An investigation into surface temperature distributions of high-magnetic-field pulsars

Abstract

Bearing in mind the application to high-magnetic-field (high-B) radio pulsars, we investigate two-dimensional (2D) thermal evolutions of neutron stars (NSs). We pay particular attention to the influence of different equilibrium configurations on the surface temperature distributions. The equilibrium configurations are constructed in a systematic manner, in which both toroidal and poloidal magnetic fields are determined self-consistently with the inclusion of general relativistic effects. To solve the 2D heat transfer inside the NS interior out to the crust, we have developed an implicit code based on a finite-difference scheme that deals with anisotropic thermal conductivity and relevant cooling processes in the context of a standard cooling scenario. In agreement with previous studies, the surface temperatures near the pole become higher than those in the vicinity of the equator as a result of anisotropic heat 1 transfer. Our results show that the ratio of the highest to the lowest surface temperatures changes maximally by one order of magnitude, depending on the equilibrium configurations. Despite such difference, we find that the area of such hot and cold spots is so small that the simulated X-ray spectrum could be well reproduced by a single temperature blackbody fitting.

Cooling of Magnetars with Exotic Matter

“…The scheme for 2D thermal evolution of magnetars is the same as that presented in our past paper [6]. We apply Tomimura-Eriguchi method for the initial models in this scheme, in which the parameters for the magnetic field profile in Ref.…”

“…We apply Tomimura-Eriguchi method for the initial models in this scheme, in which the parameters for the magnetic field profile in Ref. [6] are set as k = 1 for strong magnetic field, and k = 0.1 for typical magnetic field of NSs, with other parameters of a = 50, µ = 10 −4 . The method is formulated to obtain the rotating equilibria with magnetic field in Newtonian, and we hence apply the GR correction to the gravitational potential assuming the spherical structures because of the slow rotation.…”

“…All models in the study are summarized in Table I, and their time evolution is governed by the 2D-thermal diffusion equation in general relativistic framework [6]. The grids for the space are set as 300 × 100, which means that we need to proceed the matrix inversion of 30, 000 × 30, 000 matrix in an implicit manner at each time-step.…”