Dynamical instabilities in two-phase media and the minimum masses of stellar systems

Two-phase media, with cool dense clouds in pressure equilibrium with a hot, tenuous background from which they have cooled, have a prominent place in astrophysics, possibly being involved in the evolution of cooling flows, active galactic nuclei, and the formation of galaxies, star clusters and individual stars. Following their formation, the cool clouds are subject to Kelvin-Helmholtz instability, which grows as they move through the background gas. The instability is suppressed if the clouds are bound by a sufficiently strong gravitational potential. Analytical estimates of the growth and stability requirements of clouds are presented and are compared with the results of two-dimensional hydrodynamical simulations. In the case of nongravitationally bound clouds, it is found that, when they move relative to the background at speeds comparable to the sound speed of the background gas, Kelvin-Helmholtz instability results in disruption of the clouds on a time scale comparable to their dynamical times. In order that a self-gravitating cloud can remain stable at the same relative velocity, it is found that its mass must exceed the critical mass for the onset of gravitational instability. The implications of this for active galactic nuclei, globular cluster formation, star formation, and the evolution of galaxies in clusters are briefly discussed.