Axion Star Nucleation in Dark Minihalos around Primordial Black Holes

We consider a general class of axion models, including the QCD and string axion, in which the PQ symmetry is broken before or during inflation. Assuming the axion is the dominant component of the dark matter, we discuss axion star formation in virialized dark minihalos around primordial black holes through gravitational Bose-Einstein condensation. We determine the conditions for minihalos to kinetically produce axion stars before galaxy formation. Today, we expect up to $sim 10^{17}$ ($sim 10^9$) axion stars in a radius of 100 parsecs around the Sun for the case of the QCD (string) axion.