An Internal Friction Model for an Unusually Large Second Derivative of the Pulsar Rotation Rate

The millisecond pulsar 1620 – 26 in the globular cluster M4 exhibits an unusually large second derivative of the pulse frequency 1,2 , which together with the other pulse timing parameters yields the braking index of 4 × 10 7 . To understand this extreme behavior of the pulsar rotation, we consider the effect of a superfluid‐crust coupling in the neutron star interior on the crust rotation. The frictional coupling between superfluid and crust becomes unstable when the temperature of the star falls down below a critical temperature. Then, the frictional instability develops a limit cycle 4 The temperature increase in a part of the limit cycle enhances friction between the crust and the superfluid so largely and accelerates the angular momentum transfer from the superfluid to the crust so rapidly that the crust rotation is even spun up. This rapidly growing friction can produce an extremely large second derivative in the crust rotation rate as observed in PSR 1620 – 26.