Distributions and Collision Rates of ALP Stars in the Milky Way

We apply current analytical knowledge on the characteristic mass and linear evolution of miniclusters down to redshift $z=0$ to the hypothetical minicluster distribution of the Milky Way. Using the mass-radius relation and a core-halo relation for stable soliton solutions composed of axion-like particles (ALPs), we connect the galactic minicluster mass distribution to that of their ALP star cores. We consider different temperature evolutions of the ALP field with masses in the range $10^{-12}\,\mathrm{eV} \leq m_a \leq 10^{-3}\,$eV and infer the abundance and properties of QCD axion- and ALP stars in our galaxy. We re-evaluate detection prospects for collisions of neutron stars with both ALP stars and miniclusters as well as relativistic ALP bursts, so-called Bosenovae. Our analysis shows that the collision rates between miniclusters and neutron stars can become as large as $\sim 10^5\,$yr$^{-1}$ galaxy$^{-1}$, but that the fraction of encounters that can lead to resonance between ALP mass and magnetosphere plasma frequency is generally well below $\sim 1\,$yr$^{-1}$ galaxy$^{-1}$, depending on the ALP model. We confirm previous results that merger rates of ALP stars are extremely small $< 10^{-12}\,$yr$^{-1}$ galaxy$^{-1}$, while their host miniclusters can merge much more frequently, up to $\sim 10^3\,$yr$^{-1}$ galaxy$^{-1}$ for the QCD axion. We find that Bosenovae and parametric resonance are much more likely to lead to observable signatures than neutron star encounters. We also suggest that a combination of accretion and parametric resonance can lead to observable radio lines for a wide range of ALP masses $m_a$ and photon-couplings $g_{a\gamma\gamma}$.