Revisiting axion-electron bremsstrahlung emission rates in astrophysical environments

The axion-electron coupling $g_{ae}$ is a generic feature of non-hadronic axion models. This coupling may induce a variety of observable signatures, particularly in astrophysical environments. Here, we revisit the calculation of the axion-electron bremsstrahlung and provide a general formulation valid for a non-relativistic plasma with any level of degeneracy and for any axion mass. We apply our result to the Sun, red giant stars and white dwarfs. In particular, we prove that the approximations used to evaluate the axion emissivity in red giants agree with the exact result within $10\%$, comparable with other uncertainties in these studies. In addition, this prescription allows the red giant and white dwarf bounds to be extended to massive axions.