Annu. Rev. Astron. Astrophys. 1996. 34: 511-550
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2.4. Kinematics of the Oldest Clusters

If the LMC contained a dynamically hot halo surrounding an inner disk, the velocity dispersion of this halo would be between vcirc / 21/2 = 56 km s-1 and vcirc / 31/2 = 46 km/s, where vcirc = 79 km s-1 is the circular velocity of the H I disk (Freeman et al 1983; see the derivation of equation 4-55 in Binney & Tremaine 1987). Unexpectedly, Freeman et al (1983) found that the oldest LMC clusters had a much smaller velocity dispersion than expected from these arguments. This very important result implies that the oldest clusters do not populate a kinematically hot halo supported by its velocity dispersion. In fact, the oldest LMC clusters form a rotating disk system. The velocities available to Freeman et al (1983) implied that the oldest LMC population, although in a disk, was not in the same disk as the H I gas.

Olszewski et al (1991), Schommer et al (1992) have enlarged the sample of clusters and improved the observed cluster velocities. They confirmed that the oldest clusters were in a disk, and they eliminated the perceived difference between the old and young disks. They were able to derive a more precise kinematic solution, albeit with substantial errors due to the small number of old clusters. They found that the oldest clusters have a disk model solution in good agreement with the model fit to the H I gas, when velocities are corrected for the transverse motion of the LMC (Jones et al 1994) and when the oldest clusters superposed on the bar of the LMC are removed. This disk has v / sigma = 2. This old-disk model has a significantly smaller circular velocity than does the H I disk (50 vs 79 km s-1) and larger velocity dispersion (23 vs 10 km s-1). In an adiabatic sense, the lower rotation speed and higher velocity dispersion are consistent in that the circular velocity of the old component lags the disk, and that some of that energy is now in the z component.

There are several interesting aspects to this set of "disk clusters" in the LMC defined by the oldest clusters. First, we return to the question discussed in Section 2.3: What is the age of this set of oldest clusters? If the oldest LMC clusters are indeed a few Gyr younger than an ancient population, then their disk kinematics could be explained merely by the fact that the clusters were created during disk formation, well after the initial population finished forming. In this case, where is this putative ancient population? The only other obvious old population is the population of RR Lyrae variables. But as shown by Suntzeff et al (1992), the number of field RR Lyraes in the LMC is consistent with the luminous mass in the old clusters, if we scale from the same populations in the outer Galactic halo. It therefore seems reasonable to associate the RR Lyraes and the oldest disk clusters with the same population. We feel the most natural explanation is that given by Freeman et al: The LMC does not have a prominent hot (supported by its velocity dispersion) halo. An obvious test would be to measure the velocity dispersion of the RR Lyraes or of the most metal-poor field stars.

A second aspect of the old cluster disk is that the disk is relatively large. The average distance from the bar of the LMC is 3.9 kpc for the total sample of old clusters and 6.1 kpc for those clusters away from the bar. This radius is two to four times the LMC disk scale length (Bothun & Thompson 1988).

Third, there are few clusters beyond 8 kpc from the bar of the LMC. Even though the velocities of these clusters formally give the same disk solution as that of the H I gas, it would be good to find other tracers to derive the rotation and the mass of the LMC out to the distances of the Reticulum cluster (11 kpc) or NGC 1841 (14 kpc). The best stellar tracer would presumably be young, because such objects could have a small velocity dispersion about a rotation solution, if no major recent perturbations of the LMC by interactions with the Milky Way or SMC exist. As pointed out above, the disk solutions for all major LMC components are similar to those of the H I gas. One can assume that the older components of the LMC continue to follow the same disk as the younger components, as the clusters imply, and use carbon stars (Demers et al 1993) or Cepheids or as-yet-uncataloged red giants to derive the rotation curve. As it stands, Figure 8 of Schommer et al (1992) is a good summary of current knowledge: The rotation curve is relatively flat from 2-8 degrees, with minimal information beyond 8 degrees (1 degree = 0.94 kpc). The mass implied by this rotation curve is ~ 1010 Modot. If the LMC were simply an exponential disk, the rotation curve should peak at 2.2 disk scale lengths, or 3.5 kpc. There is no evidence for a Keplerian falloff at this point, whose position would change outwardly slightly if a low-mass halo were added. If the rotation curve is flat out to the distance of NGC 1841, then substantial dark matter is needed.

Fourth, the cluster systems of the Magellanic Clouds, the Milky Way, M31, and M33 have been compared by Schommer et al (1992), Schommer (1993) in terms of their spatial and kinematic distributions. The Milky Way and M31 both have disk globular cluster systems (Mayall 1946, Morgan 1958, Kinman 1959, Zinn 1985, Huchra et al 1991) that are metal rich and spatially concentrated to the inner parts of the cluster system. M33, with a wide range of cluster colors similar to the LMC and distinct from the Milky Way or M31, shows a trend of kinematics with color. The set of reddest M33 clusters (Schommer et al 1991) has no global rotation, a velocity dispersion of approximately the expected isothermal value of ~ 70 km s-1, and v / sigma = 0.6. As we examine bluer M33 clusters (color presumably being related to age), rotation increases and line-of-sight velocity dispersion decreases. It is important to remember here that M33 is about twice as luminous as the LMC; it is hard to say if this mass difference is critical or incidental. It will be important to understand why some old cluster systems rotate and why some disk systems are inner-cluster system phenomena while others are outer-cluster system phenomena.

No global statements can be made about the kinematics of SMC clusters; no systematic survey of cluster abundances and velocities has been made. The dominant reason seems to be the small number of SMC clusters, coupled with the fact that most of the SMC clusters are in fairly crowded fields. A second reason is that it has always been tacitly assumed that the SMC kinematics will be quite complicated. It would be fascinating to know if the SMC has a halo that is even remotely spherical, or if it is unrecognizable because of its interactions.

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