Context. The standard cooling models of neutron stars predict temperatures of T??107?yr. However, the likely thermal emission detected from the millisecond pulsar J0437-4715, of spin-down age ts?~?7?×?109?yr, implies a temperature T?~?105?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 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 are unlikely to have a significant heating effect on old neutron stars. The thermal evolution for the other mechanisms is computed with 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 any 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 is therefore strongly sensitive to their initial rotation period.
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