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

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...

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Bibliographic Details
Published in:The Astrophysical journal 2017-12, Vol.851 (2), p.137
Main Authors: Gralla, Samuel E., Lupsasca, Alexandru, Philippov, Alexander
Format: Article
Language:English
Subjects:
Astrophysics
Axes of rotation
Charge distribution
Circuits
Current distribution
Dipoles
Emission
Magnetic fields
Magnetic poles
Moments of inertia
plasmas
Polar caps
Polar regions
Pulsar magnetospheres
Pulsars
pulsars: general
Quadrupoles
Relativity
stars: rotation
Stellar magnetic fields
Stellar mass
Stellar rotation
Stellar winds
Theory of relativity
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Summary: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. We present results for dipole and quadrudipole fields (superposed dipole and quadrupole) inclined relative to the axis of rotation. The inclined dipole polar cap results are the first to include general relativity, and they confirm its essential role in the pulsar problem. The quadrudipole pulsar illustrates the phenomenon of thin annular polar caps. More generally, our method lays a foundation for detailed modeling of pulsar emission with realistic magnetic fields.
ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/aa978d