Session 50 - Pulsars in the UV and Visible.
Topical, Oral session, Wednesday, June 10
Friars,

## [50.10] Theory of Braking Indices

A. Melatos (Astronomy Dept, UC Berkeley)

A variant of the vacuum-dipole theory of pulsar spin-down is presented that correctly predicts the braking indices of the Crab pulsar, PSR B0540-69 and PSR B1509-58 as measured from absolute pulse numbering. In the theory, the neutron star and its inner magnetosphere are modeled phenomenologically as a single unit, a conducting sphere of radius r_v rotating rigidly in vacuo. The `vacuum radius' r_v is chosen to correspond to the point in the magnetosphere where the outflowing plasma becomes three-dimensional and cross-field currents can flow. For young, Crab-like pulsars, one finds r_\ast \ll r_v; the model therefore differs from the standard vacuum rotator, which has radius r_\ast and is treated as point-like.

Given three observable pulsar parameters --- the rotation frequency ømega, its time derivative \dotømega, and the angle \alpha between the rotation and magnetic axes --- and with zero free parameters, the theory yields braking index values n=ømega\ddotømega/\dotømega^2 for the above three pulsars that agree with timing data to 4 per cent. The theory also makes testable predictions regarding the second deceleration parameter m [e.g.\ m < n(2n-1)] and implies that n approaches 3.0 for every pulsar as it ages (with consequences for the P-\dotP diagram). The success of the theory has several implications for magnetospheric structure, e.g.\ the role of charge separation in the inner magnetosphere, and the dominance of displacement current over conduction current beyond r_ v.