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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.

Context. We study the non-linear evolution of magnetic fields in neutron star crusts with special attention to the influence of the Hall drift. Aims. Our goal is to understand the conditions for fast dissipation due to the Hall term in the induction equation. We study the interplay of Ohmic dissipation and Hall drift in order to find a timescale for the overall crustal field decay. Methods. We solve numerically the Hall induction equation by means of a hybrid method (spectral in angles but finite differences in the radial coordinate). The microphysical input consists of the most modern available crustal equation of state, composition and electrical conductivities.Results. We present the first long term simulations of the non-linear magnetic field evolution in realistic neutron star crusts with a stratified electron number density and temperature dependent conductivity. We show that Hall drift influenced Ohmic dissipation takes place in neutron star crusts on a timescale of 10 6 years. When the initial magnetic field has magnetar strength, the fast Hall drift results in an initial rapid dissipation stage that lasts ∼ 10 4 years. The interplay of the Hall drift with the temporal variation and spatial gradient of conductivity tends to favor the displacement of toroidal fields toward the inner crust, where stable configurations can last for ∼ 10 6 years. We show that the thermally emitting isolated neutron stars, as the Magnificent Seven, are very likely descendants of neutron stars born as magnetars.

Abstract.The classical vacuum gap model of Ruderman & Sutherland, in which spark-associated sub-beams of subpulse emission circulate around the magnetic axis due to the E × B drift of spark plasma filaments, provides a natural and plausible physical mechanism explaining the subpulse drift phenomenon. Moreover, this is the only model with quantitative predictions that can be compared with observations. Recent progress in the analysis of drifting subpulses in pulsars has provided a strong support for this model by revealing a number of sub-beams circulating around the magnetic axis in a manner compatible with theoretical predictions. However, a more detailed analysis revealed that the circulation speed in a pure vacuum gap is too high when compared with observations. Moreover, some pulsars demonstrate significant time variations in the drift rate, including a change of the apparent drift direction, which is obviously inconsistent with the E × B drift scenario in a pure vacuum gap. We attempted to resolve these discrepancies by considering a partial flow of iron ions from the positively charged polar cap, coexisting with the production of outflowing electron-positron plasmas. The model of such a charge-depleted acceleration region is highly sensitive to both the critical ion temperature T i ∼ 10 6 K (above which ions flow freely with the corotational charge density) and the actual surface temperature T s of the polar cap, heated by the bombardment of ultra-relativistic charged particles. By fitting the observationally deduced drift-rates to the theoretical values, we managed to estimate polar cap surface temperatures in a number of pulsars. The estimated surface temperatures T s correspond to a small charge depletion of the order of a few percent of the Goldreich-Julian corotational charge density. Nevertheless, the remaining acceleration potential drop is high enough to discharge through a system of sparks, cycling on and off on natural time-scales described by the Ruderman & Sutherland model. We also argue that if the thermionic electron outflow from the surface of a negatively charged polar cap is slightly below the Goldreich-Julian density, then the resulting small charge depletion will have similar consequences as in the case of the ions outflow. We thus believe that the sparking discharge of a partially shielded acceleration potential drop occurs in all pulsars, with both positively ("pulsars") and negatively ("anti-pulsars") charged polar caps.

We confront theoretical models for the rotational, magnetic, and thermal evolution of an ultramagnetized neutron star, or magnetar, with available data on the anomalous X-ray pulsars (AXPs). We argue that, if the AXPs are interpreted as magnetars, their clustering of spin periods between 6 and 12 s (observed at present in this class of objects), their period derivatives, their thermal X-ray luminosities, and the association of two of them with young supernova remnants can only be understood globally if the magnetic field in magnetars decays significantly on a timescale of the order of 104 yr.

We explore the thermal evolution of a neutron star undergoing episodes of intense accretion, separated by long periods of quiescence. By using an exact cooling code, we follow in detail the flow of heat in the star due to the time-dependent accretion-induced heating from pycnonuclear reactions in the stellar crust, to the surface photon emission, and to the neutrino cooling. These models allow us to study the neutron stars of the soft Xray transients. In agreement with recent work of Brown, Bildsten, & Rutledge, we conclude that the soft component of the quiescent luminosity of Aql X-1, of 4U 1608Ϫ522, and of the recently discovered SAX J1808.4 can be understood as thermal emission from a cooling neutron star with negligible neutrino emission. However, we show that, in the case of Cen X-4, despite its long recurrence time, strong neutrino emission from the neutron star inner core is necessary to understand the observed low ratio of quiescent to outburst luminosity. This result implies that the neutron star in Cen X-4 is heavier than the one in the other systems and the pairing critical temperature in its center must be low enough (well below 10 9 K) to avoid a strong suppression of the neutrino T c emission.

An analysis of the role of general relativistic effects on the decay of neutron star's magnetic field is presented. At first, a generalized induction equation on an arbitrary static background geometry has been derived and, secondly, by a combination of analytical and numerical techniques, a comparison of the time scales for the decay of an initial dipole magnetic field in flat and 1 curved spacetime is discussed. For the case of very simple neutron star models, rotation not accounted for and in the absence of cooling effects, we find that the inclusion of general relativistic effects result, on the average, in an enlargement of the decay time of the field in comparison to the flat spacetime case. Via numerical techniques we show that, the enlargement factor depends upon the dimensionless compactness ratio ǫ = 2GM c 2 R , and for ǫ in the range (0.3 , 0.5), corresponding to compactness ratio of realistic neutron star models, this factor is between 1.2 to 1.3. The present analysis shows that general relativistic effects on the magnetic field decay ought to be examined more carefully than hitherto. A brief discussion of our findings on the impact of neutron stars physics is also presented.

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.