Inclined Pulsar Magnetospheres in General Relativity: Polar Caps for the Dipole, Quadrudipole and Beyond

Understand

In the canonical model of a pulsar, rotational energy is transmitted through the surrounding plasma via two electrical circuits, each connecting to the star over a small region known as a "polar cap." For a dipole-magnetized star, the polar caps coincide with the magnetic poles (hence the name), but in general, they can occur at any place and take any shape.

• In light of their crucial importance to most models of pulsar emission (from radio to X-ray to wind), we develop a general technique for determining polar cap properties.
• We consider a perfectly conducting star surrounded by a force-free magnetosphere and include the effects of general relativity.
• Using a combined numerical-analytical technique that leverages the rotation rate as a small parameter, we derive a general analytic formula for the polar cap shape and charge-current distribution as a function of the stellar mass, radius, rotation rate, moment of inertia, and magnetic field.