A galactic disk as a two-fluid system: Consequences for the critical stellar velocity dispersion and the formation of condensations in the gas

We examine the consequences of treating a galactic disk as a two-fluid system for the stability of the entire disk and for the stability and form of the gas in the disk. We find that the existence of even a small fraction of the total disk surface density in a cold fluid (that is, the gas) makes it much harder to stabilize the entire two-fluid disk. (C/sub s/,min)/sub 2-f/, the critical stellar velocity dispersion for a two-fluid disk in an increasing function of μ/sub g//μ/sub s/, the gas fraction, and μ/sub t//kappa, where μ/sub g/, μ/sub s/, and μ/sub t/ are the gaseous, stellar, and total disk surface densities and kappa is the epicyclic frequency. In the Galaxy, we find that (C/sub s/,min)/sub 2-f/ as a function of R peaks when μ/sub t//kappa peaks-at galactocentric radii of Rapprox.5-7 kpc; two-fluid instabilities are most likely to occur in this region. This region is coincident with the peak in the molecular cloud distribution in the Galaxy. At the higher effective gas density resulting from the growth of a two-fluid instability, the gas may become unstble, even when originally the gas by itself is stable. The wavelength of a typical (induced) gas instability in the inner galaxy is approx.400 pc, and it contains approx.107 M/sub sun/ of interstellar matter; these instabilities may be identified with clusters of giant molecular clouds. We suggest that many of the spiral features seen in gas-rich spiral galaxies may be material arms or arm segments resulting from sheared two-fluid gravitational instabilities. The analysis presented here is applicable to any general disk galaxy consisting of stars and gas