Two-fluid gravitational instabilities in a galactic disk

A two-fluid scheme has been formulated in which the stars and gas in a galactic disk are represented as two isothermal fluids and the two fluids interact gravitationally with each other. The disk is supported by rotation and random motion. The characteristics of two-fluid gravitational instabilities are studied, and it is concluded that even when both fluids in a two-fluid system are separately stable, the joint system may be neutrally stable or even unstable to the growth of gravitational instabilities. For any galactic disk, the contribution per unit surface density toward the formation of two-fluid instabilities is larger for the gas than for the stars, due to the former's lower velocity dispersion. The ratio of the amplitude in the gas to that in the stars is a monotonically increasing function of the wavenumber of the two-fluid perturbation. The wavelength of a typical instability in the inner galaxy is about 2-3 kpc.