Abstract
Cosmologically stable, light particles that came into thermal contact with the Standard Model in the early universe may persist today as a form of hot dark matter. For relics with masses in the eV range, their role in structure formation depends critically on their mass. We trace the evolution of such hot relics and derive their density profiles around cold dark matter halos, introducing a framework for their indirect detection. Applying this framework to axions -- a natural candidate for a particle that can reach thermal equilibrium with the Standard Model in the early universe and capable of decaying into two photons -- we establish stringent limits on the axion-photon coupling $g_{a \gamma} $ using current observations of dwarf galaxies, the Milky Way halo, and galaxy clusters. Our results set new bounds on hot axions in the $\mathcal{O}(1-10)\,$eV range.