Phase transitions between dilute and dense axion stars

TL;DR

This paper investigates phase transitions between dilute and dense axion stars using a Newtonian model, revealing critical points, stability conditions, and the phase diagram, with implications for QCD and ultralight axions.

Contribution

It introduces an analytical model for axion star phase transitions, identifying a critical self-interaction parameter and mapping the phase diagram including stability and collapse conditions.

Findings

Existence of a critical self-interaction strength $|\lambda|_c$ for phase transition.

Stable dilute axion stars exist below a maximum mass, collapsing into black holes above it.

Dense axion stars can explode or collapse depending on mass and self-interaction.

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 $V(|\psi|^2)$ involving an attractive $|\psi|^4$ term and a repulsive $|\psi|^6$ 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 $\lambda\le 0$. We show the existence of a critical point $|\lambda|_c\sim (m/M_P)^2$ 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 $|\lambda|<|\lambda|_c$, a system of self-gravitating axions forms a stable dilute axion star below a general relativistic maximum mass $M_{\rm max,GR}^{\rm dilute}\sim M_P^2/m$ and collapses into a black hole above that mass. For strong self-interactions $|\lambda|>|\lambda|_c$, a system of self-gravitating axions forms a stable dilute axion star below a Newtonian maximum mass $M_{\rm max,N}^{\rm dilute}=5.073 M_P/\sqrt{|\lambda|}$, collapses into a dense axion star above that mass, and collapses into a black hole above a general relativistic maximum mass $M_{\rm max,GR}^{\rm dense}\sim \sqrt{|\lambda|}M_P^3/m^2$. Dense axion stars explode below a Newtonian minimum mass $M_{\rm min,N}^{\rm dense}\sim m/\sqrt{|\lambda|}$ 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 $(|\lambda|_*,M_*/(M_P^2/m))$ separating dilute axion stars, dense axion stars, and black holes. We make numerical applications for QCD axions and ultralight axions.