Superfluid Friction and Late‐Time Thermal Evolution of Neutron Stars

Abstract

The recent temperature measurements ofthe two older isolated neutron stars PSR 1929+10 and PSR 0950+08(ages of 3x10^6 and 2x10^7 yr, respectively) indicate that theseobjects are heated. A promising candidate heat source is frictionbetween the neutron star crust and the superfluid it is thought tocontain. We study the effects of superfluid friction on the long-termthermal and rotational evolution of a neutron star. Differentialrotation velocities between the superfluid and the crust (averagedover the inner crust moment of inertia) of omega~0.6 rad s^-1 forPSR 1929+10 and ~0.02 rad s^-1 for PSR 0950+08 would account fortheir observed temperatures. These differential velocities could besustained by the pinning of superfluid vortices to the inner crustlattice with strengths of ~1 MeV per nucleus. Pinned vortices cancreep outward through thermal fluctuations or quantum tunneling. Forthermally activated creep, the coupling between the superfluid andcrust is highly sensitive to temperature. If pinning maintains largedifferential rotation (~30 rad s^-1), a feedback instability couldoccur in stars younger than ~10^5 yr causing oscillations of thetemperature and spin-down rate over a period of ~0.3t_age. For starsolder than ~10^6 yr, however, vortex creep occurs through quantumtunneling and the creep velocity is too insensitive to temperaturefor a thermal-rotational instability to occur. These older starscould be heated through a steady process of superfluid friction.