  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.

Astrophysics;High Energy Physics - Phenomenology