TY - JOUR
T1 - Inclined Pulsar Magnetospheres in General Relativity
T2 - Polar Caps for the Dipole, Quadrudipole, and beyond
AU - Gralla, Samuel E.
AU - Lupsasca, Alexandru
AU - Philippov, Alexander
N1 - Funding Information:
We thank Feryal Özel, Dimitrios Psaltis, Anatoly Spitkovsky, and Alexander Tchekhovskoy for helpful conversations. This work was supported by NSF grants 1205550 to Harvard University and 1506027 to the University of Arizona, by the NASA Earth and Space Science Fellowship Program (grant NNX15AT50H to A.P.) and by the Porter Ogden Jacobus Fellowship, awarded to A.P. by the graduate school of Princeton University. The simulations presented in this paper used computational resources supported by the PICSciE-OIT High Performance Computing Center and Visualization Laboratory, and by the NASA/Ames HEC Program (SMD-16-6663, SMD-16-7816).
Funding Information:
This work was supported by NSF grants 1205550 to Harvard University and 1506027 to the University of Arizona, by the NASA Earth and Space Science Fellowship Program (grant NNX15AT50H to A.P.) and by the Porter Ogden Jacobus Fellowship, awarded to A.P. by the graduate school of Princeton University. The simulations presented in this paper used computational resources supported by the PICSciE-OIT High Performance Computing Center and Visualization Laboratory, and by the NASA/Ames HEC Program (SMD-16-6663, SMD-16-7816).
Publisher Copyright:
© 2017. The American Astronomical Society. All rights reserved.
PY - 2017/12/20
Y1 - 2017/12/20
N2 - 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.
AB - 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.
KW - magnetic fields
KW - plasmas
KW - pulsars: general
KW - stars: rotation
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U2 - 10.3847/1538-4357/aa978d
DO - 10.3847/1538-4357/aa978d
M3 - Article
AN - SCOPUS:85039708700
VL - 851
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 2
M1 - 137
ER -