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Let us now consider how the various models fare in explaining the GC systems of real ellipticals. I will focus on a comparison of two thoroughly-studied ellipticals: M49 and M87, the first- and second-ranked members of the Virgo cluster, respectively. Although they differ in V-band luminosity by only ~ 20%, the GC specific frequency of M87 exceeds that of M49 by a factor of 2-3 (Harris 1991). Together, these galaxies form a "second parameter" pair in terms of their GC systems, and any viable formation scenario must account for the observed differences and similarities.

Figure 2

Figure 2. Color distributions for GCs belonging to M87 and M49, based on HST photometry from Kundu et al. (1999) and Kundu & Whitmore (2001). The solid and dashed curves for the best-fit double Gaussians used to estimate the GC formation efficiencies given in Table 1. The relative numbers of MP and MR GCs in the two galaxies is remarkably similar, despite the factor of 2-3 difference in specific frequency.

The primary motivation of the Ashman & Zepf (1992) merger model was an explanation of the higher specific frequencies of early-type galaxies relative to disk galaxies. In this picture, mergers serve to increase specific frequency through the formation of MR GCs. Thus, galaxies with high specific frequencies - of which M87 is the prototype - are expected to have predominantly MR GC systems according to this model. In the specific case of M87, this "excess" population relative to M49 should amount to approx 7000 additional MR GCs.

As Figure 3 shows, this expectation is not borne out by the observations. The measured GC color distributions for the two galaxies (based on deep HST imaging in identical filters from Kundu et al. 1999 and Kundu & Whitmore 2001) are remarkably similar. Parameterizing each distribution with a double-Gaussian yields the percentages of MP and MR GCs given in Table 1. This table also give the total number of GCs belonging to each galaxy, Ntot, from McLaughlin (1999), who showed that the observed difference in specific frequency between these two galaxies is likely due to the greater mass in X-ray emitting gas in the vicinity of M87.

Figure 3

Figure 3. Kinematic properties of GCs in M87. The panels show smoothed profiles for the velocity dispersion, rotation amplitude, position angle of the rotation axis, and the ratio of rotation amplitude to line-of-sight velocity dispersion. The dashed and dotted lines in the third panels show the orientation of the galaxy's minor and major axes, respectively. Results for the MP GCs are shown on the left; MR GCs are on the right. Only those points that are separated by more than 90" appeq 6.5 kpc are independent. The dotted and solid curves show the 68% and 95% confidence intervals on measured parameters.

Defining the GC formation efficiency, epsilontot, as the total mass in GCs normalized to the total baryonic mass (i.e., stars and gas), McLaughlin found the GC formation efficiencies given in Table 1. The overall efficiency with which GCs formed in M87 and M49 are not only consistent with each other, they are indistinguishable from the "universal" GC formation efficiency of <epsilontot> = 0.26±0.05% found by McLaughlin (1999) from an analysis of nearly one hundred early-type galaxies (see also Blakeslee et al. 1997). In any event, it is clear from Table 1 and Figure 1 that the similar relative number of MP and MR GCs in the two galaxies is certainly at odds with the predictions of the merger model.

Table 1. GC Formation Efficiencies for M87 and M49

  M87 M49

Ntot 13,600±600 6,850±550
epsilontot 0.28±0.04% 0.23±0.05%
fMP 57±5% 54±5%
fMR 43±5% 46±5%
epsilonMP 0.16±0.03% 0.12±0.03%
epsilonMR 0.12±0.02% 0.11±0.03%

Combining the values of fMP and fMR from Table 1 with McLaughlin's best estimates for epsilontot in the two galaxies, I find the values of epsilonMP and epsilonMR given in Table 1. To within the uncertainties, the MP and MR GC systems have identical formation efficiencies. The observed values of epsilonMP are roughly consistent with the formation efficiency of MP GCs, epsilonMP = 0.2%, used by Beasley et al. (2002) in their semi-analytic simulations. However, their assumed value of epsilonMR = 0.7% exceeds the measured value by a factor of six. Strictly speaking, the GC formation efficiencies in Table 1 are measured relative to the baryonic mass, whereas those of Beasley et al. are measured with respect to the total mass (i.e., including dark matter). However, inside ~ 50 kpc, the R-band mass-to-light ratios of M49 and M87 are virtually identical, with UpsilonR ~ 35 (Côté et al. 2001; 2003), so the comparison should be valid in this case.

Now let us examine the kinematical properties of the two GC systems. A dynamical analysis of the M87 GC system based on Washington photometry and radial velocities for 278 confirmed GCs was presented recently in Côté et al. (2001) and a similar analysis for the M49 GC system, based on velocities for 263 GCs, is now underway (Côté et al. 2003). Figure 2 shows the radial variation in kinematic parameters (i.e., velocity dispersion, sigmap, projected rotation amplitude, OmegaR, position angle of the rotation axis, Theta0, and the ratio of rotation amplitude to velocity dispersion, OmegaR / sigmap) for the MP and MR GCs in M87. Global results for the two galaxies are presented in Table 2.

Table 2. Kinematics of GC Subpopulations in M87 and M49

  M87 M49

  <sigmap> <OmegaR> <OmegaR / sigmap> <sigmap> <OmegaR> <OmegaR / sigmap>
  (km s-1) (km s-1)   (km s-1) (km s-1)  

All 383+31-7 171+39-30 0.45±0.09 316+27-8 48+52-26 0.15+0.15-0.08
MP 397+36-14 186+58-41 0.47+0.13-0.11 342+33-18 93+69-37 0.27+0.19-0.11
MR 365+38-18 155+53-37 0.43+0.14-0.12 265+34-13 -26+64-79 0.10+0.27-0.25

A detailed discussion of the results is beyond the scope of this review, but the main findings can be summarized as follows. In M87, both the MP and MR GC systems show significant rotation, with <OmegaR / sigma> approx 0.45. The MR GCs rotate about the galaxy's minor axis everywhere, as do the MP GCs beyond R ~ 15 kpc. Inside this radius, however, the MP GCs appear to rotate about the major axis. In the case of M49, the MP GCs show modest minor axis rotation everywhere, with <OmegaR / sigmap> appeq 0.27, while the MR GCs show little or no rotation. (The formal best-fit actually suggests that the MR GCs are counter-rotating).

Clearly, the GC subsystems in M87 and M49 show some rather dramatic kinematic differences. This apparent complexity becomes is all the more puzzling when one considers that the two spiral galaxies have the best studied GC systems, the Milky Way and M31, have <OmegaR / sigma> appeq 0.32 and <OmegaR / sigma> appeq 0.85 for the MP components, respectively. For their MR GC subpopulations, rotation is even more important, with <OmegaR / sigma> appeq 1.05 and <OmegaR / sigma> appeq 1.10 respectively (Côté 1999; Perrett et al. 2002).

What implications do these results have for GC formation models? First, the rotation observed for MP GCs in these galaxies suggests that, if these GCs did indeed originate in numerous, low-mass proto-galactic fragments as suggested by several of the "proto-galactic" models discussed above, then these low-mass fragments must first have coalesced into larger entities before being incorporated into the final galaxy (assuming that the observed rotation reflects the orbital angular momentum of the progenitor galaxies). Secondly, the rapid rotation among the MR GCs in M87 (and in the two spirals) indicates that their formation in mergers may be unlikely, given that angular momentum transport should produce a slowly rotating population. On the other hand, the MR GCs in M49 are consistent with no net rotation, suggesting that angular momentum transport during a major merger may have been effective in this case.

Finally, I consider the critical issue of ages for the MP and MR GCs subpopulations in these galaxies, focusing on two complementary techniques that have been brought to bear upon this issue: integrated-light spectroscopy, and the magnitude difference between the turnovers of the GC luminosity functions (LFs) for the GC subpopulations. The former technique yields absolute ages for the GC subpopulations, while the latter approach gives only their relative ages.

The various age measurements are summarized in Table 3, which reports DeltaT ident TMP - TMR for each GC subpopulation and, when available, the corresponding absolute ages. In the case of M87, the spectroscopy of Cohen et al. (1998) suggests an old age for both components, with no evidence for a trend between age and metallicity. On the other hand, Kundu et al. (1999) found a rather large age difference from the V and I luminosity functions, with the MR GCs being several Gyr younger. A more recent application of this technique, however, which relies on Strömgren photometry from from HST and makes use of the greater age sensitivity of the u-band, points to a very small age difference, in agreement with the spectroscopic results (Jordán et al. 2002). For M49, both techniques indicate that the GC subpopulations are coeval to within the measurement errors.

Table 3. Age Determinations for GC Subpopulations in M87 & M49

Galaxy TMP TMR DeltaT ident TMP - TMR Source Ref.

M87 13.7±1.8 12.7±2.2 +1.0±3.3 Spectra 1
    ...     ...   approx 3-6 LF (VI) 2
    ...     ...   +0.2±1.5(sys.)±2.0(ran.) LF (uvby) 3
M49   ...     ...   -0.6±3.2 LF (VI) 4
  14.5±4 13.8±6 +0.7±7.2 Spectra 5

REFERENCES: (1) Cohen et al. (1998); (2) Kundu et al. (1999); (3) Jordán et al. (2002); (4) Puzia et al. (1999); (5) Beasley et al. (2000).

The agreement between the photometric and spectroscopic results is generally encouraging. For these two galaxies at least, the MP and MR GCs seem to be truly old objects. Although the error bars remain large, it seems that, if GC formation in mergers of any sort - minor or major - has played the dominant role in producing the MR GCs in these galaxies, then the merger/assembly process must have occurred at high redshift (i.e., z gtapprox 4 in the currently fashionable LambdaCDM models). In my opinion, these results suggest that the disparate metallicities of the GC subpopulations in these galaxies likely reflect environmental differences in the local sites of GC formation.

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