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3.1. Specific Frequency

Harris & van den Bergh (1981) introduced specific frequency (SN = NGC × 100.4(MV + 15)) as a measure of the richness of a GC system normalized to host galaxy luminosity. This statistic has been widely used in toy models to assess the feasibility of galaxy formation mechanisms, e.g., the formation of gEs from disk-disk mergers. NGC was originally calculated by doubling the number of GCs brighter than the turnover of the GCLF. This definition makes both practical and physical sense. The faint end of the GCLF is usually poorly defined (suffering both contamination and incompleteness), and ~ 90% of the mass of the GC system resides in the bright half. This approach is implicit when fitting a Gaussian (or t5) functions to observed GCLFs, since observations rarely sample the faintest clusters.

SN comparisons among galaxies are only valid if all galaxies have the same stellar mass-to-light (M/L) ratios. For this reason, Zepf & Ashman (1993) introduced the quantity T - the number of GCs per 109 Modot of galaxy stellar mass. Since M/L is not generally known in detail for a particular galaxy, it is usually applied as a scaling factor that is different for each galaxy type, e.g., stellar M/LV = 10 for Es and 5 for Sbc galaxies like the Galaxy. In this section we quote observational results in terms of SN, but convert to T for comparisons among galaxies. An even better approach would be to directly estimate stellar masses for individual galaxies. Olsen et al. (2004) discuss the use of K-band magnitudes for this purpose.

Soon after the merger model was proposed, van den Bergh (1982) argued that elliptical galaxies could not arise from the merger of spiral galaxies, since spirals have systematically lower SN values than ellipticals. Schweizer (1987) and Ashman & Zepf (1992) suggested that this problem could be solved if new GCs were formed in the merging process. Observations of large numbers of YMCs in recent mergers seemed to support this solution. However, the SN will only increase through the merger if the GC formation efficiency is higher than it was when the existing GC system was formed. Studies of YMCs in nearby spirals (Larsen & Richtler 2000) suggest that galaxies with larger star formation rates have more of their light in young clusters, but it seems unlikely that local mergers are more efficient at forming GCs than in the gas-rich, violent early universe (see Harris 2001).

In recent years there have been few wide-field imaging studies of the sort needed to accurately estimate SN. Nonetheless, a trend has emerged that suggests reconsideration of some earlier results. Newer SN values tend to be lower than older ones. This revision stems, for the most part, from improved photometry that is now deep enough to properly define the GCLF turnover and reject contaminants. Imaging studies that cover a wide field of view are also important, because they avoid uncertain extrapolations of spatial profiles from the inner regions of galaxies. In some cases, like the Fornax gE NGC 1399, the luminosity of the galaxy was underestimated. When corrected, the SN value for this galaxy was revised downward by a factor of two, from SN ~ 12 to 5-6 (Ostrov et al. 1998; Dirsch et al. 2003).

It has been argued for some time that the evolutionary histories of central cluster galaxies are different than other Es of similar mass. Somehow this special status has resulted in high SN (or T). In addition, galaxies in high-density environments tend to have higher SN than those in groups. McLaughlin (1999) argued that high SN values in central galaxies arise because bound hot gas has been ignored for these galaxies, and that they do not reflect an increased GC formation efficiency with respect to other galaxies (see Blakeslee, Tonry, & Metzger 1997 for additional arguments in favor of the hypothesis that high SN is due to large galactic mass-to-light ratios). The properties of the E galaxy NGC 4636 may also be consistent with this view. Despite its relatively low-density environment, it has SN ~ 6, a value typical of central cluster galaxies (Dirsch et al. 2005). However, the galaxy has a dark matter halo (traced by a halo of hot X-ray gas) that is unusually massive for its luminosity.

The classic Harris (1991) diagram of SN vs. luminosity implied a monotonic increase of SN with galaxy mass for high-mass galaxies; that diagram also showed an increase toward low luminosities for dwarf galaxies. Both of these trends are less apparent in newer data. The situation for dwarf galaxies is discussed in more detail in Section 10, though it is worth noting here that it is difficult to make robust estimates of the number of GCs in low-mass galaxies outside of the Local Group. In our view, the run of SN with galaxy mass and environment remains uncertain. Additional discussion may be found in McLaughlin (1999) and the reviews by Elmegreen (1999) and Harris (2001).

3.1.1 SUBPOPULATIONS     Many of the problems with direct SN comparisons can be circumvented by considering the metal-poor and metal-rich subpopulations separately. In particular, recent mergers should only affect the metal-rich peak; independent of the details of new star formation, the SN of metal-poor GCs will not increase. Rhode, Zepf, & Santos (2005) have exploited this fact by studying T for metal-poor GCs in 13 massive nearby galaxies, nearly equally split between early- and late-type. In Figure 4 we show both Tblue and Tred vs. stellar galaxy mass. The Tblue values are taken from their paper, and the Tred data were kindly provided by K. Rhode. Rhode et al. found an overall correlation between Tblue and galaxy mass. The spirals are all consistent with Tblue ~ 1, while cluster Es lie higher at Tblue ~ 2-2.5. NGC 4594 also has Tblue ~ 2 (note in their classification NGC 4594 is an S0, not an Sa). Other field/group Es, including NGC 5128, NGC 1052, and NGC 3379, have values similar to those of the spirals. Since M / LV increases with galaxy mass (with a relation as steep as propto L0.10; e.g., Zepf & Silk 1996), it is reasonable to expect at least a weak trend of T with galaxy mass. However, Rhode et al. (2005) argue that this can account for only ~ 1/3 of the observed trend. Because no global GC color studies of M87 have been published, this galaxy was not included in the Rhode et al. study. Its SN value is ~ 3 times larger than the Virgo gE NGC 4472 (Harris, Harris & McLaughlin 1998). If both galaxies have similar total fractions of metal-poor GCs, the Tblue value for M87 would be ~ 8, though this value would be much lower if the mass of its hot gas halo were included along with the stellar mass (McLaughlin 1999).

Figure 4

Figure 4. Tblue and Tred (top and bottom panels, respectively) vs. galaxy mass for a range of spirals and Es (Rhode et al. 2005). Filled squares are cluster Es, open squares are field/group Es and S0s, open circles are field/group spirals, and the open star is the Sa/S0 galaxy NGC 4594. There is a general trend of increasing Tblue and Tred with galaxy mass (Data courtesy K. Rhode).

Based solely on the metal-poor GCs, these comparisons seem to rule out the formation of cluster gEs (and some massive Es in lower-density environments) by major mergers of disk galaxies. However, the relative roles of galaxy mass and environment are still unclear. Spirals in clusters like Virgo and Fornax and more massive field/small group Es remain to be studied in detail. The metal-poor GC subpopulations of some lower-mass Es in low-density environments are still consistent with merger formation. The biggest caveat to these interpretations is the effect of biasing - that structure formation is not self-similar. Present-day spirals are mostly located in low-density environments like loose groups and the outskirts of clusters. High-Tblue disk galaxies may have been common in the central regions of proto-galaxy clusters at high redshift but have merged themselves out of existence (or could, in some cases, have been converted to S0s) by the present day. Rhode et al. (2005) argue that the observed trend of high Tblue for cluster galaxies might be expected in hierarchical structure formation, since halos in high-density environments will collapse and form metal-poor GCs first (see also West 1993). If GC formation is then truncated (by reionization, for example), such halos will have a larger number of metal-poor GCs than similar mass halos in lower density environments. See Section 11 for additional discussion of biasing.

The Tred data show a similar correlation with galaxy mass, although with a smaller dynamic range. Note that the Tred values for the spirals (~ 0.5-1) are normalized to the total galaxy mass in stars. Most have bulge-to-total ratios of < 0.3, so if Tred had been normalized just to the spheroidal component, it would be substantially higher than plotted. These data appear consistent with the hypothesis of near-constant formation efficiency for metal-rich GCs in both spirals and field Es with respect to spheroidal stellar mass (Forbes, Brodie, & Larsen 2001; see also Kissler-Patig et al. 1997). The massive cluster Es have both higher Tred and Tblue. Again, however, because of the sample under study (with few field Es and no cluster spirals), it is unclear whether environment or mass is the predominating influence. This distinction is moot for the most massive Es since they are found almost exclusively in clusters, but is still relevant for typical Es.

Estimating the spread in Tred at a given galaxy mass should help constrain the star-formation histories of early-type galaxies. The stellar mass of an E might have been built entirely through violent, gas-rich mergers (with metal-rich GC formation), or, alternatively, many of the stars could instead have formed quiescently in mature spiral disks (with little metal-rich GC formation). Tred for the latter E should be significantly lower than for the former E.

3.2. Radial and Azimuthal Distributions

Most of the existing information on the global spatial distributions of GCs dates from older studies that could not separate GCs into subpopulations. The projected radial distributions are often fitted with power laws over a restricted range in radius, and it is clear that more luminous galaxies have shallower radial distributions (Harris 1986; see the compilation in Ashman & Zepf 1998). Considering the GC system as a whole, typical projected power law indices range from ~ -2 to -2.5 for some low-luminosity Es (this is also a good fit to the Galactic GC system; Harris 2001) to ~ -1.5 or a bit lower for the most massive gEs. However, it should be kept in mind that power laws provide a poor fit over the entire radial range. Most GC radial distributions have cores, and gradually become steeper in their outer parts. King models capture some of this behavior. In nearly all cases, the GCs have a more extended spatial distribution than the galaxy field stars.

There have been a few wide field imaging programs which considered GC subpopulations separately. In their study of the Virgo gE NGC 4472, Geisler et al. (1996) were the first to show clearly that color gradients in GC systems are driven solely by the different radial distributions of the subpopulations. The metal-poor and metal-rich GCs themselves show no radial color gradients. Rhode & Zepf (2001) found a color gradient for the total GC system in NGC 4472 interior to ~ 8', but no gradient when the full radial extent of the GC system (22' ~ 110 kpc) was considered. Dirsch et al. (2003) studied the GC system of the Fornax gE NGC 1399 out to ~ 25'(~ 135 kpc); this work was extended to larger radii by Bassino et al. (2006). The radial distributions of the two subpopulations are shown in Figure 5, along with the profile of the galaxy itself. The metal-poor and metal-rich subpopulations have power law slopes of ~ -1.6 and ~ -1.9, respectively. These differences persist to large radii, and lead to an overall color gradient in the GC system. The radial distribution of the metal-rich GCs is a close match to that of the galaxy light, and suggests that they formed contemporaneously.

Figure 5

Figure 5. Radial surface density distribution of metal-poor (open circles) and metal-rich (filled circles) GCs in the Fornax gE NGC 1399. The solid line is the scaled galaxy light profile in the R-band. The metal-rich GCs are more centrally concentrated, and closely follow the underlying galaxy light. The radial distribution of the metal-poor GCs is flatter; they dominate the GC system at large radii (Bassino et al. 2006).

Another notable finding is the rather abrupt truncation of GC systems at large galactocentric radius. Rhode & Zepf (2001) found that the surface density of GCs in NGC 4472 falls off faster than a de Vaucoleurs or power law fit at ~ 20'(~ 100 kpc). A similar drop-off occurs at 11' in NGC 4406 (Rhode & Zepf 2004), and at 9' in NGC 4636 (Dirsch et al. 2005). This may be evidence of truncation by the tidal field of the cluster.

Dissipationless mergers (whether disk-disk or E-E) tend to flatten the radial slopes of existing GC systems and create central cores (Bekki & Forbes 2005). These cores are observed and have sizes of a few kpc (Forbes et al. 1996). These results apply to pre-existing GCs, which certainly includes metal-poor GCs, as well as metal-rich GCs that existed before the merger. Thus, the trends predicted by the Bekki & Forbes simulation appear qualitatively consistent with observations. The observations are also consistent with more extensive merger histories for more massive galaxies; these gradually produce larger cores and flatter GC radial distributions. A desirable extension to this work would be to place these simulations in a cosmological framework in which merging occurs according to a full N-body merger tree. Also, as data become available, comparisons between observations and simulations could be restricted to metal-poor GCs. With this approach, any new metal-rich GCs that might have formed in the merger are irrelevant.

Ashman & Zepf (1998) noted that little was known about the two-dimensional spatial distributions of GC systems. Scant progress has been made in the intervening years. Existing data are consistent with the hypothesis that both subpopulations have ellipticities and position angles similar to those of the spheroids of their parent galaxies (e.g., NGC 1427, Forte et al. 2001; NGC 1399, Dirsch et al. 2003; NGC 4374, Gómez & Richtler 2004; NGC 4636, Dirsch et al. 2005). This also holds for the dEs in the Local Group (Minniti et al. 1996). It may be that in some galaxies (e.g., the E4 NGC 1052; Forbes, Georgakakis, & Brodie 2001) the metal-rich GCs follow the galaxy ellipticity more closely than the metal-poor GCs, but whether this is a common phenomenon is unknown. Naively, if the metal-rich GCs formed along with the bulk of the galaxy field stars, they should closely trace the galaxy light. The spatial distribution of the metal-poor GCs will depend in detail upon the assembly history of the galaxy.

3.3. Variations with Galaxy Morphology

3.3.1. SPIRALS     Our views on the GC systems of spiral galaxies are heavily shaped by the properties of the Milky Way (and, to a lesser degree, M31). This is discussed in detail in Section 5. A principal result from the Galaxy is that the metal-poor and metal-rich GCs are primarily associated with the halo and bulge, respectively. Forbes et al. (2001) introduced the idea that the bulge GCs in spirals are analogous to the "normal" metal-rich GCs in early-type galaxies, and that in both spirals and field Es the metal-rich GCs have SN ~ 1 when normalized solely to the bulge luminosity. The constancy of bulge SN appeared consistent with observations of a rather small set of galaxies (Milky Way, M31, M33, NGC 4594) but needed further testing.

Goudfrooij et al. (2003) provided such a test with an HST/WFPC2 imaging study of seven edge-on spirals, ranging across the Hubble sequence (the previously-studied NGC 4594 was part of the sample). Edge-on galaxies were chosen to minimize the effects of dust and background inhomogeneities on GC detection. Corrections for spatial coverage were carried out by comparison to the Galactic GC system; this does not appear to introduce systematic errors (see Goudfrooij et al. for additional discussion). Kissler-Patig et al. (1999) had previously found that one of these galaxies, NGC 4565, has a total number of GCs similar to the Galaxy. The small WFPC2 field of view and the low SN (or T) values of spirals as compared to Es resulted in the detection of only tens of GCs in some of the Goudfrooij et al. galaxies. While bimodality was not obvious in all of the color distributions, each galaxy had GCs with a range of colors, consistent with multiple subpopulations. Using a color cut to divide the samples into metal-poor and metal-rich GCs, Goudfrooij et al. found that all of the galaxies in their study had (i) a subpopulation of metal-poor GCs with SN ~ 0.5-0.6 (normalized to total galaxy light), and (ii) constant bulge SN, with the exception of the rather low-luminosity Sa galaxy NGC 7814, which appeared to have few GCs of any color. NGC 7814 was later the target of a ground-based study by Rhode & Zepf (2003) with the WIYN telescope. They found a significant metal-rich GC subpopulation with a bulge SN squarely in the middle of the range found for the other galaxies, which showed that the single WFPC2 pointing on the sparse GC system of NGC 7814 gave an incomplete picture of the galaxy. In this case even small radial leverage was important: Rhode & Zepf found that the surface density of GCs dropped to zero at just 12 kpc (3') projected.

Chandar, Whitmore, & Lee (2004) studied GCs in five nearby spirals. Their galaxies (e.g., M51, M81) tended to be closer and generally better-studied than those in the Goudfrooij et al. sample, but they were also at less favorable inclination angles. As a result, their GC candidate samples were more prone to contamination and more affected by (sometimes unknown amounts of) reddening. This was partially mitigated by their wide wavelength coverage, including (in some cases) U-band imaging, to help constrain the reddening of individual GCs. Chandar et al. found evidence for bimodal GC color distributions in M81 and M101. Interestingly, M51, which had rather deep imaging, showed no evidence for metal-rich GCs. They found that NGC 6946 and M101 had subpopulations of clusters with sizes similar to GCs but extending to fainter magnitudes; the typical log-normal GCLF was not seen. In NGC 6946 the imaging was quite shallow and these faint objects were found to be blue, suggesting that they might be contaminants. However, in M101 the imaging was deeper and the faint objects had red colors, consistent with old stellar populations. This may be evidence that some spirals possess clusters unlike those typical of Es, and these clusters may be related to the faint red objects seen in some S0s (see next subsection). Chandar et al. also compiled data from the literature on the GC systems of spirals, and argued that SN / T depends on Hubble type, but not on galaxy mass. This is consistent with the findings of Goudfrooij et al. (2003).

In principle, the SN value should depend on whether a particular bulge formed "classically", with intense star formation, or through secular processes in quiescent gas disks (e.g., Kormendy & Kennicutt 2004). In the former case we might expect a bulge SN similar to that found for Es, but in the latter case the star formation is likely to be sufficiently slow and extended that few or no GCs are formed along with the bulge stars. This may result in a rather low bulge SN compared to Es of similar mass. The implication is that all the bulges of galaxies in the Goudfrooij et al. sample formed predominantly through the "classical" route. The generally old ages of the metal-rich GCs in spirals (see Section 4) is evidence that the majority of bulge star formation, by whatever mechanism, happened at relatively early epochs.

Kormendy & Kennicutt (2004) argue that a large fraction of spiral bulges are built by secular evolution, and that these "pseudobulges" are especially common in late-type spirals. The diagnostics for pseudobulges are many, but include cold kinematics, surface brightness profiles with low Sersic indices, and, in some cases, young stellar populations. It is worth emphasizing that many of these pseudobulges could be composite bulges with young to intermediate-age stars superposed on an old classical bulge. In this case, the bulge SN could serve as a diagnostic of the degree to which a given bulge can have been built by classical or secular processes. The Milky Way itself could be an example of such a bulge. Its bulge is dominated by an old stellar population, but has a rather low velocity dispersion for its mass. The kinematics of the metal-rich GCs could be consistent with association with either a bulge or a bar (Côté 1999).

3.3.2 S0s     The leading theory for the formation of most S0s involves their transformation from spirals as groups and clusters virialize (e.g., Dressler et al. 1997). This can occur in a variety of ways, including ram pressure stripping and minor mergers that disrupt the disk sufficiently to halt star formation. In this context, it may be more appropriate to compare the GC systems of S0s to those of spirals, rather than make the traditional comparison with Es. Nonetheless, the GC systems of S0s appear to be quite similar to those of Es when compared at fixed mass. Kundu & Whitmore (2001b) studied a variety of S0s with WFPC2 snapshot imaging, and in many galaxies found broad color distributions consistent with multiple subpopulations. Peng et al. (2006b) used deeper imaging from the ACS Virgo Cluster Survey and found color bimodality in nearly all of the massive S0s in their sample. These S0s fall right on the GC color-galaxy luminosity relations of the Es. If indeed S0s descend from spirals, this is yet another piece of evidence that massive galaxies of all types along the Hubble sequence have very similar GC color distributions, and hence are likely to have experienced similar violent formation processes at some point in their history.

One interesting finding so far confined to S0s was the serendipitous discovery of a new class of star cluster, now known informally as the Faint Fuzzies (FFs). These objects were first detected in the nearby (10 Mpc) S0 NGC 1023. Along with a normal, bimodal system of compact GCs, this galaxy hosts an additional population of faint (MV > -7) extended (Reff ~ 7-15 pc) star clusters. In deep HST/WFPC2 images, these objects are confined to an annular distribution closely corresponding to the galaxy's isophotes (Larsen & Brodie 2000). Spectroscopic follow-up with Keck/LRIS showed that the FFs are metal-rich ([Fe/H] ~ -0.5), old (> 8 Gyr), and rotating in the disk of the galaxy (Brodie & Larsen 2002). With old ages, inferred masses of ltapprox 105 Modot, and sizes ~ 5 times larger than a typical globular or open cluster, these objects occupy a distinct region of age-size-mass parameter space for star clusters. As a population, they have no known analogs in the Milky Way or elsewhere in the Local Group. Similar objects have been found in the S0 galaxy NGC 3384 (Brodie & Larsen 2002) and NGC 5195, a barred S0 interacting with M51 (Lee, Chandar & Whitmore 2005; Hwang & Lee 2006). Peng et al. (2006) found FFs in ~ 25% of the S0s in the ACS Virgo Cluster Survey. Due to biases in sample selection, however, this fraction is probably not yet well-constrained. The FFs have relatively low surface brightness, and their properties may be consistent with M propto R2 (unlike GCs, which show no M - R relation). In some cases, their colors are redder than those of the metal-rich GCs in the same galaxy, which may suggest higher metallicities.

Brodie, Burkert, & Larsen (2004) and Burkert, Brodie & Larsen (2005) showed that the properties of the FFs in NGC 1023 were consistent with having formed in a rotating ring-like structure and explored their origin. Numerical simulations suggest that objects with the sizes and masses of FFs can form inside giant molecular clouds, provided star formation occurs only when a density threshold is exceeded. Such special star forming conditions may be present during specific galaxy-galaxy interactions, in which one galaxy passes close to the center of a disk galaxy, precipitating a ring of star formation. They speculated that the FFs might then be signposts for the transformation of spiral galaxies into lenticulars via such interactions. Alternatively, such conditions might also occur in the inner resonance rings associated with the bars at the centers of disk galaxies. In this case, the old ages of the FFs would suggest that barred disks must have been present at early times.

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