8.1. Scale Height
The scale height of the LMC disk can be estimated from the observed line-of-sight velocity dispersion . For carbon stars, the scatter of the velocity measurements around the best-fitting rotating disk model (Figure 7) yields = 20.2 ± 0.5 km s-1. The ratio of rotation velocity to velocity dispersion is therefore V / = 2.9 ± 0.9. For comparison, the thin disk of the Milky Way has V / 9.8 and its thick disk has V / 3.9. In a relative sense one might therefore expect the LMC disk to be similar, but somewhat thicker than the Milky Way thick disk. Weinberg (2000) argued from N-body simulations that such considerable thickness could be the result of Milky Way tidal effects on the LMC.
The radial profile of the velocity dispersion contains information on the LMC scale height as function of radius. The carbon star velocity dispersion is close to constant as function of radius, and this is not what is expected for a disk with a constant scale height. To fit this behavior one must assume that the scale height increases with radius in the disk (Alves & Nelson 2000). This can arise naturally as a result of tidal forces from the Milky Way, which become relatively more important (compared to the LMC self-gravity) as one moves to larger radii. Alves & Nelson considered an isothermal disk with a vertical density profile proportional to sech2(z / z0), where z0 can vary with disk radius. Application to the carbon star data of van der Marel et al. (2002) yields z0 = 0.27 kpc at the LMC center, rising to z0 = 1.5 kpc at a radius of 5.5 kpc.
The LMC carbon stars are part of the intermediate-age population which is believed to be fairly representative for the bulk of the mass in the LMC. In this sense, the results inferred for the carbon star population are believed to be characteristic for the LMC as a whole. However, it is certainly not true that all populations have the same kinematics. As in the Milky Way, younger populations have a smaller velocity dispersion (and hence a smaller scale height) than older populations. A summary of measurements for various populations is given by Gyuk, Dalal & Griest (2000). The youngest populations (e.g., supergiants, HII regions, HI gas) have dispersions of only 6 km s-1. Old long-period variables have dispersions 30 km s-1 (Bessell, Freeman & Wood 1986) and so do the oldest star clusters (Freeman et al. 1983; Schommer et al. 1992). These values are considerably below the LMC circular velocity (see Section 5.2). This has generally been interpreted to mean that the LMC does not have an old pressure supported halo similar to that of the Milky Way.
The first possible evidence for the presence of a pressure supported halo was presented recently by Minniti et al. (2003). They measured a dispersion 53 ± 10 km s-1 for a sample of 43 RR Lyrae stars within 1.5° from the LMC center. This value is consistent with what would be expected for a pressure supported halo in equilibrium in the gravitational potential implied by the circular velocity (Alves 2004a). The RR Lyrae stars make up ~ 2% of the visible mass of the LMC, similar to the value for the Milky Way halo. However, it is surprising that the surface density distribution of the LMC RR Lyrae stars is well fit by an exponential with the same scale length as inferred for other tracers known to reside in the disk (Alves 2004a). This is very different from the situation for the Milky Way halo, where RR Lyrae stars follow a power-law density profile. This suggests that maybe the RR Lyrae stars in the LMC did form in the disk, instead of in a halo. In this scenario they might simply have attained their large dispersions by a combination of disk heating and Milky Way tidal forces (Weinberg 2000). To discriminate between halo and disk origins it will be important to determine whether the velocity field of the RR Lyrae stars has a rotation component. This will require observations at larger galactocentric distances.