Phase transitions between dilute and dense axion stars

Pierre-Henri Chavanis

doi:10.1103/PhysRevD.98.023009

paper

Phase transitions between dilute and dense axion stars

arXiv:1710.06268 · doi:10.1103/PhysRevD.98.023009

Abstract

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 $λ \leq 0$ . We show the existence of a critical point $∣ λ ∣_{c} \sim (m / M_{P})^{2}$ 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 general relativistic maximum mass $M_{max, GR}^{dilute} \sim M_{P}^{2} / m$ and collapses into a black hole above that mass. For strong self-interactions $∣ λ ∣ > ∣ λ ∣_{c}$ , a system of self-gravitating axions forms a stable dilute axion star below a Newtonian maximum mass $M_{max, N}^{dilute} = 5.073 M_{P} / ∣ λ ∣$ , collapses into a dense axion star above that mass, and collapses into a black hole above a general relativistic maximum mass $M_{max, GR}^{dense} \sim ∣ λ ∣ M_{P}^{3} / m^{2}$ . Dense axion stars explode below a Newtonian minimum mass $M_{min, N}^{dense} \sim m / ∣ λ ∣$ 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 $(∣ λ ∣_{*}, M_{*} / (M_{P}^{2} / m))$ separating dilute axion stars, dense axion stars, and black holes. We make numerical applications for QCD axions and ultralight axions.

Phase transitions between dilute and dense axion stars

Abstract

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