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We investigate the luminosity and cooling of highly magnetized white dwarfswith electron-degenerate cores and non-degenerate surface layers where coolingoccurs by diffusion of photons. We find the temperature and density profiles inthe surface layers or envelope of white dwarfs by solving the magnetostaticequilibrium and photon diffusion equations in a Newtonian framework. We alsoobtain the properties of white dwarfs at the core-envelope interface, when thecore is assumed to be practically isothermal. With the increase in magneticfield, the interface temperature increases whereas the interface radiusdecreases. For a given age of the white dwarf and for fixed interface radius orinterface temperature, we find that the luminosity decreases significantly fromabout $10^{-6}\, L_{\odot}$ to $10^{-9}\, L_{\odot}$ as the magnetic fieldstrength increases from about $10^9$ to $10^{12}\,$G at the interface and hencethe envelope. This is remarkable because it argues that magnetized white dwarfsare fainter and can be practically hidden in an observed Hertzsprung--Russelldiagram. We also find the cooling rates corresponding to these luminosities.Interestingly, the decrease in temperature with time, for the fields underconsideration, is not found to be appreciable.

Luminosity and cooling of highly magnetized white dwarfs: suppression of luminosity by strong magnetic fields