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Description
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 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.
Our analysis shows that the galactic 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.
For Bosenovae, 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.
Our results suggest that Bosenovae and parametric resonance are much more likely to lead to observable signatures than neutron star encounters.\
We also propose a new detection mechanism in which the combined accretion and parametric resonance in solitonic cores can lead to observable radio lines for a wide range of ALP masses $m_a$ and photon-couplings $g_{a\gamma\gamma}$.
We present different accretion models for galactic ALP stars in a companion paper and calculate the correspondig radio-line flux to constrain $g_{a\gamma\gamma}$.
We find that upcoming radio telescopes such as SKA have sufficient sensitivity to reach down to $g_{a\gamma\gamma} \simeq 10^{-11}\,{\rm GeV}^{-1}$ and even $10^{-12}\,{\rm GeV}^{-1}$, depending on the ALP masses $m_a=10^{-7}-10^{-3}\,{\rm eV}$ and the accretion models.
