The Impact of Magnetic Field on the Thermal Evolution of Neutron Stars

The impact of strong magnetic fields G on the thermal evolution of neutron stars is investigated, 13 B 1 10 including crustal heating by magnetic field decay. For this purpose, we perform 2D cooling simulations with anisotropic thermal conductivity considering all relevant neutrino emission processes for realistic neutron stars. The standard cooling models of neutron stars are called into question by showing that the magnetic field has relevant (and in many cases dominant) effects on the thermal evolution. The presence of the magnetic field significantly affects the thermal surface distribution and the cooling history of these objects during both the early neutrino cooling era and the late photon cooling era. The minimal cooling scenario is thus more complex than generally assumed. A consistent magnetothermal evolution of magnetized neutron stars is needed to explain the observations. Subject headings: radiation mechanisms: thermal — stars: magnetic fields — stars: neutron Online material: color figure It has been long hoped that the comparison of theoretical models for the cooling of neutron stars (NSs) with the direct observation of their thermal emission would help to unveil the physical conditions in the interior of these fascinating objects (Page et al. 2004; Yakovlev & Pethick 2004). Our knowledge of the cooling history of a NS has been improving as we refine the physical ingredients that play a key role in the thermal evolution of NSs. In the past, the field became more exciting every time that a new relevant idea was introduced (direct Urca, superfluidity in dense matter, fast processes due to exotic matter, etc.). However, despite the fact that a number of NSs are known to have large magnetic fields, most studies assumed weak magnetic fields. The main reason for this simplification was that the observed distribution of magnetic fields in radio pulsars peaks in a region where its effect was thought not to be relevant. The increasing evidence that most of the nearby NSs with reported thermal emission in the X-ray band of the electromagnetic spectrum have anisotropic surface temperature distributions (Zavlin 2007; Haberl 2007), the striking appearance of magnetars (Kaspi 2007), and the discovery of thermal emission from some high-field radio pulsars (Gonzalez et al. 2005) are indicating that most NSs which can be potentially used to contrast theoretical cooling curves have actually large magnetic fields ( G). The conclusion is that a realistic NS cooling 13 B 1 10 model must not avoid the inclusion of high magnetic fields. The so-called minimal cooling scenario (see, e.g., Page et al. 2004; Yakovlev & Pethick 2004 for recent reviews) defines the cooling model in which the emissivity is given by slow processes in the core, such as modified Urca and nucleonnucleon bremsstrahlung, and enhanced by the neutrino emission from the formation and breaking of Cooper pairs of superfluid neutrons. On the other hand, if fast neutrino processes (i.e., direct Urca) take place, the evolution of a NS changes dramatically, resulting in the enhanced or fast cooling scenario. Nevertheless, direct Urca only operates in the inner core of high-mass NSs for some equations of state. In this Letter, we want to revisit the minimal cooling model 1 Departament de Fı́sica Aplicada, Universitat d’Alacant, Apartat de Correus 99, E-03080 Alicante, Spain. 2 Theoretical Physics, Tandar Laboratory, National Council on Atomic Energy (CNEA-CONICET), Av. Gral. Paz 1499, 1650 San Martı́n, Pcia. Buenos Aires, Argentina. considering the effects of magnetic field. If a minimal model must include the minimum number of ingredients (but all the necessary ones) to explain the observations, the magnetic field should be taken into account as well. The effect of the magnetic field on the surface temperature distribution caused by the anisotropic heat transport in the envelope was studied in a pioneering paper by Greenstein & Hartke (1983). The observational consequences of these models were analyzed for the pulsars Vela and Geminga, among others (Page 1995). Potekhin & Yakovlev (2001) calculated the angular distribution of temperatures in magnetized envelopes taking into account the quantizing effect of the magnetic field on the electrons, and the suppression (enhancement) of the electron thermal conductivity in the direction perpendicular (parallel) to magnetic field lines. Nevertheless, the anisotropy generated in the envelope is not strong enough to be consistent with the observed thermal distribution of some isolated NSs, and it should originate deeper in the NS crust. The understanding of the kinetic properties of matter in NS crusts and envelopes has also been recently improved, with special attention received by the role of ions and phonons (Chugunov & Haensel 2007), which can be relevant at low temperatures and densities. In addition, the effect of impurities on the heat conduction in a nonperfect lattice is also an open problem that must be considered in the near future. More recently, crustal confined magnetic fields were considered to be responsible for the surface thermal anisotropy observed in some isolated NSs. Temperature distributions in the crust were obtained as stationary solutions of the diffusion equation with axial symmetry (Geppert et al. 2004). The approach assumed an isothermal core and a magnetized envelope as inner and outer boundary conditions, respectively. The results showed important deviations from the crust isothermal case for crustal confined magnetic fields with strengths B 1 G and temperature K. Same conclusions have been 13 8 10 T ! 10 obtained considering not only poloidal but also toroidal components of the magnetic field (Pérez-Azorı́n et al. 2006a; Geppert et al. 2006). These models succeeded in explaining simultaneously the observed X-ray spectrum, the optical excess, the pulsed fraction, and other spectral features of some isolated NSs, such as RX J0720.4 3125 (Pérez-Azorı́n et al. 2006b). Although former studies of anisotropic temperature distriL168 AGUILERA, PONS, & MIRALLES Vol. 673