Since GCs are more extended than the stellar light of galaxies, they are useful kinematic tracers of the dark matter halo at large galactocentric radii. GC kinematics also encode detailed signatures of the assembly histories of galaxies; the implications of such observations are just beginning to be understood. Large kinematic samples of GCs (> 50) have been observed in only four gEs: NGC 1399, M87, NGC 4472, and NGC 5128 (discussed above). Small samples have been studied in several other galaxies, but the numbers are too few to allow the subpopulations to be effectively separated. Aside from noting that there appear to be signatures of strong rotation in the S0s NGC 3115 (Kuntschner et al. 2002) and NGC 524 (Beasley et al. 2004), we will confine our detailed discussion to these four well-studied galaxies.
The largest sample of GC velocities at present exists for NGC 1399, the central gE in the Fornax cluster. Richtler et al. (2004) have analyzed kinematics for 468 GCs at projected radii of 2-9' (~ 11-49 kpc). The velocity dispersions for the metal-poor and metal-rich GCs are ~ 290 km/s and ~ 255 km/s, respectively, and do not appear to vary with galactocentric radius. They report a slight tangential bias for the metal-poor GCs, but both subpopulations are generally consistent with isotropic orbits. The larger dispersion for the metal-poor GCs is consistent with their extended spatial distribution. Neither subpopulation shows significant rotation, although a weak signature is observed in metal-poor GCs beyond 6'.
It has been suggested from simulations (Bekki et al. 2003) that NGC 1399 might have stripped the outermost GCs from the nearby E NGC 1404, leaving it with an anomalously low SN (NGC 1399 has a high SN of ~ 5-6, typical of cluster Es). Bassino et al. (2006) have found that three other Fornax Es - NGC 1374, NGC 1379, and NGC 1387 - all have SN lower than typical of cluster Es, and also suggest that they may have suffered GC loss to NGC 1399. New GC velocities for NGC 1399, out to ~ 80 kpc, show an asymmetric velocity distribution of the metal-poor GCs at these large radii (Schuberth et al. 2006). This could be interpreted as a signature of GCs that have been stripped from nearby Es but have not yet reached equilibrium in the NGC 1399 potential.
NGC 4472 has been studied by Zepf et al. (2000) and Côté et al. (2003), with ~ 140 and ~ 260 velocities, respectively, measured over projected radii of ~ 1.5-8' (~ 7-40 kpc). The velocity dispersions of the metal-poor and metal-rich GCs are ~ 340 km/s and ~ 265 km/s, respectively. The metal-poor GCs rotate around the galaxy's minor axis with a velocity of ~ 90-100 km/s; the metal-rich GCs show weak evidence for counter-rotation around the same axis. There is a hint that the outermost (beyond ~ 25 kpc) metal-poor GCs may rotate about the major axis, but this conclusion relies on few GCs. The orbits of both subpopulations are consistent with isotropy to the radial limit of the data.
The kinematics of GCs in M87 are rather different from those in either NGC 4472 or NGC 1399. From a sample of ~ 280 velocities, Côté et al. (2001) find that both the metal-poor and metal-rich GCs rotate around the minor axis at ~ 160-170 km/s, with respective velocity dispersions of ~ 365 and ~ 395 km/s, when averaged over the whole system. The metal-poor GCs actually appear to rotate around the major axis within ~ 16 kpc but switch to minor axis rotation only at larger radii. Côté et al. suggest that this change is due to the increasing gravitational dominance of the cluster potential beyond ~ 18 kpc. The GC system as a whole appears quite isotropic, but the data are consistent with a tangential bias for the metal-poor GCs and an opposing radial bias for the metal-rich GCs; these biases are poorly constrained in the present sample.
The results for four well-studied gEs (including NGC 5128, discussed in the previous section) present a heterogeneous picture. Although no two galaxies seem to be kinematically similar thus far, we will briefly discuss the extent to which the accumulated information can constrain galaxy formation. K. Bekki and collaborators have used numerical simulations to study the properties of GCs in merging galaxies. Bekki et al. (2002) found that, in disk-disk major mergers, newly formed metal-rich GCs are centrally concentrated and extended along the major axis of the remnant. Angular momentum transferred to the metal-poor GCs causes them to rotate and extend their spatial distribution. These results are strongly dependent on the numerical details of the simulations, and could change if, for example, a different prescription for star formation was used. Simulations of dissipationless major mergers for galaxies with both a disk and bulge extended these results (Bekki et al. 2005). However, the initial conditions (velocity dispersion and anisotropy) of the GC system strongly affect the outcome of such simulations. Pre-existing metal-poor and metal-rich GCs acquire significant amounts of rotation beyond ~ 10 kpc, regardless of the orbital properties of the merging galaxies. Mergers with larger mass ratios leave relatively spherical GC distributions with less rotation. With such a generic prediction of rotation, it is unclear how galaxies like NGC 1399, which shows no rotation in either subpopulation, could have been created. It may be that the merging histories of gEs leave a variety of complex rotational signatures, and that much of the observed differences are due to natural variations in remnant properties and projection effects.
It is instructive to consider the results of cosmological simulations of the assembly of dark matter and stellar halos of massive galaxies. Even though the GCs are more extended than the stellar light of the galaxy, they are still more centrally concentrated than the dark matter, so are expected to have a lower velocity dispersion than the dark matter at fixed radii (if the anisotropy of the dark matter and GCs are similar). While providing some constraints, present data sets are still too small to fully determine the anisotropy ( = 1 - v2 / vr2) of the GC system (e.g., Wu & Tremaine 2006). A wide range of numerical simulations suggest that a general relation holds between and galactocentric radius for both halo tracers and the dark matter: ~ 0 (isotropy) in the inner parts, with radial anisotropy increasing outward to ~ 0.5 at the half-mass radius of the tracer population (Hansen & Moore 2006; Dekel et al. 2005; Diemand, Madau, & Moore 2005; Abadi et al. 2005). Very large samples of GCs (~ 500-1000) will be needed to test these predictions.
Studies of lower-mass Es are also important, and several groups are pursuing hybrid approaches, using both GCs and planetary nebulae (PNe) to constrain the potential. Romanowsky et al. (2003) suggested, on the basis of PNe kinematics in three "normal" Es (NGC 821, NGC 3379, and NGC 4494), that these galaxies lacked dark matter. A more conventional interpretation is that the observed PNe originate in stars ejected during mergers and are on highly radial orbits (Dekel et al. 2005). GCs (especially those in the metal-poor subpopulation) are expected to have lower orbital anisotropy than PNe, due both to their extended spatial distribution and the increased probability of destruction for GCs on radial orbits. Two recent studies of GC kinematics in NGC 3379 suggest that the galaxy possesses a "normal" CDM dark halo and are more consistent with the Dekel et al. interpretation (Pierce et al. 2005; Bergond et al. 2006). Thus, GCs may be the best tracers of the mass distribution of Es at large radii.
7.2. Disk Galaxies
The best recent review of the kinematics of Galactic GCs is found in Harris (2001). The metal-rich GCs rotate at ~ 90-150 km/s, and the rotation rises out to a radius of ~ 8 kpc, beyond which there are few metal-rich GCs. This increasing rotational velocity may represent a transition from bulge to thick disk, though the maximum velocity of ~ 150 km/s is still less than expected for a typical thick disk in a massive spiral. There is little net rotation over the metal-poor subpopulation as a whole. Moreover, no individual radial bin of metal-poor GCs rotates, but somewhat surprisingly, a strong signature of prograde rotation (140 km/s) is seen in the most metal-poor GCs ([Fe/H] < -1.85). This effect is dominated by very metal-poor GCs in the inner halo. The degree of rotational support is similar in this very metal-poor group (v / ~ 1.2) to the total subpopulation of metal-rich GCs (~ 1.3).
M31 has been discussed above: the metal-rich GCs rotate with v / ~ 1.1, and the kinematic state of the metal-poor GCs remains unclear. If the identification of the disk objects as young clusters (no matter what the mass) is secure, then the old metal-poor subpopulation is probably pressure-supported.
The situation in M33 is also uncertain, since the ages of many HST-confirmed star clusters are unknown. Chandar et al. (2002) found that the old metal-poor GCs have a velocity dispersion of ~ 80 km/s and are not rotating. They suggested that there is a small population of old inner GCs with disk-like kinematics, but an adequate test of this must await a significant increase in the kinematic sample.
Olsen et al. (2004) have suggested that GCs in several Sculptor Group spirals have kinematics consistent with the rotating HI gas disks in these galaxies (in NGC 253, the kinematics are consistent with asymmetric drift from an initial cold rotating disk). Candidates were selected from outside the bright optical disk, so contamination from open clusters in the disk is unlikely to have occurred. Few GCs were observed in each galaxy, and the low systemic velocities of the galaxies inevitably biased the GC selection; those with low velocities cannot be efficiently distinguished from foreground stars. Nonetheless, even with this bias, the line-of-sight velocity dispersions of the GCs are low: from ~ 35-75 km/s out to ~ 10 kpc or so. Given the mixed evidence for old disk GCs presented thus far, this preliminary result is worth following up.
The disk galaxies present a somewhat cleaner kinematic picture than the Es, though the number of galaxies studied is still small. If indeed the metal-poor GCs in M31 turn out to be pressure-supported, then this appears to be a common feature of disk galaxies. In the two galaxies with bulges (M31 and the Galaxy) the metal-rich GCs have substantial rotational support. At the very least, these results can serve as valuable starting conditions for simulations of major mergers.