Thermal activation rate of dilute axion stars close to the maximum mass

Abstract

We compute the thermal activation rate of metastable self-gravitating Bose-Einstein condensates with attractive self-interaction (e.g., dilute axion stars) by using the instanton theory. Explicit analytical results are given close to the maximum mass $M_{\max }$ [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)] by using the normal form of the saddle-node bifurcation close to that point. We show that the lifetime of metastable states is extremely long, scaling as $t_{\mathrm{life}}\sim e^N{t}_D$, where $N$ is the number of bosons in the system and $t_D$ is the dynamical time ($N\sim 10^{57}$ and $t_D\sim 10\mathrm{hrs}$ for typical QCD axion stars; $N\sim 10^{96}$ and $t_D\sim 100\mathrm{Myrs}$ 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 compare our results with similar results obtained for Bose-Einstein condensates in laboratory, globular clusters and self-gravitating Brownian particles in astrophysics, the Brownian mean field model (BMF) in statistical mechanics, and bacterial populations in biology. Our presentation parallels the calculation of the quantum tunneling rate of dilute axion stars given in a previous paper [P.H. Chavanis, Phys. Rev. D 102, 083531 (2020)]. These calculations can find application in various domains of physics and astrophysics.