Numerical simulations of Hall magnetohydrodynamics in neutron star crusts with Landau-quantized electrons*

In strongly-magnetized neutron star crusts (B ≥ 10¹⁴ G), electrons are quantized into a moderate number of Landau levels. This can dramatically change the thermodynamic (specific heat capacity, magnetization, differential magnetic susceptibility) and transport properties (electrical and thermal conductivity) of the crust. In a neutron star crust, magnetic field evolution is best described using the formalism of Hall magnetohydrodynamics (MHD). We include for the first time the effects of Landau quantization on both thermodynamic and transport properties of neutron star crusts in Hall magnetothermal evolution simulations. Comparing simulations including Landau-quantization effects those excluding these effects, we assess their importance to the overall magneto-thermal history of neutron stars, in particular their impact on Ohmic heating and evolution of the magnetic field topology.