The stellar kinematics of galactic disks

Stellar velocity dispersion measurements of a sample of 12 galactic disks are summarized. The observed radial functionality is parameterized such that one dispersion value is assigned to each galaxy. Comparison of the galaxy dispersion with absolute magnitude and maximum rotation reveals that the dispersion is larger for the more massive systems; the relation between dispersion and intrinsic brightness of the old disk population appears to be linear. Combination of the data for face-on and inclined systems makes the conclusion plausible that the ratio between vertical and radial dispersion in external systems equals 0.6, as for the solar neighbourhood.

From the vertical disk dispersion the maximum rotation of a disk can be calculated once the ratio of scalelength to scaleheight (h/z0) is known. This ratio is derived as a function of disk brightness from the observed dispersion for a simple one colour, one mass-to-light ratio disk model. It appears to be rather constant, possibly increasing towards the fainter systems. Then, for realistic h/z0 values, the stellar velocity dispersions only allow the disk to have a maximum rotation of on average 63% of the observed maximum rotation. The disk is then still dominant in the central parts of the galaxy but generally the maximum disk hypothesis predicting a maximum disk rotation of 85-90% of the observed, does not apply. Exploring the consequences for the Tully-Fisher relation, it is found that this relation for disks only must be positioned at lower rotational velocities than what is observed. A dark halo and bulge must supply the additional rotation.

A relation is calculated between Toomre's Q parameter and the mass-to-light ratio for a disk. When this relation is projected onto the observed velocity dispersion - maximum rotational velocity data it is found that the same M/L ratio for galactic disks implies that the Q value is also equal for all disks, and vice versa. A universal Q value can indeed be expected when a process of self regulation is responsible. for the appearance of regular spiral structure. For an (M/L)B of two which is calculated for the one colour disk model from the observed dispersion one finds Q to range between 2 and 2.5. The latter coincides with the general stability criterion for galaxies as derived in numerical experiments.

Finally, the effect of a dark halo on the observable velocity dispersion has been investigated. It appears that the hitherto adopted radially decreasing dispersion proportional to the square root of the surface density, as expected for an isolated disk, is a good approximation. This is certainly valid for radii within two scalelengths for which dispersions have been measured.