On the Evolution of Magnetic White Dwarfs

We present the first radiation magnetohydrodynamic simulations of the atmosphere of white dwarf stars. We demonstrate that convective energy transfer is seriously impeded by magnetic fields when the plasma-β parameter, the thermal-to-magnetic-pressure ratio, becomes smaller than unity. The critical field strength that inhibits convection in the photosphere of white dwarfs is in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG field strengths observed in magnetic white dwarfs, implying that these objects have radiative atmospheres. We have employed evolutionary models to study the cooling process of high-field magnetic white dwarfs, where convection is entirely suppressed during the full evolution (B ≳ 10 MG). We find that the inhibition of convection has no effect on cooling rates until the effective temperature (T_eff) reaches a value of around 5500 K. In this regime, the standard convective sequences start to deviate from the ones without convection due to the convective coupling between the outer layers and the degenerate reservoir of thermal energy. Since no magnetic white dwarfs are currently known at the low temperatures where this coupling significantly changes the evolution, the effects of magnetism on cooling rates are not expected to be observed. This result contrasts with a recent suggestion that magnetic white dwarfs with T_eff ≲ 10,000 K cool significantly slower than non-magnetic degenerates.