Axion Stars in the Infrared Limit

TL;DR

This paper develops a simplified theoretical framework for axion stars in the infrared limit, revealing how their mass and radius depend on a key parameter and identifying stability conditions relevant to dark matter and astrophysical phenomena.

Contribution

It introduces a novel expansion method in the infrared limit for axion stars, providing analytical insights into their properties and stability that extend previous models.

Findings

Mass and radius increase linearly with the parameter at small values.

Maximum mass occurs at a specific parameter value, beyond which stars are unstable.

Results relate to dark matter constraints and Fast Radio Burst phenomenology.

Abstract

Following Ruffini and Bonazzola, we use a quantized boson field to describe condensates of axions forming compact objects. Without substantial modifications, the method can only be applied to axions with decay constant, $f_a$, satisfying $\delta=(f_a\,/\,M_P)^2\ll 1$, where $M_P$ is the Planck mass. Similarly, the applicability of the Ruffini-Bonazzola method to axion stars also requires that the relative binding energy of axions satisfies $\Delta=\sqrt{1-(E_a\,/\,m_a)^2}\ll1$, where $E_a$ and $m_a$ are the energy and mass of the axion. The simultaneous expansion of the equations of motion in $\delta$ and $\Delta$ leads to a simplified set of equations, depending only on the parameter, $\lambda=\sqrt{\delta}\,/\,\Delta$ in leading order of the expansions. Keeping leading order in $\Delta$ is equivalent to the infrared limit, in which only relevant and marginal terms contribute to the equations of motion. The number of axions in the star is uniquely determined by $\lambda$. Numerical solutions are found in a wide range of $\lambda$. At small $\lambda$ the mass and radius of the axion star rise linearly with $\lambda$. While at larger $\lambda$ the radius of the star continues to rise, the mass of the star, $M$, attains a maximum at $\lambda_{\rm max}\simeq 0.58$. All stars are unstable for $\lambda>\lambda_{\rm max}$ . We discuss the relationship of our results to current observational constraints on dark matter and the phenomenology of Fast Radio Bursts.