Phase transitions between dilute and dense axion stars

We study the nature of phase transitions between dilute and dense axion stars interpreted as self-gravitating Bose-Einstein condensates. We develop a Newtonian model based on the Gross-Pitaevskii-Poisson equations for a complex scalar field with a self-interaction potential V(|ψ|2) involving an attractive |ψ|4 term and a repulsive |ψ|6 term. Using a Gaussian Ansatz for the wave function, we analytically obtain the mass-radius relation of dilute and dense axion stars for arbitrary values of the self-interaction parameter λ≤0. We show the existence of a critical point |λ|c∼(m/MP)2, where m is the axion mass and MP is the Planck mass, above which a first-order phase transition takes place. We qualitatively estimate general relativistic corrections on the mass-radius relation of axion stars. For weak self-interactions |λ||λ|c, a system of self-gravitating axions forms a stable dilute axion star below a Newtonian maximum mass Mmax,Ndilute=5.073MP/|λ| [Phys. Rev. D 84, 043531 (2011)], collapses into a dense axion star above that mass, and collapses into a black hole above a general relativistic maximum mass Mmax,GRdense∼|λ|MP3/m2. Dense axion stars explode below a Newtonian minimum mass Mmin,Ndense=98.9m/|λ| and form dilute axion stars of large size or disperse away. We determine the phase diagram of self-gravitating axions and show the existence of a triple point (|λ|*,M*/(MP2/m)) separating dilute axion stars, dense axion stars, and black holes. We make numerical applications for QCD axions and ultralight axions. Our approximate analytical results are in good agreement with the exact numerical results of Braaten et al. [Phys. Rev. Lett. 117, 121801 (2016)] for Newtonian dense axion stars. They are also qualitatively similar to those obtained by Helfer et al. [J. Cosmol. Astropart. Phys. 03 (2017) 055] for general relativistic axion stars, but they differ quantitatively for weak self-interactions presumably due to the use of a different self-interaction potential V(|ψ|2). We point out analogies between the evolution of self-gravitating axions (bosons) at zero temperature evolving from dilute axion stars to dense axion stars and black holes and the evolution of compact degenerate (fermion) stars at zero temperature evolving from white dwarfs to n