Spin-down of an oblique rotator with a current-starved outer magnetosphere

Abstract

A variant of the vacuum-dipole model of rotation-powered pulsars is presented that accounts for the observed spin-down properties of all three pulsars with braking indices measured from absolute pulse numbering (the Crab, PSR B0540 -69 and PSR B1509 -58). In the model, the neutron star and inner magnetosphere are treated phenomenologically as a single unit, a magnetized, perfectly conducting sphere of radius rv rotating rigidly in vacua. The 'vacuum radius' rv corresponds to the innermost point in the magnetosphere where field-aligned flow breaks down and the plasma becomes three-dimensional, that is, the point where cyclotron losses occur slowly enough to allow electrons (or positrons) to m..