Abstract
The energy loss rate of a magnetized electron gas emitting axions $a$ due to the process ${e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+a$ 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 ${g}_{\mathrm{ae}}\ensuremath{\lesssim}{10}^{\ensuremath{-}10}$ 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 ${g}_{\mathrm{ae}}\ensuremath{\lesssim}9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(T/10}^{7}\mathrm{K}{)}^{5/4}{(B/10}^{10}\mathrm{G}{)}^{\ensuremath{-}2}$, where $T$ is the internal temperature of the white dwarf.
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