Stability of a gas-dust disk at inflections of the angular velocity

Abstract

The instability of a rotating, oblate, quasi-homogeneous system consisting of a gas-dust mixture is analyzed. Disturbances affecting a limited zone and subject to self-gravitation are studied. Cases in which the instability is the result of differential rotation are considered. A thick-disk approximation (in a cylindrical geometry) is used. The division of such instabilities into two types is established. The first type of disturbance is characterized by an azimuthal redistribution of material and an increment of the order of √Gρ (G is the gravitational constant and ρ is the density). Disturbances of the second type have substantially smaller increments, but occur under more general conditions, and have primarily radial density redistributions. Specific examples of disturbances of the second type are constructed.