Temperature distribution in magnetized neutron star crusts

Abstract

Abstract. We investigate the influence of different magnetic field configurations on the temperature distribution in neutron star crusts. We consider axisymmetric dipolar fields which are either restricted to the stellar crust, "crustal fields", or allowed to penetrate the core, "core fields". By integrating the two-dimensional heat transport equation in the crust, taking into account the classical (Larmor) anisotropy of the heat conductivity, we obtain the crustal temperature distribution, assuming an isothermal core. Including classical and quantum magnetic field effects in the envelope as a boundary condition, we deduce the corresponding surface temperature distributions. We find that core fields result in practically isothermal crusts unless the surface field strength is well above 10 15 G while for crustal fields with surface strength above a few times 10 12 G significant deviations from crustal isothermality occur at core temperatures inferior or equal to 10 8 K. At the stellar surface, the cold equatorial region produced by the suppression of heat transport perpendicular to the field by the Larmor rotation of the electrons in the envelope, present for both core and crustal fields, is significantly extended by that classical suppression at higher densities in the case of crustal fields. This can result, for crustal fields, in two small warm polar regions which will have observational consequences: the neutron star has a small effective thermally emitting area and the X-ray pulse profiles are expected to have a distinctively different shape compared to the case of a neutron star with a core field. These features, when compared with X-ray data on thermal emission of young cooling neutron stars, would provide a first step toward a new way of studying the magnetic flux distribution within a neutron star.

The magnificent seven: magnetic fields and surface temperature distributions

“…This could point to magnetic field configurations of an off-centered dipole or the involvement of higher-order multi-pole components. Studies of the effects of a strong magnetic field on the temperature distribution in the neutron star crust show that configurations which include dipolar poloidal and toroidal components can indeed reproduce the observed temperature distributions (Geppert et al 2004.…”

“…Again, a simple model with two hot spots with temperatures T ∞ 1 = 92 eV and T ∞ 2 = 84 eV and full angular sizes of 8 • and 10 • which are separated by ∼ 160 • can reproduce the data. A more physical temperature distribution based on the crustal field models by Geppert et al (2004) which can produce relatively strong temperature gradients from the magnetic poles to the equator was equally successful.…”

RX J1856.5-3754 as a possible strange star candidate

“…1. Details of the crust microphysics are as described in Geppert et al (2004Geppert et al ( , 2006. We consider a strange star model with a radius of reaches 10 13 G highly nonuniform temperature profiles develop in the thin strange star crust: such profiles are sufficiently non-uniform to produce the wanted surface temperature distribution, i.e.…”

“…The large values of B θ in the crust have the effect of inhibiting radial heat flow except in regions close to the magnetic axis where B r dominates over B θ (Geppert et al 2004). …”

“…An interpretation of these results is that the surface temperature of the star is highly non-uniform (Pons et al 2002;Trümper et al 2004), possibly due to the presence of a strong magnetic field. Models of surface temperature distribution with purely poloidal magnetic fields (Page 1995;Geppert et al 2004) do predict non-uniform surface temperature distributions, , but such inhomogeneities are not strong enough to produce such small X-ray emitting regions surrounded by large cold regions detectable in the optical band as observed. However, inclusion of a toroidal component of the magnetic field, confined to the neutron star crust, has a dramatic effect (Pérez-Azorín et al 2006;Geppert et al 2006; see also Pons 2007;Page 2007): this field component inhibits heat from the stellar core to flow to the surface through most of the crust, except for small domains surrounding the magnetic axis, and results in highly non-uniform surface temperature distributions producing good fits to the observed thermal spectra, from the optical up to the X-ray band.…”