Axion cyclotron emissivity of magnetized white dwarfs and neutron stars

The energy loss rate of a magnetized electron gas emitting axions a due to the process $e^{-}\to e^{-}+a$ is derived for arbitrary magnetic field strength B. Requiring that for a strongly magnetized neutron star the axion luminosity is smaller than the neutrino luminosity we obtain the bound $g_{ae}\lsim 10^{-10}$ for the axion electron coupling constant. This limit is considerably weaker than the bound derived earlier by Borisov and Grishina using the same method. Applying a similar argument to magnetic white dwarf stars results in the more stringent bound $g_{ae}\lsim 9x10^{-13} (T/10^7 K)^{5/4} (B/10^{10} G)^{-2}$ where T is the internal temperature of the white dwarf.