Instability of rotating Bose stars

Light bosonic (axionlike) dark matter may form Bose stars - clumps of nonrelativistic Bose-Einstein condensate supported by self-gravity. We study rotating Bose stars composed of condensed particles with nonzero angular momentum l. We analytically prove that these objects are unstable at arbitrary l≠0 if particle self-interactions are attractive or negligibly small. They decay by shedding off the particles and transporting the angular momentum to the periphery of the system until a Saturn-like configuration appears: One (or several) spin-zero Bose stars and clouds of diffuse particles orbit around the mutual center. In the case of no self-interactions, we calculate the profiles and dominant instability modes of the rotating stars: numerically at 1≤l≤15 and analytically at l≫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.