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Inclination angle and braking index evolution of pulsars with plasma-filled magnetosphere: application to high braking index of PSR J1640-4631

The recently discovered rotationally powered pulsar PSR J1640-4631 is the first to have a braking index measured, with high enough precision, that is greater than three. An inclined magnetic rotator in vacuum or plasma would be subject not only to spin-down but also to an alignment torque. The vacuum model can address the braking index only for an almost orthogonal rotator that is incompatible with the single peaked pulse profile. The magnetic dipole model with the corotating plasma predicts braking indices between $3-3.25$. We find that the braking index of $3.15$ is consistent with two different inclination angles, $18.5\pm 3$ degrees and $56 \pm 4$ degrees. The smaller angle is preferred given the pulse profile has a single peak and the radio output of the source is weak. We infer the change in the inclination angle to be at the rate $-0.23$ degrees per century, three times smaller in absolute value than the rate recently observed for the Crab pulsar.