Context: The standard cooling models of neutron stars predict temperatures $T<10^{4}$ K for ages $t>10^{7}$ yr. However, the likely thermal emission detected from the millisecond pulsar J0437-4715, of spin-down age $t_s \sim 7\times10^9$ yr, implies a temperature $T\sim 10^5$ K. Thus, a heating mechanism needs to be added to the cooling models in order to obtain agreement between theory and observation. Aims: Several internal heating mechanisms could be operating in neutron stars, such as magnetic field decay, dark matter accretion, crust cracking, superfluid vortex creep, and non-equilibrium reactions ("rotochemical heating"). We study these mechanisms in order to establish which could be the dominant source of thermal emission from old pulsars. Methods: We show by simple estimates that magnetic field decay, dark matter accretion, and crust cracking mechanism are unlikely to have a significant effect on old neutron stars. The thermal evolution for the other mechanisms is computed using the code of Fernández and Reisenegger. Given the dependence of the heating mechanisms on the spin-down parameters, we study the thermal evolution for two types of pulsars: young, slowly rotating "classical" pulsars and old, fast rotating millisecond pulsars. Results: We find that magnetic field decay, dark matter accretion, and crust cracking do not produce detectable heating of old pulsars. Rotochemical heating and vortex creep can be important both for classical pulsars and millisecond pulsars. More restrictive upper limits on the surface temperatures of classical pulsars could rule out vortex creep as the main source of thermal emission. Rotochemical heating in classical pulsars is driven by the chemical imbalance built up during their early spin-down, and therefore strongly sensitive to their initial rotation period.
Explaining the thermal emission of old neutron stars with rotochemical heating and magnetized superconducting protons
Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Universidad Metropolitana de Ciencias de la Educación（教育与科学都市大学）；Institut de Recherche en Astrophysique et Planétologie (IRAP)（天体物理学与行星学研究所在）；Indiana University（印第安纳大学）
Pontificia Universidad Católica de Chile（智利天主教宗座大学）；Universidad Metropolitana de Ciencias de la Educación（教育科学都会大学）；Institut de Recherche en Astrophysique et Planétologie (IRAP)（天体物理学与行星学研究所在）；Indiana University（印第安纳大学）；Pennsylvania State University（宾夕法尼亚州立大学）；The George Washington University（乔治华盛顿大学）；Texas State University（德克萨斯州立大学）
