Ritam Mallick Stefan Schramm
Magnetars are compact stars which are observationally determined to have a very strong surface magnetic fields of the order of $10^{14}-10^{15}$G. The centre of the star can even have a magnetic field several orders of magnitude larger. We study the effect of the magnetic field on the mass and shape of such a star. In general, we assume a non-uniform magnetic field inside the star which varies with density. The magnetic energy and magnetic pressure as well as the metric are expanded as multipoles in spherical harmonics up to the quadrupole term to the total energy and pressure. Solving the Einstein equations for the expanded gravitational potential, one obtains the correction terms of the expansion as functions of magnetic pressure. These are related to the excess mass and deformation of the star. Within a nonlinear model for the hadronic EoS the excess mass and deformation of the star are quite significant if the surface magnetic field is $10^{15}$G and the central field is about $10^{18}-10^{19}$G. However, higher magnetic fields leads to a violation of the assumption of a perturbative correction as the correction terms then becomes larger than the original term. This provides an upper limit for the central magnetic field within this approach. The excess mass for such huge magnetic fields is at least one order of magnitude lower than the original stellar mass. The deformation of the star is quite large for reasonable values of the magnetic field. The equatorial radius becomes extended, whereas the pole shrinks and the star exhibits an oblate spheroid shape.
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http://arxiv.org/abs/1307.5185
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