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#### Equilibrium models of relativistic stars with a toroidal magnetic field

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1207.4035

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MNRAS427_3406.full.pdf

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##### Citation

Frieben, J., & Rezzolla, L. (2012). Equilibrium models of relativistic stars with
a toroidal magnetic field.* Monthly Notices of the Royal Astronomical Society: Letters,*
*427*, 3406-3426. doi:10.1111/j.1365-2966.2012.22027.x.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-EEC2-8

##### Abstract

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 magnetisation, 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 unmagnetised 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 and that allows one to compute the
surface deformation and the quadrupole distortion up to significant levels of
rotation and magnetisation, essentially covering all known magnetars. Such
formula replaces Newtonian equivalent expressions that overestimate the
quadrupole distortion by about a factor of five and are inadequate for
strongly-relativistic objects like neutron stars.