THE RADIUS DEPENDENCE OF VELOCITY DISPERSION IN SPIRAL GALAXIES

The analytical model discussed in two previous papers is used to solve for the radial profile of the radial velocity dispersion on the plane of symmetry of an old galactic disc population. For a realistic total mass distribution consistent with an almost flat rotation curve and an exponential density profile, it is found that for relatively small radii a constant-anisotropy model provides a reasonable approximation to the solution (as found observationally by Lewis & Freeman), while for large R the solution is consistent with an approximately constant Toomre-Q profile, as suggested theoretically by Toomre and numerically by Sellwood & Carlberg. Possible applications of this result are discussed.