GLOBAL SPIRAL MODES IN A 3-PHASE GRAVITATING DISK

We analyze the global modal properties of self-gravitating disks with exponential density distributions both in one- and three-component app roaches. We take into account the observational properties of galactic disks, namely, that the radial dependence of the stellar velocity dis persion c(s) is proportional to the square of the stellar surface dens ity. The stability properties of a one-component disk are determined m ainly by its central velocity dispersion and its maximal rotational ve locity. Disks with the central velocity dispersion less than unity in units G = R(d) = M(d) = 1 are unstable to tightly wound spirals, if th e minimal value of Toomre's Q-parameter is less than or close to unity . Here G is the gravitational constant, and R(d) and M(d) are the radi us and mass of the disk, respectively. Higher velocity dispersions inc rease the wavelength of unstable modes, as well as the probability of their generation. Disks with c(s) > 1.0 at the center can be unstable if the minimal value of the Q-parameter is less than 1.8. The stabilit y of multicomponent disks is jointly determined by self-gravity and ma ss transformations between different phases. In this paper we discuss the situation in which the stability properties of the disk are primar ily determined by self-gravity. If the admixture of clouds and gas are small, the shape and the growth rate of the principal unstable mode d oes not change significantly. However, a significant cold component in the system increases the value of the growth rate of an unstable mode . A new effect, in comparison to the one-component approach, is an ang ular phase separation between spirals of different components. Such di splacements have been observed in the spiral arms of some nearby galax ies and can thus be considered as a confirmation of the validity of a global modal approach to self-gravitating multi-phase galactic disks.