What should the gradient of the velocity dispersion of gas clouds in galactic disks be?

The dispersion equation is obtained, describing the dynamics of disturbances in a rotating gravitating thin gas disc with arbitrary distributions of the surface density σ₀(r), angular velocity Ω(r), and velocity dispersion c_s of the particles forming the disc (gas clouds in the case of galactic gas subsystems). A new type of instability in such systems, the entropy-gradient instability, is found. It is shown that such a disc is stable under minimum value of c_s, provided the density σ₀(r) decreases towards the disc periphery much faster than the velocity dispersion c_s(r) which agrees with the data of observations of gas subsystems of galaxies.