FRICTIONAL INSTABILITIES IN NEUTRON-STAR INTERIORS

The neutron superfluid in an inner crust of neutron stars is thought to be weakly coupled to the crust (charged components) and responsible for the slow postglitch relaxation of the pulse frequency. The linear stability analysis predicts that the system of superfluid and crust coupled through a temperature-sensitive frictional interaction is unstable for the thermal and rotational disturbances when the internal temperature falls down below a critical value. We have calculated the thermal and rotational evolution of neutron stars directly including the superfluid-crust coupling in the fully nonlinear equations. The frictional instability sets in at the critical temperature as predicted from the linear analysis. The subsequent thermal and rotational evolution is quite different from the evolution predicted by the previous models which assume the stable coupling between superfluid and crust. The neutron star exhibits a limit cycle-like behavior in which the temperature and the angular velocity difference between superfluid and crust oscillate. The temperature increase in a fraction of a cycle largely enhances friction between superfluid and crust, which causes so high a rate of the angular momentum transfer from the superfluid to the crust that the crust rotation is spun up. We suggest that the rotational behavior following the frictional instability may be responsible for an unusually large second derivative of the rotation rate observed in PSR 1620-26. We also discuss the other implications of our study on the pulsar observations.