Are strongly magnetized degenerate stars cooling by axion emission?

We considered recently as a new axion production mechanism the process $e^- \to e^- +a$ in a strong magnetic field $B$. Requiring that for a strongly magnetized neutron star the axion luminosity is smaller than the neutrino luminosity we obtained 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 we obtained $g_{ae}\lsim 9 \cdot 10^{-13} (T/10^7)^{5/4} (B/10^{10})^{-2}$, where $T$ is the internal temperature of the white dwarf. Here we note that the observed lack of magnetized white dwarfs with low-temperature in the galactic disc could also be interpreted as a signature of axion emission. Moreover, we speculate that axion emission could explain why the putative galactic halo population of white dwarfs is so dim.