  We study numerically evolution of a self-gravitating nonequilibrium Bose gas
contained in a fixed volume. We find that, even when the volume is small enough
to prevent collisionless instability, a compact phase-correlated object (a Bose
star) can form, by gravity alone, from a disordered initial state. We interpret
this effect and the associated growth of the density contrast as consequences
of a new type of gravitational instability---a nonlinear instability due to
stimulated gravitational scattering of the bosons. Our results imply that
formation of Bose stars, in regions that have fallen out of the Hubble
expansion, may be a quite general phenomenon, not requiring a large preexisting
correlation length or any short-range interactions.
