Analysis of Dark Matter Axion Clumps with Spherical Symmetry

TL;DR

This paper analyzes the stability of spherical axion dark matter clumps considering gravitational and self-interactions, identifying stable and unstable regimes, and clarifying misconceptions about ultra-dense solutions.

Contribution

It provides a detailed stability analysis of spherical axion clumps, clarifies the conditions for stability, and corrects previous misconceptions about ultra-dense stable solutions.

Findings

Large clumps are stable, small ones are unstable

There is a maximum particle number for stable clumps

A single stable branch exists with repulsive self-interactions

Abstract

Recently there has been much interest in the spatial distribution of light scalar dark matter, especially axions, throughout the universe. When the local gravitational interactions between the scalar modes are sufficiently rapid, it can cause the field to re-organize into a BEC of gravitationally bound clumps. While these clumps are stable when only gravitation is included, the picture is complicated by the presence of the axion's attractive self-interactions, which can potentially cause the clumps to collapse. Here we perform a detailed stability analysis to determine under what conditions the clumps are stable. In this paper we focus on spherical configurations, leaving aspherical configurations for future work. We identify branches of clump solutions of the axion-gravity-self-interacting system and study their stability properties. We find that clumps that are (spatially) large are stable, while clumps that are (spatially) small are unstable and may collapse. Furthermore, there is a maximum number of particles that can be in a clump. We map out the full space of solutions, which includes quasi-stable axitons, and clarify how a recent claim in the literature of a new ultra-dense branch of stable solutions rests on an invalid use of the non-relativistic approximation. We also consider repulsive self-interactions that may arise from a generic scalar dark matter candidate, finding a single stable branch that extends to arbitrary particle number.