Annu. Rev. Astron. Astrophys. 1978. 16: 103-39 Copyright © 1978 by Annual Reviews. All rights reserved

3.3. Velocity Dispersion Measurements

It is well known that observations of velocity dispersions can provide information on the dynamics of galaxies; for instance, in the central bulges of spiral and elliptical galaxies the velocity dispersion in the stars can be used with the virial theorem to estimate the total masses there, assuming that the kinetic energy is mainly in random motions. We do not review those results here; for recent data see for example Williams (1977) and Illingworth (1977) and references therein. Our concern in this section is with measurements of the Z-component of the velocity dispersion in the gas; in flattened disks this can give information on the thickness of the gas layer or the mass density in the plane. Gottesman & Davies (1970) and de Jager & Davies (1971) found upper limits to the random HI cloud motions of 12 km/sec in M31 and 10 km/sec in M33; however, they estimated that the velocity gradients over their telescope beam could seriously affect the interpretation. Using higher angular resolution Emerson (1976) confirmed that the arms dispersion of the HI in M31 is indeed 12 km/sec. With the help of a mass model determined from the rotation curve, and the assumption of a simple hydrostatic equilibrium in Z (neglecting magnetic fields), he found that the HI layer increases in Z-thickness from about 200 pc around R = 6 kpc to 1500 pc at R = 25 kpc from the center. From another method, involving analysis of the differential radial velocities along the line of sight, Whitehurst et al. (1978) find a thickness of the HI plane in M31 of about 1.4 kpc between half-density points and large distortion in the outer regions.

There are, of course, necessary assumptions: the measured line-of-sight dispersion is assumed to be a good estimate of the Z-dispersion (note however that M31 is highly inclined), and the mass density is assumed to be constant over the whole Z-extent of the gas layer at every R. This mass density is then derived from the rotation curve with an assumed thickness of the total disk. A similar treatment of M33 provides similar results (Warner et al. 1973): the rms dispersion falls from about 15 km/sec near the nucleus to 9 km/sec at 6 kpc, and the HI-layer thickness increases from about 300 pc at 0.5 kpc to 800 pc at 5 kpc radius. Finally, Tully (1974b) has derived information on the thickness of the gaseous disk of M51 from his extensive H-line study; the values range from ~ 60 pc in the central regions to 270 pc out in the main part of the optical disk. The rms velocity dispersions are respectively 30 and 17-20 km/sec for the two areas. The large thicknesses apply to the giant HII regions where pressure support may play a greater role (see discussion in Tully (1974b).

A promising future development will be to actually measure the HI-layer thickness from high-resolution radio observations of edge-on galaxies. Along with velocity dispersions obtained from face-on systems, an independent estimate of the mass density near the equatorial plane should then be available which, when coupled with the rotation curve data, would provide some useful constraints on the actual 3-dimensional distribution of mass in disk galaxies.