An analytic treatment of magnetically deformed neutron stars

Abstract

AbstractIn this study, we develop an analytic treatment, which would allow us to model magnetic deformation of neutron stars in the quasi‐Newtonian framework. We assume non‐magnetic, spherical relativistic stars as backgrounds and regard the magnetic fields as the perturbation. We analyze the problem by taking density profiles from various analytic approaches. The first density profile is the n = 1 solution of the Lane‐Emden equation, the second one is a parabolic ansatz for density and the last density distribution is a fourth‐order polynomial with a free parameter fit to a relativistic solution obtained from a microphysical equation of state (EoS). In this article, the EoS of neutron matter is obtained from the lowest order constraint variational (LOCV) method. Furthermore, both purely poloidal and purely toroidal magnetic field configurations are obtained by solving the Euler's magnetohydrodynamic equations. We almost incorporate all the magnetic field configurations assessed from different density profiles. In order to study the structure of the neutron stars, the magnetic pressure, and density should be treated as perturbations of non‐magnetized stars. We find out that the stellar shape is prolate for positive distortion (purely toroidal magnetic field) and oblate for negative distortion (purely poloidal magnetic field). The magnetic effect on the gravitational mass is also explained.