Magneto-thermal evolution of neutron stars

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 onedimensional 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 T b − T s -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 10 5 −10 6 years of an NS's life. As a consequence, all neutron stars born with fields over a critical value (>5 × 10 13 G) reach similar field strengths (≈2−3 × 10 13 G) at late times. Irrespective of the initial magnetic field strength, the temperature becomes so low after 10 6 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.

The Tale of the Two Tails of the Oldish PSR J2055+2539

“…While the majority of X-ray-emitting isolated neutron stars (NSs;see, e.g., Kaspi et al 2006) exhibit thermal emission coming from the whole NS surface, no such component is required to fit our XMM-Newton spectra. Using the blackbody model, for an NS radius of 10 km and a distance of 600 pc, the 3σ upper limit on the surface temperature is 7.5×10 5 K. This low temperature fits well the behavior of old pulsars (e.g., the J0357+3205 pulsar-Morla hereafter-upper limit temperature is half this value;Marelli et al 2013): we note that the cooling mechanism is highly dependent on the magnetic field of the pulsar, so that different magnetothermal evolution paths are expected (see, e.g., Pons et al 2009). Taking into account the thermal radiation from hot spot(s), straight estimates of neutron star polar cap size based on a simple dipole magnetic field geometrygive a polar cap radius R PC =R(RΩ/c) 1 2 , where R is the neutron star radius, Ω is the angular frequency, and c is the speed of light (De Luca et al 2005).…”

Magnetic field evolution in superconducting neutron stars

“…This transition is crucial in understanding how changes of the core magnetic field are translated to the crust. The analysis presented in this paper does, therefore, not reconcile the discrepancy between short crustal decay timescales (Pons, Miralles & Geppert 2009) and the much longer core evolution. In order to significantly reduce the latter different dissipative mechanisms have to be invoked.…”

A simple mechanism for the anti-glitch observed in AXP 1E 2259+586

“…(1) it is clear that the net effect of the decay of the toroidal magnetic field, which is expected due to the combination of Ohmic and Hall effects in the neutron star interior, as it is shown in numerical simulations [see, fon instance, 23,24], is to make an initially stable prolate configuration unstable. The "more spherical" configuration has greater moment of inertia respect to the rotation axis, z in this case, and thus, in the abscense of an external torque, due to the conservation of the angular momentum, this could easily account for the sudden spin-down observed.…”