Quantum tunneling rate of dilute axion stars close to the maximum mass

Abstract

We compute the quantum tunneling rate of dilute axion stars close to the maximum mass [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)] using the theory of instantons. We confirm that the lifetime of metastable states is extremely long, scaling as $t_{\rm life}\sim e^N\, t_D$ (except close to the critical point), where $N$ is the number of axions in the system and $t_D$ is the dynamical time ($N\sim 10^{57}$ and $t_D\sim 10\, {\rm hrs}$ for typical QCD axion stars; $N\sim 10^{96}$ and $t_D\sim 100\, {\rm Myrs}$ for the quantum core of a dark matter halo made of ultralight axions). Therefore, metastable equilibrium states can be considered as stable equilibrium states in practice. We develop a finite size scaling theory close to the maximum mass and predict that the collapse time at criticality scales as $t_{\rm coll}\sim N^{1/5}t_D$ instead of being infinite as when fluctuations are neglected. The collapse time is smaller than the age of the universe for QCD axion stars and larger than the age of the universe for dark matter cores made of ultralight axions. We also consider the thermal tunneling rate and reach the same conclusions. We compare our results with similar results obtained for Bose-Einstein condensates in laboratory, globular clusters in astrophysics, and quantum field theory in the early Universe.