Ultra-light bosonic dark matter may form Bose stars - clumps of nonrelativistic Bose-Einstein condensate supported by self-gravity. In rotating Bose stars, the condensed particles occupy a level with nonzero angular momentum l. We analytically prove that these latter objects are unstable at arbitrary nonzero l if particle self-interactions are attractive or negligibly small. Their decays proceed by shedding off the angular momentum to the periphery of the system until a Saturn-like configuration appears: one or several spin-zero Bose stars surrounded by orbiting clouds of diffuse bosons. We calculate the profiles and dominant instability modes of the rotating stars: numerically at moderate l and analytically at l>>1. Their lifetimes are always comparable to the inverse binding energies - hence, these objects cannot be considered long-living. We discuss possible astrophysical and cosmological implications of Bose star rotational instabilities. Based on the preprint arXiv:2104.00962 by A.S. Dmitriev, D.G. Levkov, A.G. Panin, E.K. Pushnaya, I.I. Tkachev.
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