Journal Article

Equilibrium models of relativistic stars with a toroidal magnetic field

J. Frieben and L. Rezzolla

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 427, issue 4, pages 3406-3426
Published in print December 2012 | ISSN: 0035-8711
Published online December 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2012.22027.x
Equilibrium models of relativistic stars with a toroidal magnetic field

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We have computed models of rotating relativistic stars with a toroidal magnetic field and investigated the combined effects of magnetic field and rotation on the apparent shape (i.e. the surface deformation), which could be relevant for the electromagnetic emission, and on the internal matter distribution (i.e. the quadrupole distortion), which could be relevant for the emission of gravitational waves. Using a sample of eight different cold nuclear physics equations of state, we have computed models of maximum field strength, as well as the distortion coefficients for the surface and the quadrupolar deformations. Surprisingly, we find that non-rotating models admit arbitrary levels of magnetization, accompanied by a growth of size and quadrupole distortion to which we could not find a limit. Rotating models, on the other hand, are subject to a mass-shedding limit at frequencies well below the corresponding ones for unmagnetized stars. Overall, the space of solutions can be split into three distinct classes for which the surface deformation and the quadrupole distortion are either prolate and prolate, oblate and prolate, or oblate and oblate, respectively. We also derive a simple formula expressing the relativistic distortion coefficients, which allows one to compute the surface deformation and the quadrupole distortion up to significant levels of rotation and magnetization, essentially covering all known magnetars. Such a formula replaces Newtonian equivalent expressions that overestimate the magnetic quadrupole distortion by about a factor of 6 and are inadequate for strongly relativistic objects like neutron stars.

Keywords: gravitational waves; stars: magnetars; stars: magnetic field; stars: neutron

Journal Article.  14699 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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