GALACTIC SLOW BAR AS AN UNSTABLE MODE OF A STELLAR DISK

This paper fills a gap in the theory of equilibrium and stability of s tellar disks: it analyzes models with an arbitrary degree of radial el ongation of stellar orbits, whereas all previous investigations consid ered only nearly circular orbits. We study a series of distribution fu nctions that are disk analogs of generalized polytropic models of sphe rical systems. The latter have been recently explored in detail and pr oved extremely fruitful. We hope that disk polytropes will be equally useful primarily for understanding the formation of bars in SB galaxie s and related structures (rings, spirals, etc.). Using N-body simulati ons we derived a crude estimate of the stability limit. It corresponds to a disk in which the radial part of kinetic energy is nearly twice as much as the transversal part. This instability leads to the formati on of a well-defined bar that slowly rotates with a velocity approxima tely equal to the precession velocity of a typical stellar orbit.