Application of an Internal Friction Model to an Anomalous Behavior of the Pulsar Rotation Observed in PSR 1620–26

Abstract

The millisecond pulsar 1620–26 in the globular cluster M4 exhibits an unusually large second derivative of the pulse frequency, which together with the other pulse timing parameters yields a braking index of 4 × 107. Shibazaki and Mochizuki (1995, ApJ 438, 288) have suggested a frictional instability in the crust-superfluid coupling, which sets in below a critical temperature, as a possible cause for this extreme behavior of the pulsar rotation. We have conducted numerical calculations for the thermal and rotational evolution of old neutron stars after being recycled in order to examine this suggestion. We confirm that the rapid growth in internal friction between the crust and the superfluid, caused by frictional instability, can produce an extremely large second derivative in the crust-rotation rate, as observed in PSR 1620–26. We find that the magnitude of the second derivative of the crust-rotation rate is determined substantially by the growth time of the instability. We show that the physical parameters of the neutron star interior, obtained by comparing our model with observations, are in range expected in current theories.