From scalar clouds around evaporating black holes to boson star

We study, for the first time, the evolution of a scalar cloud bound to an evaporating black hole. Our simulations of the associated Schr\"odinger-Poisson system for non-relativistic and spherically symmetric clouds reveal that a scalar cloud may (partially) survive as a self-gravitating boson star if the black hole evaporates adiabatically until its mass becomes less than one half of the cloud's mass. This yields a novel mechanism for boson star formation and shows that, as previously conjectured, bosonic dark matter production by light primordial black holes may result in micro-boson stars with very large occupation numbers, greatly enhancing their potential detectability even for very weakly interacting dark matter particles.