Deformation of a magnetized neutron star

TL;DR

This paper investigates how extremely strong magnetic fields in magnetized neutron stars, especially magnetars, influence their mass and shape by solving Einstein's equations with a non-uniform magnetic field model.

Contribution

It introduces a multipole expansion approach to model the magnetic field's effect on neutron star structure, including the correction of mass and radius due to magnetic fields.

Findings

Magnetic fields of $10^{15}$G at the surface and $10^{18}$G at the center significantly increase star mass and size.

The star's excess mass and equatorial radius change by about 3-4% at high central magnetic fields.

The model demonstrates the importance of magnetic field distribution in neutron star deformation.

Abstract

Magnetars are compact stars which are observationally determined to have very strong surface magnetic fields of the order of $10^{14}-10^{15}$G. The centre of the star can potentially have a magnetic field several orders of magnitude larger. We study the effect of the 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 pressure as well as the metric are expanded as multipoles in spherical harmonics up to the quadrupole term. Solving the Einstein equations for the gravitational potential, one obtains the correction terms as functions of the magnetic field. Using a nonlinear model for the hadronic EoS the excess mass and change in equatorial radius of the star due to the magnetic field are quite significant if the surface field is $10^{15}$G and the central field is about $10^{18}$ G. For a value of the central magnetic field strength of $1.75\times10^{18}$ G, we find that both the excess mass and the equatorial radius of the star changes by about $3-4\%$ compared to the spherical solution.