Axion-photon conversion in transient compact stars: Systematics, constraints, and opportunities

We study magnetic conversion of ultra-relativistic axion-like particles (ALPs) into photons in compact-star environments, focusing on the hot, transient conditions of core-collapse supernova (SN) remnants and neutron-star mergers (NSMs). We address previously overlooked uncertainties, particularly the suppression caused by ejected matter near the stellar surface, a region crucial to the conversion process. We derive analytical expressions for the transition rate; they reveal the influence of key parameters and their uncertainties. We update constraints using historical gamma-ray data from SN~1987A and find $g_{a\gamma}<5\times10^{-12}~{\rm GeV}^{-1}$ for $m_a\lesssim10^{-9}$ eV. We also forecast sensitivities for a future Galactic SN and for NSMs, assuming observations with Fermi-LAT or similar gamma-ray instruments. We distinguish ALPs -- defined as coupling only to photons and produced via Primakoff scattering -- from axions, which also couple to nucleons and emerge through nuclear bremsstrahlung. We omit pionic axion production due to its large uncertainties and inconsistencies, though it could contribute comparably to bremsstrahlung under optimistic assumptions. For the compact sources, we adopt time-averaged one-zone models, guided by numerical simulations, to enable clear and reproducible parametric studies.