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.