Atmospheric heating and magnetism driven by $^{22}$Ne distillation in isolated white dwarfs

The origin of atmospheric heating in the cool, magnetic white dwarf GD 356 remains unsolved nearly 40 years after its discovery. This once idiosyncratic star with $T_{\rm eff}\approx7500$ K, yet Balmer lines in Zeeman-split emission is now part of a growing class of white dwarfs exhibiting similar features, and which are tightly clustered in the HR diagram suggesting an intrinsic power source. This paper proposes that convective motions associated with an internal dynamo can power electric currents along magnetic field lines that heat the atmosphere via Ohmic dissipation. Such currents would require a dynamo driven by core $^{22}$Ne distillation, and would further corroborate magnetic field generation in white dwarfs by this process. The model predicts that the heating will be highest near the magnetic poles, and virtually absent toward the equator, in agreement with observations. This picture is also consistent with the absence of X-ray or extreme ultraviolet emission, because the resistivity would decrease by several orders of magnitude at the typical coronal temperatures. The proposed model suggests that i) DAHe stars are mergers with enhanced $^{22}$Ne that enables distillation and may result in significant cooling delays; and ii) any mergers that distill neon will generate magnetism and chromospheres. The predicted chromospheric emission is consistent with the two known massive DQe white dwarfs.