Axion stars, which are self-gravitating Bose-Einstein condensates of QCD axions or axionlike particles, are compelling dark-matter candidates whose stability controls their cosmological and astrophysical impact. We develop a unified framework for axion-star stability that combines a nonrelativistic Schrödinger-Poisson description with catastrophe theory. Starting from the Einstein-Klein-Gordon theory with a periodic axion potential, we derive the effective equations of motion and conserved quantities for axion stars and construct a one-parameter family of starlike solutions. Using a Gaussian variational ansatz, we obtain an analytic one-dimensional energy functional $E(R;N)$ and show that the appearance and disappearance of axion-star equilibria as a function of particle number $N$ is governed by Arnold $A_2$, $A_3$, and $A_4$ catastrophes. Including sextic self-interactions generates two distinct stable branches (dilute and dense axion stars) separated by an unstable branch. We further show how the catastrophe criteria extend beyond the sextic truncation to the full cosine and QCD-corrected axion potentials, for which the fold conditions are evaluated from the full variational energy. We distinguish explicitly between collective-coordinate stability within the ansatz and full radial perturbative stability, and we state the domain of validity of the nonrelativistic approximation. Our results provide a compact classification of axion-star phases and identify model-dependent critical masses directly linked to collapse, bosenovalike emission, and black-hole formation.

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• Axion-like particles
• Stars