Superfluid Friction and Late‐Time Thermal Evolution of Neutron Stars

The recent temperature measurements of the two older isolated neutron starsPSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr,respectively) indicate that these objects are heated. A promising candidateheat source is friction between the neutron star crust and the superfluid it isthought to contain. We study the effects of superfluid friction on thelong-term thermal and rotational evolution of a neutron star. Differentialrotation velocities between the superfluid and the crust (averaged over theinner crust moment of inertia) of $\bar\omega\sim 0.6$ rad s$^{-1}$ for PSR1929+10 and $\sim 0.02$ rad s$^{-1}$ for PSR 0950+08 would account for theirobserved temperatures. These differential velocities could be sustained bypinning of superfluid vortices to the inner crust lattice with strengths of$\sim$ 1 MeV per nucleus. Pinned vortices can creep outward through thermalfluctuations or quantum tunneling. For thermally-activated creep, the couplingbetween the superfluid and crust is highly sensitive to temperature. If pinningmaintains large differential rotation ($\sim 10$ rad s$^{-1}$), a feedbackinstability could occur in stars younger than $\sim 10^5$ yr causingoscillations of the temperature and spin-down rate over a period of $\sim 0.3t_{\rm age}$. For stars older than $\sim 10^6$ yr, however, vortex creep occursthrough quantum tunneling, and the creep velocity is too insensitive totemperature for a thermal-rotational instability to occur. These older starscould be heated through a steady process of superfluid friction.Comment: 26 pages, 1 figure, submitted to Ap