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11.1. Classical Scenarios

In Section 2.1 we described the three principal scenarios that have been suggested as explanations for GC bimodality: major disk-disk mergers, in situ formation through multiphase dissipational collapse, and dissipationless accretion. How do these models account for the other observed properties of GC systems? Here we discuss the arguments made in the literature for and against these scenarios, as well as additional constraints from newer data described in this article.

11.1.1. MAJOR MERGERS     As noted in Section 2.1, the observation of young massive star clusters in many merger remnants throughout the 1990s gave a significant boost to the major disk-disk merger model for GC bimodality (Ashman & Zepf 1992). While some of these objects definitely have masses and sizes that should allow them to evolve into old GCs (e.g., Maraston et al. 2004; Larsen, Brodie, & Hunter 2004), others may have abnormal IMFs that preclude their long-term survival (e.g., McCrady, Gilbert, & Graham 2003; Smith & Gallagher 2001; Brodie et al. 1998), though important uncertainties in dynamical mass estimates due to mass segregation remain (McCrady, Graham, & Vacca 2005). In a broader context, despite the fact that YMCs and GCs are remarkably similar in many respects, it remains unclear whether (after a Hubble time of evolution) young GC systems will have properties consistent with those of old GC systems in local galaxies. The issue here is that observations of intermediate-age GCs may be at odds with the expected signatures of a simple dynamical evolution scenario (see Section 8).

Even before color bimodality had been observed, several authors used GCs to constrain the feasibility of the disk-disk merger picture for forming Es. Harris (1981) and van den Bergh (1984) noted that typical Es had more populous GC systems than spirals. Massive disk galaxies have SN ~ 1; Es have SN ~ 2-5 depending on environment, with even higher values for brightest cluster galaxies (BCGs) like M87. This is often termed the "SN problem". Schweizer (1987) explicitly addressed this concern by suggesting that many new GCs might be formed in the merger. As has been pointed out by multiple authors, this will only raise the SN if GCs form with a higher efficiency relative to field stars than they did in the protogalactic era. Since GC formation efficiency appears to increase with star formation rate, SN may only increase if the star formation rate in a present-day merger is higher than it was when the GCs in spirals were originally formed.

Several other problems with the major merger model were pointed out in Forbes et al. (1997). For example, they showed that there is a correlation between SN and the fraction of metal-poor GCs, such that the highest SN galaxies also have the highest proportion of metal-poor GCs. However, the major merger scenario predicts the opposite behavior: the mechanism to increase the SN of spirals is the formation of new metal-rich GCs in the merger; this should result in larger metal-rich GC subpopulations in more massive Es. Ashman & Zepf (1998) gave a candid analysis of the then current situation on the merger front and suggested that the gEs that dominated the high SN end of the Forbes et al. relation could be expected to have augmented their metal-poor GC population by the accretion of lower-mass galaxies (see below) during their complex formation histories. Moreover, they pointed out that the SN values in the literature were likely to be very uncertain because so few galaxies had been scrutinized with high-quality wide-field imaging. As discussed in Section 3, more recent work confirms that SN values for Es tend to come down with improved observations. In general, however, there are still fewer metal-rich than metal-poor GCs in present-day Es, and this remains in conflict with the major merger prediction. Rhode et al. (2005; see Section 3.1) considered the SN (or T) values of the individual subpopulations and concluded that massive cluster Es cannot have been formed from mergers of local spirals, although some lower-mass field Es could still have formed in this manner. Harris (2001) reached essentially the same conclusion from an analysis of the required gas content and GC formation efficiencies.

Another constraint on the major merger model can be found in the metal-poor GC metallicity-galaxy luminosity correlation (Strader et al. 2004a). In the mean, the metal-poor GC subpopulations of spirals have lower metallicities than those of massive Es. This seems to be a strong argument against the major merger scenario. However, this conclusion does not take into account the expected effects of biasing - see Section 11.2. It is notable that even some low-mass dEs have bimodal GC color distributions that follow the same peak relations as massive galaxies (Section 10.2), even though these galaxies have presumably not suffered a major merger. So, even if major disk-disk mergers were a viable route to producing bimodality in some cases, they could not be the sole process in operation. In addition, the ages of metal-rich GCs in Es (see Section 4) imply a formation epoch z gtapprox 2. This restricts most putative major mergers to higher redshifts.

As discussed in Section 2.1, the Forbes et al. (1997) multi-phase collapse scenario arose as a response to issues with the merger model. There has been little observational evidence to date against the Forbes et al. scenario, but, to a considerable extent, this is because it made few specific predictions of observable quantities. Its usefulness was as a framework within which to consider alternative explanations for GC color bimodality, and it identified aspects of the picture still under consideration, e.g., the need to truncate GC metal-poor formation at high redshift. More recent scenarios described below in Section 11.2 are generally consistent with this broad framework.

We emphasize that the arguments presented here against the major merger scenario apply principally to the formation of massive Es from present-day spirals with relatively small bulges. Current GC observations are consistent with dissipational formation of Es at relatively high redshift (z gtapprox 2) - including major mergers, as long as the disk progenitors have higher SN than spirals in the local universe. Subsequent dissipationless merging could then form the most massive gEs, under the constraint of "biased" merging discussed in Section 11.2.

11.1.2. DISSIPATIONLESS ACCRETION     The accretion scenario of Côté et al. (1998) was explicitly designed to be consistent with hierarchical structure formation. It assumes a protogalactic GC metallicity-galaxy mass relation produced through a dissipational process at high redshift. The GC systems of present-day galaxies are envisaged to have formed through subsequent dissipationless merging. Since in this scenario the intrinsic GC metallicities of massive protogalaxies are quite high, such galaxies must accrete large numbers of metal-poor GCs from dwarf galaxies to produce bimodality. Côté et al. (2002) used Monte Carlo simulations to show that the acquisition of the necessary numbers of low-metallicity GCs required the low-mass end of the the protogalactic mass function to have a very steep slope (~ -2). However, even with such a steep mass function, Ashman, Walker, & Zepf (2006) found that, when they ran simulations similar to those of Côté et al., color distributions like those observed in massive galaxies occurred in only a small fraction (~ 5%) of their simulations. Another potential problem is that the accreted dwarfs would be expected to contribute many metal-poor field stars that are not observed, unless the dwarfs are primarily gaseous (e.g., Hilker 1998).

The fact that metal-poor GCs in dwarfs have much lower metallicities than those in massive Es (by 0.5-0.6 dex) would, at first sight, seem to be direct evidence against the accretion scenario. This argument was made in Strader et al. (2004a). However, this line of reasoning does not account for the effects of biased structure formation, which may be the key to properly understanding the implications of the metal-poor GC metallicity-galaxy mass relation.

As already emphasized, in the light of our current understanding of hierarchical galaxy assembly, all galaxy formation scenarios must be accretion/merger scenarios at some level. The major merger and the accretion models (as published) both provided an important focus for theoretical discussion and observational effort by making fairly explicit predictions against which the observations could be compared. The preponderance of new evidence now suggests that, while elements of each remain viable, the details are pointing us in new directions (see below).

11.2. Hierarchical Merging and Biasing: Recent Scenarios

Beasley et al. (2002)> explored GC bimodality in a cosmological context using the semi-analytic galaxy formation model of Cole et al. (2000), and this work contained elements of all three classic scenarios. While largely phenomenological, it makes the most specific predictions of any model proposed, and because the scenario is in the context of a full model of cosmological structure formation, it implicitly accounts for many of the issues discussed below (e.g., biasing). Metal-poor GCs were assumed to form in the early universe in gas disks in low-mass dark matter halos. As in Forbes et al. (1997), Beasley et al. found it necessary to invoke the truncation of metal-poor GC formation at high redshift (in this case, z > 5) in order to produce bimodality. The metal-rich GCs were generally formed during gas-rich mergers. Their predictions for the metal-rich subpopulation included: a correlation between GC metallicity and galaxy luminosity, significant age and metallicity substructure, and decreasing mean ages and metallicities in lower-density environments.

Following suggestions from Santos (2003), Strader et al. (2005) and Rhode et al. (2005) proposed hierarchical scenarios for GC formation intended to account for the metal-poor GC metallicity-galaxy mass relation and the correlation of metal-poor SN (or Tblue) with galaxy mass. Metal-poor GCs are proposed to form in low-mass dark matter halos at very high redshift, typically z ~ 10-15. Halos in high-density environments collapse first. As discussed in Strader et al., this scenario can reproduce the observed correlations with galaxy mass, given reasonable assumptions (including the truncation of metal-poor GC formation at high z, plausibly by reionization). It can also explain other observations, such as the radial distribution of metal-poor GCs (Moore et al. 2006) and possibly the mass-metallicity relation for individual metal-poor GCs (Strader et al. 2006; Harris et al. 2006). Metal-rich GCs form in the subsequent dissipational merging that forms the host galaxy. When the bulk of this "action" took place is not well-constrained but, for galaxies at ~ L* and above, most GCs appear to have formed at z gtapprox 2 (Strader et al. 2005; Puzia et al. 2005). Some additional dissipationless merging for massive Es appears to be required, based on the evolution of the "red sequence" luminosity function of early-type galaxies from z ~ 1 to the present (Faber et al. 2005; Bell et al. 2004) and the dichotomy of core parameters (Section 4.1). The ages of metal-rich GCs do not constrain such dissipationless merging, but in the future the radial distributions and kinematics may offer interesting insights. We call this picture of GC formation the synthesis scenario.

It has been mentioned several times in the preceding sections that biasing is a key factor in understanding structure formation. Could the metal-poor GC subpopulations of massive Es have been built from major mergers of present-day lower-mass disk galaxies or by the accretion of many dwarf galaxies, since both dwarfs and spirals have metal-poor GCs of lower metallicity than those in massive Es?

To simultaneously accommodate: (i) the metal-poor GC metallicity-galaxy mass relation and (ii) the theoretical and observational evidence that most massive galaxies have undergone some degree of merging/accretion since z ~ 2, we must argue that the metal-poor GC relation was different at higher redshift. A present day L* galaxy cannot have been assembled from present-day sub-L* galaxies. Instead, the merging must have been biased, in the sense that galaxies with metal-poor GC systems that would lie above the relation connecting GC metallicity and host galaxy mass at z = 0 would tend to have merged into more massive galaxies by the present (see Figure 12 for a schematic diagram of this process). This can be understood as a direct result of hierarchical structure formation: high-sigma peaks in the most overdense regions (destined to become, e.g., galaxy clusters) collapse and form metal-poor GCs first. These metal-poor GCs will be more highly enriched than those forming in halos that collapse later, either because they have more time to self-enrich, or because the density of nearby star-forming halos is larger and they could capture more outflowing enriched gas. These first-forming metal-poor GCs will tend to be concentrated toward the center of the overdensity and will quickly agglomerate into larger structures. Similar mass fluctuations in the less-overdense outer regions will tend to be accreted into larger structures more slowly. Some may survive to form more stars and become dwarf satellites of the central galaxy. This picture, at least as it relates to dark matter halos, is well-understood and accepted. But the important point for GC formation scenarios is that these surviving dwarfs are not representative of the halos that merged to form the central galaxy. The latter collapsed first and may have very different star (and GC) formation histories from those that collapsed later.

Figure 12

Figure 12. A schematic plot of the evolution of the metal-poor GC metallicity-galaxy luminosity relation due to biased galaxy merging. The solid lines show the z = 0 relations for both subpopulations; the dashed line shows a conceptual metal-poor relation at higher redshift.

This process will operate on a variety of scales. For example, the dwarf satellites of the Galaxy have metal-poor GCs with lower metallicities than those of halo GCs in the Galaxy. Moreover, the disk or E galaxies that merged to form gEs like M87 and NGC 4472 must have had metal-poor GCs with metallicities higher than those typical for Es and spirals in the Virgo cluster today. The metal-poor GCs, although they formed at very high redshift, already "knew" to which galaxy they would ultimately belong. The metal-poor relation rules out merger and accretion models, but only in the local universe for structure forming at the present day. Nonetheless, it is consistent with hierarchical galaxy formation, and is a strong end constraint for any galaxy formation model. To illustrate biasing, Figure 13 shows two snapshots (z = 12 and 0) of a high-resolution dark matter simulation of the formation of a 1012 Modot galaxy (Diemand et al. 2005; Moore et al. 2006). Low-mass, high-sigma peaks collapse first in a filamentary structure and end up centrally concentrated in the final galaxy.

Figure 13

Figure 13. Two snapshots of a high-resolution dark matter simulation of the formation of a ~ 1012 Modot galaxy (Moore et al. 2006; Diemand et al. 2005). The top panel represents the simulation at z = 12, and the bottom panel represents the present day. The blue to pink colors indicate dark matter of increasing density, while the green regions are those at z = 12 with virial temperatures > 104 K (such that atomic line cooling is effective, and gas can cool to form stars). At z = 12, these green regions represent halos with masses 108 - 1010 Modot, and these same green particles are marked in the z = 0 snapshot. These high-sigma peaks collapse in a filamentary structure at high z but are concentrated toward the center of the final galaxy. The boxes can be identified as dwarf satellites of the final galaxy.

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