Quantum tunneling rate of dilute axion stars close to the maximum mass
Résumé
We compute the quantum tunneling rate of dilute axion stars close to the maximum mass [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)PRVDAQ1550-799810.1103/PhysRevD.84.043531] using the theory of instantons. We confirm that the lifetime of metastable states is extremely long, scaling as tlife∼eNtD (except close to the critical point), where N is the number of axions in the system and tD is the dynamical time (N∼1057 and tD∼10 hrs for typical QCD axion stars; N∼1096 and tD∼100 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 tcoll∼N1/5tD instead of being infinite when fluctuations are neglected. The collapse time at criticality 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.