Axions and axion-like particles are compelling candidates for the missing dark matter of the universe .
As they undergo gravitational collapse , they can form compact objects such as axion stars or even black holes .
In this paper , we study the formation and distribution of such objects .
First , we simulate the formation of compact axion stars using numerical relativity with aspherical initial conditions that could represent the final stages of axion dark matter structure formation .
We show that the final states of such collapse closely follow the known relationship of initial mass and axion decay constant f _ { a } .
Second , we demonstrate with a toy model how this information can be used to scan a model density field to predict the number densities and masses of such compact objects .
In addition to being detectable by the LIGO/VIRGO gravitational wave interferometer network for axion mass of 10 ^ { -9 } < m _ { a } < 10 ^ { -11 } eV , we show using peak statistics that for f _ { a } < 0.2 M _ { pl } , there exists a “ mass gap ” between the masses of axion stars and black holes formed from collapse .