2023ApJ...951...40R

The braking index is of great importance for interpreting the spin-down mechanism of pulsar rotation. The sudden spin-down rate transition of PSR B0540-69, the lowest braking index n = 0.031, and its variations up to 1.2 in its later phases, without glitches or changes in X-ray pulsed flux or shape, are the most enigmatic problem that challenges our understanding of the correlation between pulsar spin-down and magnetospheric emission. Here we discuss the above issue on the external and internal grounds of pulsar dynamics. It is found that the increase of the open field line region of the pulsar magnetosphere would give a plausible explanation for the state transition and the braking index of 0.031 of PSR B0540-69, and changes in the moment of inertia of PSR B0540-69 after the state transition may account for the variable braking indices in its subsequent phases. Results indicate that, on the one hand, a change in the magnetosphere size of a pulsar would influence the external braking torque and have a substantial impact on the observed braking index; and, on the other hand, a sudden change in external torque may trigger the mechanism that could slowly increase the moment of inertia of the pulsar and cause an observable effect on the spin frequency second derivatives. This is hardly explained under the regular glitch hypothesis. In this respect, PSR B0540-69 would be the ideal candidate to study the inside and outside dynamics of a pulsar.