Instability of rotating Bose stars.

We study rotating Bose stars, i.e. gravitationally bound clumps of Bose-Einstein condensate composed of nonrelativistic particles with nonzero angular momentum $l$. We analytically prove that these objects are unstable at arbitrary $l\ne 0$ if particle self-interactions are attractive or negligibly small. In the latter case we calculate the profiles and dominant instability modes of the rotating stars: numerically at $1 \leq l \leq 15$ and analytically at $l\gg 1$. Notably, their lifetimes are always comparable to the inverse binding energies; hence, these objects cannot be considered long-living. Finally, we numerically show that in models with sufficiently strong repulsive self-interactions the Bose star with $l=1$ is stable.