THE INCLINATION ANGLE AND EVOLUTION OF THE BRAKING INDEX OF PULSARS WITH PLASMA-FILLED MAGNETOSPHERE: APPLICATION TO THE HIGH BRAKING INDEX OF PSR J1640-4631

Abstract

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 3. 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, which is incompatible with the single-peaked pulse profile. The magnetic dipole model with the corotating plasma predicts braking indices between 3 and 3.25. We find that the braking index of 3.15 is consistent with two different inclination angles, 18 degrees.5 +/- 3 degrees and 56 degrees +/- 4 degrees. The smaller angle is preferred given that 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 degrees.23 per century, three times smaller in absolute value than the rate recently observed for the Crab pulsar.