Self-Similar Growth of Bose Stars

We analytically solve the problem of Bose star growth in the bath of gravitationally interacting particles. We find that after nucleation of this object, the bath is described by a self-similar solution of the kinetic equation. Together with the conservation laws, this fixes mass evolution of the Bose star. Our theory explains, in particular, the slowdown of the star growth at a certain "core-halo" mass, but also predicts formation of heavier and lighter objects in magistral dark matter models. The developed "adiabatic" approach to self-similarity may be of interest for kinetic theory in general.