΥGC,tot starting from single-mode stellar metallicity distribution functions Υ∗(t, ri, Z)
(commonly known as G-dwarf-like diagrams) for the CSP inhabiting different radii of a
prototypical elliptical galaxy according to Equation 2.
3.1.1. The Comparison Sample
As stressed in the introduction, the multi-modality in GCSs varies as a function of host
galaxy properties (e.g. mass, morphological type, etc.). Here we try to match the distri-
butions resulting from the recent compilation of spectroscopic data by Puzia et al. (2006,
hereafter P06), which samples the typical bimodal color distribution of GCs in nearby galax-
ies (see also Puzia et al. 2004, 2005). This is illustrated in Figure 1, where we plot the
(V−I)0 color distribution of the P06 sample of GCs in elliptical galaxies (top panel) together
with those of GCs in NGC 4472 and the Milky Way (middle and bottom panel). NGC 4472
is the most luminous elliptical in the Virgo galaxy cluster and hosts a GC system with a
prototypical color bimodality (e.g. Puzia et al. 1999). To allow direct comparison with the
P06 sample, we use GCs in NGC 4472 that are brighter than V ≃ 22.5 since the P06 sample
includes only the brightest GCs in nearby early-type galaxies in order to maximize the S/N
of their spectra. The resulting color distribution is remarkably similar to the one of the P06
sample, which assures that the P06 sample includes a representative sampling of the GC
color bimodality in massive elliptical galaxies.
However, the comparison with the Milky Way GCs shows that the P06 sample covers
few of the most metal-poor GCs. Therefore, the bimodality which we refer to in the fol-
lowing may not be the same as the one observed in spirals or in some elliptical galaxies,
where a substantial population of metal-poor clusters with [Z/H] . −1.5 is present (e.g.
Gebhardt & Kissler-Patig 1999).
– 9 –
We do not include the dynamical evolution of GCs in our model, since we are considering
only the brightest (most massive, i.e. > 105.5M⊙, see also Puzia et al. 2004, A&A 415, 123)
clusters in nearby galaxies as comparison sample. The comparison sample includes GCs much
brighter than the typical turnover magnitude of the globular cluster luminosity function and
we, therefore, do not expect significant differential dynamical evolution for these massive
systems (see Gnedin & Ostriker 1997, for details). In fact, it has been shown (e.g. Fall
& Zhang, 2001) that the timescales for both evaporation by two body relaxation and tidal
stripping of star clusters is longer than a Hubble time for GCs more massive than ∼ 105.5M⊙.
In our model, the number of clusters formed in a star-formation burst of a given strength
is adjusted to match the observations. Hence, the absolute scaling of GC numbers is arbi-
trary, i.e., within physical limitations of the star formation rate any number of GCs can be
reproduced by adjusting the function f in Equation 2.
If, however, metal-poor and metal-rich GCs are on systematically different orbits and
experience significantly different dynamical evolutions the effect of tidal disruption might
be slowly changing relative GC numbers with time. Another complication is the variation
of the initial star-cluster mass function, in particular as a function of metallicity. Modeling
these effects requires detailed knowledge of the orbital characteristics and chemo-dynamical
processes that lead to star cluster formation, and goes far beyond the scope of this work.
We keep these potential systematics in mind, but expect negligible impact on our analysis.
3.1.2. A Simple Model
In order to make a first-order comparison between our model predictions and the ob-
served ΥGC,tot at t=13 Gyr, we first focus on the simple case in which:
ΥGC,tot(Z) = fred ·Υ∗(t = 13Gyr, r1, Z) +
fblue ·Υ∗(t = 13Gyr, r2, Z) , (3)
with fred , fblue = const and r1 = 0.1Reff , r2 ≥ 1Reff . The first term (red) corresponds
to a population typical of the galaxy core (well inside r < 1Reff). The second term (blue)
represents Υ∗ in the outer regions. In order to take into account the different amounts of
stars formed in each galactic region, we point out that the stellar metallicity distributions
entering Equation 2 were not normalized.
As a first step, we take several values for the weights fred , fblue in order to mimic
different mixtures of the two GC populations. In particular, we used the relative numbers of
– 10 –
the red (here identified as the metal-rich core population) and the blue globular clusters (the
halo metal-poor population) as a function of galactocentric radius for the elliptical galaxy
NGC 1399 (Dirsch et al. 2003). Our particular choice is driven by observationally motivated
values for the weights, although we realize that NGC 1399 is a quite peculiar, massive cD
elliptical and might not be representative of less massive
systems. In the context of this first step, the weights might reflect the effects of the
projection on the sky of a three-dimensional structure. However, we show below that the
results do not strongly depend on the weights. Therefore they might be interpreted as mean
values and could be changed if one decides to model a particular galaxy, with a different
ellipticity, inclination, and luminosity profile.
In Figure 2 we show the globular-cluster metallicity distribution ΥGC by mass (compu-
tation based on Υ∗,m) in two radial bins for three particular choices of weights. In particular
in the following we will use the ratios fred = 0.77,fblue = 0.23, fred = 0.60,fblue = 0.40 and
fred= fblue = 0.50 in order to define the theoretical innermost, intermediate and outermost
sub-sample of the GCS, respectively. These ΥGC will be compared against subsamples of
the P06 data, obtained by selecting GCs with either r < 1Reff (in the case of the innermost
population) or r ≥ 1Reff (for the intermediate and the outemost cases, respectively), unless
otherwise stated.
3.1.3. Globular Cluster Metallicity Distribution
In order to plot the different cases on the same scale we normalize each ΥGC by its
maximum value. In the left panel of Figure 2 the shaded histogram represents the innermost
population. Our predictions match the data very well, especially in the metal-rich slope
and the mean of the distribution. The same happens for the pure core populations, which
shows how the GCS might be used to probe the CSP in ellipticals. It should be remarked
that a second peak centered at super-solar metallicity appears in the distribution predicted
by our models, although not evident in the data of the particular radial sub-sample. The
right panel of Figure 2 illustrates model predictions which are more representative of the
galaxy as a whole (either at 1Reff , i.e. the intermediate population, or at several effective
radii, the outermost population), and we consider them as the fiducial case. These two
cases look quite similar to each other and have clear signs of bimodality in remarkable
agreement with the spectroscopic data (solid empty histogram, sub-sample of the P06 data
with r ≥ Reff). A Kolmogorov-Smirnov test returns > 99% probability that both model
predictions and observations are drawn from the same parent distribution in the left panel of
Figure 2. The right panel statistics gives a lower likelihood of 98.4% that both distributions
– 11 –
have the same origin, which is mainly due to the observed excess of metal-poor GCs at
large galactocentric radii compared to the model predictions. The prediction of a super-
solar metallicity globular cluster sub-population is entirely new and a result of the radially
varying and violent formation of the parent galaxy. Moving to the low-metallicity tail, we
predict slightly fewer low metallicity objects than expected from observations. But we recall
the systematics mentioned in Section 3.1.1.
In Figure 3 (left panel) we show the results for a pure core GCs, namely one in which we
adopt fred :fblue = 1:0. In this quite extreme case the observed GCs have been selected with
radius r < 0.5Reff . The histogram reflects the shape of a G-dwarf-like diagram expected for
a typical CSP inhabiting the galactic core. This finding is particularly important, because it
might offer the opportunity to resolve the SSPs in ellipticals, at variance with data coming
from the integrated spectra which deal with luminosity-weighted quantities. Whereas in
Figure 3 (right panel), the intermediate population is compared to a sub-sample of P06 GCs
with 0.5 < r < 0.5Reff . This is to show that the multimodality is not an artifact due to the
particular radial binning adopted in this paper.
Figure 4 shows the V -band luminosity-weighted ΥGC for which the computation is based
on Υ∗,l. This metallicity distribution has been obtained by converting the mass in each [Z/H]
bin of the previous figure into LV , by means of theM/LV ratio computed by Maraston (2005)
as a function of [Z/H] for 13 Gyr old SSPs. Due to the well-known increase of the M/LV
in the high metallicity tail of the distribution2, we notice in Figure 4 that now the second
peak has a smaller intensity in all the cases. The corresponding diffuse-light population goes
undetected in integrated-light studies. In any case, the conclusions reached by analyzing
Figure 2 are not significantly altered. We conclude that our analysis is not significantly
biased by some metallicity effect which may alter the shape of the observed ΥGC,tot by
luminosity. We stress the power of GCSs in disentangling stellar sub-populations in massive
ellipticals, due to their nature as simple stellar populations that can be directly compared
to SSP model predictions, unlike diffuse light measurements.
Even with this simple parametrization, where f in Equation 3 does not depend on
metallicity, we suggest that the bimodality for the metal-rich GCs is the result of different
shapes of Υ∗,m (and the Υ∗,l) at different galactocentric radii.
2See PMC06 for a comparison between G-dwarf like diagrams for Υ∗,m and Υ∗,l predicted for the same
– 12 –
3.1.4. Globular Cluster [Mg/Fe] Distributions
Finally, in Figure 5 we show the [Mg/Fe] distributions for GCs divided in radial bins as in
Figure 2. According to PMC06, these [Mg/Fe] distributions are narrower, more symmetric,
and exhibit a smaller radial variation with respect to the [Z/H] distributions. In any case, a
small degree of bimodality is still present. We point out the impressive agreement with the
spectroscopic observations by P06. There is a rather large discrepancy between data and
models at the high-[Mg/Fe] end. Hence, the corresponding Kolmogorov-Smirnov likelihood
tests return a probaility of 1% (for inner sample) and 95% (for the outer ones). If we limit
the model predictions to [Mg/Fe] < 0.8 dex, the agreement slightly improves, reaching a 10%
probablity in the inner region. However, the inner field data still does not reach the extreme
[Mg/Fe] values of the models. In fact, due to the monotonic decrease of the [Mg/Fe] as a
function of either metallicity or time (see PM04), the lack of low-metallicity GCs, evident
from Figure 2, translates into a lack of α-enhanced clusters.
The [Mg/Fe] bimodality of our model predictions and the match with the spectroscopic
measurements strongly imply that globular clusters in massive elliptical galaxies form on two
different timescales. Their chemical compositions are consistent with an early mode with a
duration of ∆t . 100 Myr and a normal formation that lasted for ∆t . 500 Myr. In fact,
according to the time-delay model (see Matteucci, 2001) and given the typical star formation
history of our model ellipticals, the [Mg/Fe] ratio in the gas - out of which the GCs form -
is quickly and continuously decreasing with time. We predict that the [Mg/Fe] ratio can be
higher than 0.65 dex (i.e. in the bins in which our predictions exhibit a deficit of GCs with
respect to the observed distribution) only in the first ∼ 100 Myr (see also Fig.3 in P06 and
related discussion). In fact, such a high value for the [Mg/Fe] can be attained only if very
massive type II SNe contribute to the chemical evolution, without any contribution from
either lower-mass type II or type Ia SNe. The normal formation, instead, is the one already
plotted in Fig. 5 and forms on a typical timescale of 0.5 − 0.7 Gyr. More quantitatively,
our initial theoretical GCMD predicts that only ∼ 4% of the GCS forms at [Mg/Fe] larger
than 0.65 dex. In order to improve the agreement with observations we require that the
above fraction should be increased to ∼ 12− 15%. Since star and globular cluster formation
are expected to be closely linked (e.g. Chandar et al. 2006) the same must be true for the
diffuse stellar population of such galaxies. We therefore foresee the presence of a similar
[Mg/Fe] bimodality in the diffuse light of massive elliptical galaxies. Unfortunately, there
are not direct observations confirming our suggestions, until the metallicity distributions for
the diffuse stellar component in ellipticals will become available for a number of galaxies.
Indeed, the detection of bimodality in the [Mg/Fe]-distribution might be a benchmark test
for our predictions.
– 13 –
We will still refer to multiple GC sub-populations. However, their differences ought
to be ascribed only to the fact that they are created during an extended (and intense) star
formation event during which the variation in chemical evolution is not negligible. The
radial differences originate from the fact that the galactic wind epoch is tightly linked to the
potential, occurring later in the innermost regions (e.g. Carollo et al. 1993; Martinelli et al.
1998). Moreover, PM04 and PMC06 found that also the infall timescale is linked to the
galactocentric radius. In particular, it lasts longer in the more internal regions, owing to the
continuous gas flows in the center of the galactic potential well. In particular, we recall that
in our model the core experiences a longer (∼ 0.7 Gyr) star-formation history with respect
to the outskirts where the typical star-formation timescale is ∼0.2 Gyr.
According to our models the metal-rich population of GCs in massive elliptical galaxies
may consist of multiple sub-populations which basically play the same role as the CSPs
populating each galactocentric shell in our framework of the global galaxy evolution. At the
same time, we point out the lack of our models to produce a significant fraction of metal-
poor GCs similar to the halo GC population in the Milky Way, with the caveat that the star
formation histories are very different. This, in turn, suggests that GCSs in giant elliptical
galaxies were assembled by accretion of a significant number of metal-poor GCs.
3.2. Metallicity Dependent Globular Cluster Formation
In this section we explore the approach outlined in Equation 2, by introducing the effect
of metallicity in the function f. In particular, we start by assuming that
f(t, ri, [Z/H]<−1)
f(t, ri, [Z/H]>−1)
= 2 , (4)
roughly following what was found for the GCS of the most nearby giant elliptical galaxy
NGC 5128 (Centaurus A) by Harris & Harris (2002, hereafter HH02) for their “inner field”,
regardless of the radius of the i-th shell. Since the final distributions are normalized, the
actual zeropoint of the function f is not relevant. Our model predictions are plotted in
Figure 6. We notice a modest increase of the low-metalliticy tail of the distribution with
respect to the simple picture sketched in Section 3.1 without metallicity dependence, as
well as a lower fraction of globular clusters populating the high-metallicity peak. Including
the metallicity dependence leads to an ambiguous change in agreement with the general
observed trend. Hence, no firm conclusions on the real need for a metallicity dependence
can be drawn. Similar results are obtained in the more realistic case in which f is a linearly
decreasing function of [Z/H].
– 14 –
At variance with HH02, we chose to adopt the same scaling irrespective of galacto-
centric radius, for the following reason. Despite the fact that the HH02 stellar metallicity
distributions Υ∗ as functions of [Z/H] confirm both the shape and the radial behavior of
our model predictions for the mass-weighted stellar metallicity distribution Υ∗,m (compare
their Fig. 7 with PMC06 Fig. 4), care should be taken when comparing their results for
Υ∗ as a function of [Fe/H]. The latter, in fact, had been obtained by assuming a particular
trend in the [α/Fe] as a function of galactocentric radius which disagrees with the results
of our detailed chemical evolution model. In particular, we find an offset of at least 0.2
dex in the sense that [Fe/H] HH02 ∼ 0.2+ [Fe/H] PM04 at a given metallicity ([Z/H]). This
disagreement becomes larger either at very low metallicity or at larger galactocentric radii,
where we expect a stronger α-enhancement. Once the PM04 value for [Fe/H] is adopted in
Fig. 18 of HH02, we find that: i) for the inner halo, the stellar Υ∗,m should be shifted by
∼ 0.2 dex toward lower metallicities, removing any metallicity effect, and ii) for the outer
halo the discrepancy between the stellar Υ∗,m and the ΥGC,tot should be reduced.
Nevertheless, we believe that some decrease with time of the function f could be mo-
tivated by theoretical arguments. In fact, recent work (e.g. Elmegreen & Efremov 1997;
Elmegreen 2004) shows that GCs of all ages preferentially form in turbulent high-pressure
regions. If we interpret the decrease in the efficiency of star formation (inside the gas clouds
that form GCs), as a function of the ambient pressure (Elmegreen & Efremov 1997) as a
proxy for the temporal behaviour of our function f, we find again a reduction of a factor
∼2−3 from the early high-pressure epochs to a late, more quiescent evolutionary phase.
3.2.1. The Ratio of Metal-poor to Metal-rich Globular Clusters
For our fiducial model we predict a ratio of metal-poor (namely with [Z/H] ≤ −1) to
metal-rich GCs of ∼0.2. Previous photometric surveys found that the typical value for GC
systems in elliptical galaxies is close to unity (Gebhardt & Kissler-Patig 1999; Kundu & Whitmore
2001a). Provided a linear color-metallicity transformation (see also Section 3.5), a possible
explanation for the discrepancy between our models and the observations might be obtained
by boosting the metal-poor population by a factor of f(t, ri, [Z/H]<−1)/f(t, ri, [Z/H]>−1) ≥
Another way to solve the discrepancy is to assume that all the missing globular clusters
have been accreted from the surroundings, e.g. from dwarf satellites (e.g. Côté et al. 1998).
We estimate the amount of the accreted metal-poor GCs, needed to achieve a ratio close to
1, as a factor of ∼4 of the number of globular clusters initially formed inside the galaxy.
– 15 –
3.3. The Role of the Host Galaxy Mass
A natural consequence of the scenario depicted in Sections 3.1 and 3.2 is that, at a
given galactocentric radius, the mean metallicity and [α/Fe] ratios of a GCS coincide with
the mass-weighted [〈Z/H〉∗] and [〈α/Fe〉∗] of the underlying stellar population, because the
GC quantities are calculated either from Υ∗,m or the Υ∗,l (see Eqs. 1 and 2 of PMC06),
unless the scaling function f is allowed to strongly vary with time. We expect this to happen
at least in the innermost GC sub-populations, in which the effects of the accretion of GCs
from the environment can be reasonably neglected. In particular, PM04 predict that more
massive galaxies should show higher [〈α/Fe〉∗] and [〈Z/H〉∗]. If accretion plays a negligible
role, we expect the same correlations for the total GC population with host galaxy mass for
the most massive systems, in agreement with current observations (e.g. van den Bergh 1975;
Brodie & Huchra 1991; Peng et al. 2006).
In fact, if we perform the same study of the above sections for a 1012M⊙ galaxy (see
Table 2 of PM04 for its properties), both peaks in ΥGC,tot shift their positions by about 0.2
dex to higher [Z/H]. This is in good agreement with the results of (Peng et al. 2006, see their
Figure 13 and 14). This trend holds for smaller objects as well. If we apply the procedure
to a 1010M⊙ galaxy (Model IIb of PM04), we find that the metal-rich peak shifts towards a
lower metallicity by 0.3 dex (with respect to our fiducial model with Mlum = 10
11M⊙), while
the other peak is now centered around [Z/H] = −0.8 dex. In particular, we find a faster
decrease in the mean metalliticy of the metal-poor GCs than for the metal-rich ones, again
in agreement with the Peng et al. results.
Interestingly, the ratio of metal-poor to metal-rich cluster increases up to ∼ 0.5 for
less massive halos. We recall that in the PM04 scenario, the low-mass galaxies are those
forming on a longer timescales and with a slower infall rate. Therefore, we suggest that
the combination of these factors is likely to at least partly explain the change of the GC
distributions in different galaxy morphologies. This is especially the case in dwarf galaxies,
where star formation is slow and still on-going, together with the fact that the probability
for a substantial change in the pressure of the interstellar medium relative to its initial values
is higher than in ellipticals, thus implying a much stronger variation of f with time.
3.4. Merger-Induced Globular Cluster Formation
It has been suggested that GC populations are produced during major merger events
which would lead to present-day ellipticals and their rich GCSs (e.g. Schweizer 1987; Ashman & Zepf
1992). Subsequent studies (e.g. Forbes et al. 1997; Kissler-Patig et al. 1998b) challenged this
– 16 –
view by pointing out the much higher SN and more metal-rich GCSs in early-type galaxies
compared to those of spiral and irregular galaxies, which are thought to represent the early
building blocks of massive ellipticals.
In the following, we study the impact of the merger hypothesis on the predictions of
our simulations. In order to do that, we extended the procedure sketched in the previous
sections to the merger models presented by Pipino & Matteucci (2006, hereafter PM06). In
this paper, the effects of late gas accretion episodes and subsequent merger-induced starbursts
on the photo-chemical evolution of elliptical galaxies have been studied and compared to the
picture of galaxy formation emerging from PM04; in particular the PM04 best model is
taken here as a reference. By means of the comparison with the colour-magnitude relations
and the [〈Mg/Fe〉V ]-σ relation observed in ellipticals (e.g. Renzini 2006), PM06 showed that
either bursts involving a gas mass comparable to the mass already transformed into stars
during the first episode of star formation and occurring at any redshift (major mergers), or
bursts occurring at low redshift (i.e. z ≤ 0.2) and with a large range of accreted mass (minor
mergers), are ruled out. The reason lies in the fact that the chemical abundances in the ISM
after the galactic wind (and before the occurrence of the merger) are dominated by Type
Ia SN explosions, which continuously enrich the gas with their ejecta (mainly Fe). When
the merger-induced starburst occurs, most stars form out of this enriched gas (thus, e.g.,
lowering the total [〈Mg/Fe〉]); at the same time, we expect the metallicities of GCs formed
out of this gas to be on average higher and their [Mg/Fe] ratios to be lower than those of
the bulk of stars and GCs formed in the initial starburst.
In this work we present the case in which the galaxy accretes a gas mass Macc = Mlum
at tacc = 2 Gyr (i.e. ∼1 Gyr after the onset of the galactic wind). We make this choice for
several reasons: i This model is quite similar to the PM06 models b and g, which were among
those in good agreement with observations of the diffuse galaxy light properties. ii) The
formation epoch of the bulk of these second generation GCs cannot occur &2 Gyr later than
tgw, because the majority of GCs in the most massive elliptical galaxies studied today appear
old within the age resolution of current photometric (∆t/t ≈ 0.4−0.5) and spectroscopic
studies (∆t/t ≈ 0.2−0.3). Finally, the composition of the newly accreted gas is assumed to
be primordial (see PM06 for a detailed discussion), but we remark that we reach roughly the
same conclusion in the case of solar composition, in order to mimic some pre-enrichment for
the newly accreted gas. We point out that, lacking dynamics, PM06 presented their results
for one-zone models. Therefore, in this section we are considering Equation 2 limited to only
one shell. In this way we can check whether the single merger hypothesis alone is enough to
produce some bimodality in the total globular-cluster metallicity distribution ΥGC,tot, and if
it is consistent with the predictions based on our fiducial model described in Section 3.2.
– 17 –
We show our results in Figure 7 and 8. We notice a clear change in the overall shape of
the metallicity distribution ΥGC,tot with respect to the cases shown in the previous sections, in
the sense that now ΥGC,tot is narrower and dominated by objects with super-solar metallicity
(and sub-solar [Mg/Fe] ratios) with a dominant population at [Z/H] ≈ 0.1, which is not
prominent in the observations of P06. The high-metallicity globular cluster populations
dominate the metallicity distribution which is at variance with both the results from previous
sections and the observations.
Our merger model does not include the accretion of globular clusters that were already
formed within the accreted satellite galaxies. The inclusion of this effect could remedy the
match between models and observations at low metallicities, as the typical GC in a dwarf
galaxy is metal-poor (e.g. Lotz et al. 2004; Sharina et al. 2005) and their addition to the
initial GC population would enhance the total number of metal-poor GCs and improve the
fit to the data. However, these clusters need to be α-enhanced to match the observations.
The impact of GC accretion on our post-merger model predictions will be studied in detail
in a future paper. Here, we remark that the time at which the purely gaseous subsequent
merger event can occur (which does not import already formed GCs), is limited by the
onset of the galactic wind, after which the type-Ia SNe dominates the nucleosynthesis, and
needs to be completed at tmrg . 1 − 2 Gyr after the first starburst. However, this time
constraint implies that such merger events would overlap with the initial starburst and be
mostly indistinguishable from each other. Such a scenario closely resembles the Searle-Zinn
scenario (Searle & Zinn 1978), in which galaxy halos are formed from the agglomeration of
gaseous protogalactic fragments. Later merger events are excluded in our models, as they
would produce GCs with sub-solar [Mg/Fe] ratios which is at variance with the observations.
Note also that the fraction of GCs at [Z/H]< −1 can be recovered in our models only
if the cluster formation at low metallicity is enhanced (e.g. using a value of 10 instead of 2
in eq.4). However, even in the case in which we adopt some f(Z) strongly declining with
total metallicity, which may alter the shape of ΥGC,tot enhancing the low-metallicity tail and
thus improving the agreement with observations, the position of both super-solar metallicity
peaks will not change, remaining at variance with the data.
3.5. Other Mechanisms responsible for Multimodality
The picture emerging from our analysis is far from being the general solution to ex-
plaining the complexity of GC color distributions, and it suggests only a scheme in which
multiple mechanisms could be at work together, either broadening or adding features to the
observed distributions.
– 18 –
For instance, Yoon et al. (2006) suggested that the color bimodality could arise from the
presence of hot horizontal-branch stars (so far not accounted for in SSP model predictions)
that results in a non-linear color-metallicity transformation producing two color peaks from
an originally single-peak metallicity distribution. We tested this scenario on our fiducial
model GC metallicity distribution, by applying to each SSP the following transformation
from [Fe/H] to the (g − z) color:
(g − z) = α + β [Fe/H] + γ [Fe/H]
+δ [Fe/H]3 + ǫ [Fe/H]
The numerical values of the coefficients are given in Table 1 and the relation was adopted from
Yoon et al. (2006) and is consistent with the best-fit relation presented in their Figure 1b.
We show our results in Figure 9.
Since we start from symmetric metallicity distributions, the non-linear transformation
seems to work and produce a color bimodality for the CSP inhabiting the < 10Reff shell
(Figure 9, solid line), although the bimodality is slightly exaggerated compared to real data
(see Figure 1). In fact, a look at the color distribution which we obtained for the sole
0.1Reff shell reveals that it still has one peak and is roughly symmetric (Figure 9, dashed
line). Obviously, since the (g − z)− [Fe/H] relationship is meant to explain the GCs color
bimodality without invoking any other effect, we did not combine the two histograms, either
according to Eq.2 or to Eq. 3 in our models, as we are comparing metallicity distributions
to spectroscopic measurements.
It is of great importance to investigate this transformation with large and homoge-
neous data sets that cover a wide enough metallicity range to allow a robust analysis of
the non-linear inflection point in the color-metallicity transformation. However, as a re-
sult of Figure 9, we point out that the color bimodality typically found for GCSs in massive
early-type galaxies might be only partly due to a non-linear color-metallicity transformation.
Another effect put forward by, e.g.,Recchi & Danziger (2005) is the claim that GCs
might have undergone a self-enrichment phase at the early stages of their formation, and
Table 1. Numerical values of coefficients used in Equation 6.
coefficient numerical value
α 1.5033
β 0.172774
γ −0.623522
δ −0.453331
ǫ −0.089038
– 19 –
therefore some GCs could have experienced a boost in metallicity which would be not rep-
resentative of the metallicity of their parent gas cloud. Finally, as already mentioned above
in Section 3.4, some GCs residing in the outermost regions of the galaxies (e.g. Lee et al.
2006) could have experienced entirely different chemical enrichment histories at the time
of their formation and later been added to a more massive system through accretion (e.g.
Côté et al. 1998). The inclusion of these effects goes far beyond the scope of this work, but
we remind the reader that all the aforementioned effects might influence the interpretation
of any globular cluster color and metallicity distribution.
4. Conclusions
By means of the comparison between PM04’s best model predictions for the radial
changes in the CSP chemical properties and the recent spectroscopic data on the metallicity
distributions of extragalactic GCSs from Puzia et al. (2006), we are able to derive some
conclusions on the GC metallicity distributions in massive elliptical galaxies. In particular,
we focused on the main drivers of the multi-modality that is observed in the majority of
GCSs in massive elliptical galaxies. Our main conclusions are:
• We show that the observed multi-modality in the GC metallicity distributions can be
ascribed to the radial variation in the underlying stellar populations in giant elliptical
galaxies. In particular, the observed GCSs are consistent with a linear combination of
the GC sub-populations inhabiting different galactocentric radii projected on the sky.
• A new prediction of our models, which is in astonishing agreement with the spectro-
scopic observations, is the presence of a super-solar metallicity mode that seems to
emerge in the most massive elliptical galaxies. In smaller objects, instead, this mode
disappears quickly with decreasing stellar mass of the host galaxy.
• Our models successfully reproduce the observed [Mg/Fe] bimodality in GCSs of mas-
sive elliptical galaxies. This, in turn, suggests a bimodality in formation timescales
during the early formation epochs of GCs in massive galaxy halos. The two modes are
consistent with an early (initial) and later (triggered) formation mode.
• Since the GC populations trace the properties of galactic CSPs in our scenario, we
predict an increase of the mean metallicity of the cluster system with the host galaxy
mass, which closely follows the mass-metallicity relation for ellipticals. Moreover, we
expect that a major fraction of the GCs (i.e. those born inside the galaxy) follows an
age-metalliticity relationship, in the sense that the older ones are also more α-enhanced
and more metal-poor.
– 20 –
• The role of host galaxy metallicity in shaping the observed GC metallicity distribution
is non-negligible, although its effects have been estimated to change the function f ≃
ψGC/ψ∗ by a factor of ∼ 2 − 5, in order to match the sample of Puzia et al. (2006).
Either a non-linear color-metallicity transformation, or a stronger metallicity effect,
and/or accretion of GCs from the surrounding environment is needed to explain a
ratio of metal-poor to metal-rich GCs close to unity, as reported for ellipticals based
on results from photometric surveys.
• Merger models which include the later accretion of primordial and/or solar-metallicity
gas predict a shape for the GC metallicity distribution which is at variance with the
spectroscopic observations.
We thank the referee for a careful reading of the paper. A.P. warmly thanks S.Recchi
for useful discussions. A.P. acknowledges support by the Italian Ministry for University
under the COFIN03 prot. 2003028039 scheme. T.H.P. acknowledges support by NASA
through grants GO-10129 and GO-10515 from the Space Telescope Science Institute, which
is operated by AURA, Inc., under NASA Contract NAS5-26555, and the support in form of
a Plaskett Research Fellowship at the Herzberg Institute of Astrophysics.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 24 –
Fig. 1.— Color distributions of GCs in nearby, massive elliptical galaxies (Puzia et al. 2006,
top panel), in NGC 4472 (Puzia et al. 1999, middle panel), and the Milky Way, taken from the
February 2003 update of the McMaster catalog (Harris 1996, bottom panel). In order to allow
a robust comparison between the P06 and NGC 4472 sample, only GCs in NGC 4472 with
with luminosities brighter than V ≃ 22.5 mag are shown. The solid lines are Epanechnikov-
kernel probability density estimates with their bootstrapped 90% confidence limits.
– 25 –
Fig. 2.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for three different radial compositions (i.e. fred/fblue). The left panel shows both
model predictions and observations related to the central part of an elliptical galaxy. The
right panel shows the same quantities for cluster populations residing at r ≥ Reff . Solid empty
histograms: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel.
– 26 –
Fig. 3.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for two different projected galactocentric radii. The left panel shows both model
predictions and observations related to the pure core of an elliptical galaxy (namely fred :
fblue = 1 : 0). The right panel shows the same quantities for cluster populations residing
either at 0.5Reff < r < 1.5Reff . Solid empty histograms: observational data taken as sub-
samples of the P06 compilation, according to the galactic regions presented in each panel.
– 27 –
Fig. 4.— Predicted globular-cluster metallicity distribution ΥGC,tot by luminosity at three
different projected galactocentric radii. Solid: innermost region; dotted: average galactic
(intermediate population); dashed: outermost part.
– 28 –
Fig. 5.— Shaded histogram: Predicted distribution of globular-cluster [Mg/Fe] values at
two different projected galactocentric radii (innermost and outermost regions). Solid empty
histogram: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel (see text).
– 29 –
Fig. 6.— Predicted globular-cluster metallicity distribution ΥGC,tot by mass as a function
of [Z/H] for three different radial compositions (i.e. different fred/fblue). In this case, the
function f has an explicit dependence on [Z/H] (see text). The left panel shows both model
predictions and observations related to the central part of an elliptical galaxy. The right
panel shows the same quantities for cluster populations residing at r ≥ Reff . Solid empty
histograms: observational data taken as sub-samples of the P06 compilation, according to
the galactic regions presented in each panel.
– 30 –
Fig. 7.— Shaded histogram: predicted total GC metallicity distribution ΥGC,tot by mass
for the < 1Reff shell, for a case in which a second episode of star formation, induced by
a gaseous merger, is taken into account (see text). Solid histogram: observations from
Puzia et al. (2006), their entire sample.
– 31 –
Fig. 8.— Shaded histogram: predicted total GC [Mg/Fe] distribution by mass for the < 1Reff
shell, for a case in which a second episode of star formation, induced by a gaseous merger,
is taken into account (see text). Solid histogram: observations by Puzia et al. (2006), their
entire sample.
– 32 –
Fig. 9.— Predicted globular-cluster metallicity distribution by mass as a function of the
(g−z) colour at two different projected galactocentric radii. Dashed: galactic core. Solid:
galactic halo out to 10 Reff .
	Introduction
	The Multimodality of Globular Cluster Systems
	Numerical Models of Globular Cluster System Formation
	A Spatially Resolved Chemical Evolution Model for Spheroid Galaxies
	The model
	The Chemical Evolution Code
	Globular Cluster Formation
	Results and discussion
	The Multi-Modality of Globular Cluster Systems in Elliptical Galaxies
	The Comparison Sample
	A Simple Model
	Globular Cluster Metallicity Distribution
	Globular Cluster [Mg/Fe] Distributions
	Metallicity Dependent Globular Cluster Formation
	The Ratio of Metal-poor to Metal-rich Globular Clusters
	The Role of the Host Galaxy Mass
	Merger-Induced Globular Cluster Formation
	Other Mechanisms responsible for Multimodality
	Conclusions
