Magneto-thermal evolution of neutron stars

¹ Departament de Física Aplicada, Universitat d'Alacant, Ap. Correus 99, 03080 Alacant, Spain e-mail: jose.pons@ua.es
² German Aerospace Center, Institute for Space Systems, Rutherfordstr. 2, 12489 Berlin, Germany

Received: 27 October 2008
Accepted: 14 December 2008

Abstract

Context. The presence of magnetic fields in the crust of neutron stars (NSs) causes a non-spherically symmetric temperature distribution. The strong temperature dependence of the magnetic diffusivity and thermal conductivity, together with the heat generated by magnetic dissipation, couple the magnetic and thermal evolution of NSs, which can no longer be formulated as separated one-dimensional problems.

Aims. We study the mutual influence of thermal and magnetic evolution in a neutron star's crust in axial symmetry. Taking realistic microphysical inputs into account, we find the heat released by Joule effect consistent with the circulation of currents in the crust, and we incorporate its effects in 2D cooling calculations.

Methods. We solve the induction equation numerically using a hybrid method (spectral in angles, but a finite-differences scheme in the radial direction), coupled to the thermal diffusion equation. To improve the boundary conditions, we also revisit the envelope stationary solutions updating the well known -relations to include the effect of 2D heat transfer calculations and new microphysical inputs.

Results. We present the first longterm 2D simulations of the coupled magneto-thermal evolution of neutron stars. This substantially improves previous works in which a very crude approximation in at least one of the parts (thermal or magnetic diffusion) has been adopted. Our results show that the feedback between Joule heating and magnetic diffusion is strong, resulting in a faster dissipation of the stronger fields during the first  years of an NS's life. As a consequence, all neutron stars born with fields over a critical value (> G) reach similar field strengths (≈ G) at late times. Irrespective of the initial magnetic field strength, the temperature becomes so low after 10⁶ years that the magnetic diffusion timescale becomes longer than the typical ages of radiopulsars, thus apparently resulting in no dissipation of the field in old NS. We also confirm the strong correlation between the magnetic field and the surface temperature of relatively young NSs discussed in preliminary works. The effective temperature of models with strong internal toroidal components are systematically higher than those of models with purely poloidal fields, due to the additional energy reservoir stored in the toroidal field that is gradually released as the field dissipates.