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It has been known for a long time that many dwarf galaxies have GC systems (e.g., Fornax dSph; Shapley 1939). In the Galaxy formation model of Searle & Zinn (1978) and in many subsequent studies of GC formation, it was envisioned that metal-poor GCs form in protogalactic dwarf-sized clumps (e.g., Harris & Pudritz 1994; Forbes et al. 1997; Côté et al. 1998; Beasley et al. 2002). The dwarf satellites around massive galaxies like the Milky Way can then be interpreted as the remnants of a large initial population of such objects, most of which merged into the forming protogalaxy. If this process happened at high redshift, most of the fragments could still have been be gaseous and thus have formed stars and/or contributed gas as they merged. At lower redshift the process could be primarily dissipationless, as envisioned by Côté et al. and seen in action through the present-day accretion of the Sgr dSph. What can GCs tell us about this process?

The faint end of the galaxy luminosity function is uniquely accessible in the Local Group. Forbes et al. (2000) provided a good census of GCs in Local Group dwarfs, which has changed only marginally since that time. The candidate GC in the dIrr Aquarius is apparently a yellow supergiant (D. Forbes, private communication), so the lowest-luminosity Local Group galaxies with confirmed GCs are the Fornax (MV = -13.1) and Sgr (MV = -13.9) dSphs, each of which has at least five GCs. The recently discovered CMaj dSph (Martin et al. 2004) appears to have at least four GCs whose properties are distinct from the bulk of the Galactic GC system (Forbes, Strader, & Brodie 2004). At least two of the GCs in each of Sgr and CMaj are of intermediate age and metallicity. The LMC has a subpopulation of old metal-poor GCs and a famous "age gap" between the old GCs and a subpopulation of intermediate-age GCs (~ 3 Gyr). It also hosts a number of younger clusters, some of which, like GCs, might be massive enough to survive a Hubble time (e.g., Searle, Wilkinson, & Bagnuolo 1980; van den Bergh 1994). The SMC has only one old GC but a more continuous distribution of massive clusters to younger ages (Mighell et al. 1998). Together these results suggest star formation histories that were at least moderately bursty (e.g., Layden & Sarajedini 2000). Lower-mass Galactic dwarfs (e.g., Leo I; MV ~ -12) do not have GCs. Less is known about the GC systems of similar-mass M31 dwarfs. Grebel et al. (2000) suggest a candidate GC in And I (MV ~ -12), but this GC could be a contaminant from M31. Outside the Local Group, Sharina et al. (2003) spectroscopically confirmed a GC in the M81 dSph DDO 78, which has a mass intermediate between Fornax and And I. Karachentsev et al. (2000) identified candidate GCs in a number of other M81 dwarfs, but these have not yet been confirmed.

As discussed in Strader et al. (2005), these observations put important constraints on the minimum mass of halos within which metal-poor GCs could form. Fornax and Sgr have total masses of gtapprox 108 Modot (Walcher et al. 2003; Law et al. 2005) and the total mass estimate for And I, assuming it has a similar M/L ratio, is a few × 107 Modot. This suggests that, at least in a relatively low-density group environment, GCs formed in halos with minimum masses of ~ 107-108 Modot. Whether GCs typically form in groups of GCs or alone is unknown. Fornax and Sgr each have several GCs, and the dIrr NGC 6822 (MV ~ -15.2) has up to three old GCs, though two of these are located far from the main body of the galaxy (Cohen & Blakeslee 1998; Hwang et al. 2005). The dIrr WLM (MV ~ -14.5) has only one old GC, which is metal-poor (Hodge et al. 1999). A caveat to these arguments is that in some models (e.g., Kravtsov, Gnedin & Klypin 2004), present-day dwarf satellites have undergone significant stripping of dark matter, and may have been much more massive initially (gtapprox 109 - 1010 Modot). However, detailed comparisons between observed velocity dispersion profiles and numerical simulations suggest little mass loss due to tidal stripping for well-studied Galactic dSphs (Read et al. 2006). It is important to realize that differences in baryonic mass loss (e.g., due to stellar feedback; Dekel & Silk 1986) may modify the amount of stellar mass in galaxies of similar halo mass. GC kinematics (see Section 10.3) offer one of the best routes to directly determine the total masses of dwarfs outside the Local Group.

10.1. Specific Frequencies and Luminosity Functions

GC systems were discovered around 11 Virgo dwarf ellipticals (dEs 2) using ground-based (CFHT) imaging (Durrell et al. 1996). The SN of these galaxies is relatively high, ~ 3-8, and the GC systems are very centrally concentrated: most GCs are within < 30" (2 kpc) at the distance of Virgo, while a typical dE has a half-light radius ltapprox 1 kpc. Strader et al. (2006) obtained radial distributions that were consistent with these earlier results, except for a few bright dEs (MV ltapprox -18) where the outermost GCs were found at 7-9 kpc. This is near the limit of the radial coverage of HST/ACS at the distance of Virgo, so it is possible that GCs may be found at even larger radii.

Miller et al. (1998) used HST/WFPC2 snapshot imaging to explore the specific frequencies of a large sample of dEs in the Virgo and Fornax clusters, including galaxies with luminosities as faint as MB ~ -13. They found a dichotomy between nucleated (dE,N) and non-nucleated (dE,noN) galaxies. dE,noN dwarfs appeared to have low SN values (~ 3), independent of galaxy luminosity. dE,N galaxies had higher SN and showed an inverse correlation between SN and luminosity. It has been suggested that dE galaxies may have originated as dIrrs or low-mass disk galaxies (e.g., Moore, Lake, & Katz 1998; see discussion below). Miller et al. argued that few dE galaxies could have formed in this manner, as the SN values even for dE,noN galaxies are larger than expected from age-fading such hosts.

Strader et al. (2006) revisited these findings in an HST/ACS study of Virgo Es which included 37 dEs. 32 of these have structural parameters consistent with "true" dEs; the other five appear to be faint power-law Es (Kormendy et al. 2006 and private communication). The ACS images offered superior areal coverage and depth compared to those available to Miller et al., but the Strader et al. sample spanned a smaller luminosity range: -15 ltapprox MB ltapprox -18. It was not possible to investigate the differences between dE,N and dE,noN galaxies, since many of the galaxies previously classified as dE,noNs either have faint nuclei or are power-law Es. There may be few true dE,noNs with MB ltapprox -15 in Virgo. Strader et al. found no strong correlation between galaxy luminosity and SN for either dEs or faint power-law Es. The faintest galaxies might have larger SN, but the effect is not strong. The lack of a SN-L trend could be due to the more restricted luminosity range of galaxies studied by Strader et al.compared to Miller et al.

Interestingly, a bimodal distribution of SN values was discernible in their sample. As shown in Figure 11, more than half of the galaxies were found to have SN ~ 1, while the SN values of the remainder ranged from 3 to 10, with a median at ~ 5. This difference spans the observed luminosity range and does not correlate with either the presence of a nucleus or the color distribution of the GCs. A natural interpretation of the SN differences is that they reflect multiple formation channels for dEs in Virgo. Mechanisms for forming dEs include "harassment", the cumulative effect of many high-speed galaxy encounters (Moore et al. 1996), stripping or age-fading of low-mass disks (Kormendy 1985), or processes similar to those responsible for the formation of more massive Es (this many be most applicable to the faint power-law Es). It is possible that the high SN galaxies (the Fornax dSph with SN ~ 29 is an extreme example) simply represent those in which stellar feedback during the first major starburst was very effective (e.g., Dekel & Silk 1986). However, if this is the case, a signature should be apparent in the GC color distributions. In particular, the presence of metal-rich GCs (see below) and a continuous (rather than bimodal) distribution of SN might be expected. Certainly, feedback will be increasingly important with decreasing galaxy mass, and would provide a simple explanation for a relation between SN and luminosity, should one be confirmed. Photometric, structural, and kinematic studies of these same dEs will be needed to discriminate among the many possible explanations.

Figure 11

Figure 11. Specific frequency (SN) of dEs (open circles) and faint power-law Es (filled circles) vs. parent galaxy MB. The size of the points is proportional to the fraction of blue GCs. There is only a weak trend of increasing SN with decreasing MB, and no substantial difference between the two galaxy classes. However, there is some evidence for a bimodal distribution of SN (Strader et al. 2006).

These same studies have also afforded the ability to study the GCLF in dEs. The power law slope (~ -1.8) measured by Durrell et al. (1996) for the massive end of the GCLF in their Virgo dEs is the same as that found in normal Es. However, they measured a GCLF turnover (MV ~ -7.0) that is fainter by ~ 0.4-0.5 mag than that typical for massive galaxies. This result may have been influenced by the difficulty of rejecting contaminants in ground-based data. Strader et al. (2006) constructed a composite of the 37 dEs in their HST sample, using the outer parts of the images to correct for background contamination. In contrast to Durrell et al., they found that the dE GCLF peak occurs at the same value as in the massive gEs in their sample (M87, NGC 4472, NGC 4649). This comparison was made in z, where there is little dependence of cluster M/L on metallicity over the relevant range, so the differences in GC color distributions between gEs and dEs should not affect the GCLF comparisons.

That the GCLF peaks for the dwarfs and the giants match so well in the Strader et al. study is perhaps puzzling. The theoretical expectation is that in low-mass galaxies dynamical friction will act to deplete the GC system, preferentially destroying massive GCs. Such GCs will spiral into the center in less than a Hubble time, forming or contributing to a nucleus. Lotz et al. (2001) performed a semi-analytic study of this phenomenon, and found that dynamical friction is expected to produce more luminous nuclei than observed. Strader et al. (2006) found that the luminosities of a subset of dE nuclei are consistent with formation through dynamical friction, but that the majority appear to be formed by a separate mechanism. This point, together with the similarity of the GCLF turnovers, implies that dynamical friction has not had a substantial effect on the GC systems of dEs. Lotz et al. (2001) suggested several explanations for the lack of observable consequences of dynamical friction, including extended dark matter halos around dEs, or tidal torquing of GCs (this latter explanation was also proposed for the Fornax dSph by Oh et al. 2000). Goerdt et al. (2006) have used numerical simulations to show that the dynamical friction timescale in Fornax is longer than a Hubble time if its dark matter halo has a core (instead of the cusp generically predicted in galaxy formation in LambdaCDM). Kinematic studies of GCs in dEs, such as those of Beasley et al. (2005), are also beginning to build a better understanding of the halo potentials of dwarf galaxies.

So far we have included little discussion of dIrrs. Their GC systems are quite difficult to study. Indeed, the contrast in our understanding of dEs and dIrrs is analogous to the information gap between Es and spirals. The relatively small GC systems of dIrrs, their ongoing star formation, and the resulting inhomogeneity of the background are serious observational challenges. A HST/WFPC2 study of 11 Virgo and Fornax dIrrs by Seth et al. (2004) found typical SN values of ~ 2, but uncovered two galaxies with much higher SN. Stellar M/L values are low in typical dIrrs, which suggests that the SN values will become much higher after nominal age-fading of the dIrr, as might be expected in transformation to a dE. However, many of the detected objects are unlikely to be old GCs. In the Local Group, the Magellanic Clouds and NGC 6822 each have a population of massive intermediate-age GCs (in addition to a small number of old GCs) that reflect the extended star formation histories of these galaxies. The same may be true of cluster dIrrs. Spectroscopy will probably be needed to determine the present fraction of intermediate-age GCs, which is crucial for isolating the differences in the formation histories of the various classes of dwarf galaxies. The combination of optical and NIR photometry, once the SSP models have been sufficiently calibrated for old GCs, offers a promising future tool for identifying younger clusters.

10.2. Color Distributions

The classical view of dwarf galaxy GCs is that they are uniformly metal-poor. This is supported by a "combined" metallicity distribution of old GCs in Local Group dwarfs (Minniti et al. 1996), which peaks at [Fe/H] ~ -1.8, 0.3 dex more metal-poor than that of the Galactic metal-poor GC subpopulation.

We now know that reality is more complicated. As noted above, the Sgr dSph (and perhaps the CMa dSph) have two GCs of intermediate metallicity and age. An HST/WFPC2 study of the color distributions of dEs in Virgo and Fornax (Lotz et al. 2004) revealed a rather wide spread in color, consistent with the presence of metal-rich GCs. However, it was not possible to distinguish subpopulations in their small GC samples.

Sharina et al. (2005) have published a study of GCs in a large sample of dSphs and dIrrs using a heterogeneous set of HST/WFPC2 images. The metal-poor GC peak appears to be ~ 0.1 redder in V - I than the peak found by Lotz, Miller, & Ferguson (2004) for their sample of dEs. There is no ready explanation for this finding, which is inconsistent with previous work. It may be that a photometric zero-point offset is to blame, as suggested by Sharina et al. themselves. The GC color distributions of both galaxy types have a tail to redder values. This may reflect a small subpopulation of metal-rich GCs, or could be due to contamination by background objects. There may also be a few metal-rich GCs in the dIrrs studied by Seth et al. (2004).

The existence of metal-rich GCs in dEs has been shown conclusively by Peng et al. (2006) and Strader et al. (2006). A large fraction of Virgo dEs, down to quite faint magnitudes (MB ~ -15), were found to have bimodal color distributions, analogous to those observed in massive Es. The slope of the metal-rich GC color-galaxy luminosity relation is not well-constrained at these low luminosities due to the small number of GCs associated with each galaxy. The new data points are consistent with either: (i) a linear extrapolation to lower magnitudes and bluer colors from the region of massive galaxies, or (ii) a slight flattening at the low mass end of the relation. It is reasonable then to ask whether these metal-rich GCs (or at least a subset) could have intermediate ages, like the two younger GCs discovered in the Sgr dSph. Beasley et al. (2005) obtained high-quality spectra for three metal-rich GCs in the Virgo dE VCC 1087. Their old ages are consistent with those of the metal-poor GCs within the errors. Although spectra of similar quality for a large sample of dEs clearly would be desirable, the results to date suggest that there is no obvious dichotomy in the color distributions of dEs and massive Es.

Using data from Peng et al. (2006), Forbes (2005) has pointed out a possible link between GC bimodality in dEs and the galaxy color bimodality observed in large surveys (e.g., Bell et al. 2004) below a critical mass of ~ 3 × 1010 Modot. Above this mass, nearly all galaxies in the Virgo Cluster Survey have bimodal GC systems; below this mass, an increasing fraction of galaxies have unimodal color distributions. One interpretation of this phenomenon is that the critical mass represents a transition from "cold", smooth accretion of gas into halos below the critical mass to "hot" accretion of gas that shocks at the virial radius and is unable to form stars (e.g., Dekel & Birnboim 2006).

10.3. Kinematics

Kinematic studies of GCs in dwarfs are challenging, principally because of the small GC systems and lack of luminous GCs. Puzia et al. (2000) found that the velocity dispersion of seven GCs in the luminous dE NGC 3115 DW1 suggested a relatively high M / LV ~ 22 ± 13. This could suggest the presence of dark matter, or that its parent S0 NGC 3115 is stripping the outermost GCs.

In the Virgo dE VCC 1087, the GCs rotate at ~ 100 km/s around the minor axis (Beasley et al. 2005). The sample of twelve GCs is dominated by metal-poor GCs, although it includes three GCs whose colors and spectroscopic metallicities are consistent with a metal-rich subpopulation (such subpopulations appear to be common in Virgo dEs; see Section 2 and 10.2). Its GC system has the largest rotational support of any galaxy studied to date, with v / sigma ~ 3.6, typical of a disk. This makes VCC 1087 a prime candidate for a dE that evolved from a disky dIrr. We note in passing that, although the LMC is often considered to have a rotating disk population of old metal-poor GCs (e.g., Schommer et al. 1992), van den Bergh (2004) has argued that the current data do not strongly discriminate between disk and halo kinematics for these GCs.

2 In deference to common usage, here we utilize the term "dwarf elliptical" for early-type galaxies with low luminosities (MB ltapprox -18). The structural parameters of many of these galaxies differ from those of "classical" Es (e.g., Kormendy 1985; Kormendy 1987) and may well suggest a different formation history. They are sometimes called spheroidal (Sph) galaxies. A small number of galaxies in this luminosity range have structural parameters consistent with power-law Es (see Section 4). Back.

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