Self-gravitating, disk-like, galactic models with stars having velocity dispersions

This paper gives numerical results for disk-like models of the self-gravitating stellar system, according to the construction scheme which has been proposed previously (Miyamoto 1974). Particular attention is devoted to a density distribution (a superposition of two Toomre's (1963) mass models) for our Galaxy. For this density distribution, four characteristic models, the central parts of which are essentially pressure-supported, are investigated. It is shown that an extremely ''hot'' state for the central part of our Galaxy is dynamically permitted. The radial velocity dispersion at the center of the four models is almost independent of the models considered. The radial velocity dispersion of stars at the galactic center is estimated to be 225 km s-1, which is much larger than the one deduced from Toomre's (1964) criterion for the local stability of the stellar disk. One of the models is constructed so as to approximate the radial velocity dispersion of 40 km s-1 for the common nearby stars as well as the Oort constants A = +15 km s-1 kpc-1 and B = -10 km s-1 kpc-1 as closely as possible at the solar vicinity. This model shows that in the central part of the Galaxy the mean rotation of stars and the ratio of the azimuthal to the radial velocity dispersion can possibly differ considerably from those anticipated from the epicyclic approximation for the motions of stars. The other three models describe: a fictitious stellar disk with isotropic velocity distribution everywhere in space, one of the simplest rotating stellar disks, and a stellar disk with a radial velocity dispersion, which is about 10 km s-1 higher than the one required by Toomre's (1964) criterion. The self-consistency in constructing the above models is kept within the error of about 1% over the stellar disks considered. (auth.)