Internal heating of old neutron stars: contrasting different mechanisms

Neutron stars are predicted to cool below 10⁵ K in less than 10 Myr. However, thermal emission has been detected from one millisecond pulsar with a long spindown age (Kargaltsev et al. 2004, ApJ, 602, 327), J0437-4715, and one old isolated neutron star, J0108-1431 (Mignani et al. 2008, 2008, A&A, 488.1027) with T ~ 10⁵ K. The upper limits for others suggest that some heating mechanism is needed. The authors examine a range of internal and extrinsic heating mechanisms in light of both these detections and the available upper limits. They exclude several mechanisms (internal magnetic field decay, accretion of dark matter, and cracking of the neutron star crust) and conclude that vortex creep during spindown and rotochemical heating -- involving the change in balance between neutrons and protons with associated neutrino emission and heating during spindown -- can provide the required sources for maintaining the surface temperature. They model the thermal evolution of neutron stars, finding that the temperatures decrease slowly with time as t^-1/3 with modified URCA cooling and t^-3/8 for vortex creep. Superfluidity can increase the duration of higher temperatures at late times for the rotochemical heating. They also examine some predictions related to vortex pinning and consider how its efficiency varies as a heat source. The available upper limits for surface temperatures, when improved, will test these ideas.