Catastrophe Structure and Stability of Axion Stars

Abstract

Axion stars are self-gravitating Bose--Einstein condensates of QCD axions or axion-like particles. Their stability determines whether they can survive as dark-matter structures and what astrophysical signatures they may produce. Here we combine a non-relativistic Schrödinger--Poisson description with catastrophe theory to develop a unified picture of axion-star stability. Beginning with the Einstein--Klein--Gordon system for a periodic axion potential, we derive the effective equations of motion and conserved quantities and construct a one-parameter family of star-like solutions. A Gaussian variational ansatz reduces the problem to an analytic energy functional $E(R;N)$. Within this model, equilibria appear and disappear through Arnold $A_2$, $A_3$, and $A_4$ catastrophes as the particle number $N$ and interaction strengths vary. A repulsive sextic interaction produces two stable branches---dilute and dense axion stars---separated by an unstable branch. The same catastrophe criteria apply beyond the sextic truncation: for the full cosine and QCD-corrected potentials, the fold conditions follow from the complete variational energy and can be evaluated numerically. We also separate stability within the collective-coordinate ansatz from full radial perturbative stability and specify the range in which the non-relativistic treatment is reliable. This framework provides a compact classification of axion-star phases and identifies model-dependent critical masses associated with collapse, bosenova-like emission, and black-hole formation.

arXiv comment10 pages, 3 figures