Three-dimensional Modeling of the Magnetothermal Evolution of Neutron Stars: Method and Test Cases

Neutron stars harbor extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution and, hence, the star's observational properties. In this work, we present the first realistic simulations of the coupled crustal magnetothermal evolution of isolated neutron stars in three dimensions accounting for neutrino emission, obtained with the pseudo-spectral code PARODY. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evolution following episodes of localized energy injection. Simulations show that a resistive tearing instability develops in about a Hall time if the initial toroidal field exceeds approximate to 10(15) G. This leads to crustal failures because of the huge magnetic stresses coupled with the local temperature enhancement produced by dissipation. Localized heat deposition in the crust results in the appearance of hot spots on the star surface, which can exhibit a variety of patterns. Because the transport properties are strongly influenced by the magnetic field, the hot regions tend to drift away and get deformed following the magnetic field lines while cooling. The shapes obtained with our simulations are reminiscent of those recently derived from NICER X-ray observations of the millisecond pulsar PSR.J0030+0451.