FRICTIONAL HEATING AND NEUTRON-STAR THERMAL EVOLUTION

Differential rotation between the neutron star crust and a more rapidl y rotating interior superfluid leads to frictional heating that effect s the star's long-term thermal evolution and resulting surface emissio n. The frictional heating rate is determined by the mobility of the vo rtex lines that thread the rotating superfluid and pin to the inner cr ust lattice. If vortex pinning is relatively strong, a large velocity difference develops between the inner crust superfluid and the crust, leading to a high rate of heat generation by friction. Here we present the results of thermal evolution simulations based on two models of t he vortex pinning forces that bracket a range of plausible pinning str engths. We include the effects of superfluidity, magnetic fields, and temperature gradients. As representative standard and accelerated neut rino emission processes taking place in the core, we consider the modi fied Urea process in normal baryonic matter, and the much faster quark Urea process. Comparison of our results with neutron star surface tem perature data, including the recent temperature measurement of the Gem inga pulsar, shows that stars with soft equations of state and modest frictional heating are in closest agreement with the data; stars with stronger frictional heating have temperatures inconsistent with the up per limit of PSR 1929+10. Stiffer stars undergoing standard cooling ge nerally have temperatures lying above the Vela detection, a situation worsened by the inclusion of frictional heating. Stars undergoing acce lerated cooling without frictional heating have temperatures that fall far below most temperature measurements; the Vela and Geminga detecti ons being the most compelling examples. Only in stiff stars, which hav e thick crusts, can the inclusion of strong frictional heating raise t he temperature at late stages in the evolution to a level consistent w ith the data. However, such a large amount of heating leads to a tempe rature at similar to 1000 yr in excess of the Crab upper limit. Suppre ssion of accelerated neutrino emission processes, perhaps by superflui d pairing in the core, may yield acceptable cooling models.