Magnetar magnetothermal evolution with Landau-quantized electrons: enhanced Joule heating due to free electron diamagnetism and the magnetar heating problem

Abstract: Magnetars are systematically more luminous than other neutron stars. Previous studies suggest that supporting such high luminosities requires a heat source beyond standard Ohmic dissipation-- the ``magnetar heating problem''. We previously demonstrated using periodic box simulations that de Haas--van Alphen (dHvA) oscillations of the Landau quantization-induced magnetization in a neutron star could repeatedly generate large-gradient field components that undergo rapid Ohmic dissipation. Using the QMFM finite volume code developed for this purpose, we perform axisymmetric 2.5D electron magnetohydrodynamics plus thermal evolution simulations of a realistic neutron star crust, including all Landau quantization effects, to quantify this enhancement to field dissipation and heating of the star. We show that Landau quantization effects generate strong, small-scale magnetic field structures whose dissipation can heat the field-confined equatorial hot spot beyond its temperature in the absence of Landau quantization. Enhanced heating is greatest for weaker initial fields $B\sim10<sup>{14}$ G, for which magnetic energy is dissipated 30% faster: in this case, the crust cools sufficiently for the dHvA oscillations to reach large amplitudes. For the stronger fields $\gtrsim B\sim5\times10<sup>{14}$ G required to power the most luminous magnetars, the enhancement is modest, as dissipation of these fields heats the crust sufficiently to thermally suppress dHvA oscillations. In cases where heating is significantly enhanced, most of the heat goes into increasing the neutrino luminosity, and surface photon luminosity is only slightly increased. For the simple crust-confined fields that we simulated, Landau quantization-enhanced Joule heating is thus insufficient to explain the magnetar heating problem.