Relativistic stars with purely toroidal magnetic fields

TL;DR

This paper develops a new numerical framework to analyze the equilibrium structures of relativistic stars with purely toroidal magnetic fields, revealing how magnetic fields influence star shape, stability, and evolution.

Contribution

It derives the first master equations for relativistic stars with purely toroidal magnetic fields and extends existing numerical schemes to solve these equations.

Findings

Magnetic fields cause prolately distorted matter distributions in non-rotating stars.

Rapid rotation results in oblate stellar surfaces but prolate internal matter distribution.

Stronger magnetic fields lower the mass-shedding angular velocity, affecting star stability.

Abstract

We investigate the effects of the purely toroidal magnetic field on the equilibrium structures of the relativistic stars. The master equations for obtaining equilibrium solutions of relativistic rotating stars containing purely toroidal magnetic fields are derived for the first time. To solve these master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for calculating relativistic rotating stars containing no magnetic field to incorporate the effects of the purely toroidal magnetic fields. By using the numerical scheme, we then calculate a large number of the equilibrium configurations for a particular distribution of the magnetic field in order to explore the equilibrium properties. We also construct the equilibrium sequences of the constant baryon mass and/or the constant magnetic flux, which model the evolution of an isolated neutron star as it loses angular momentum via the gravitational waves. Important properties of the equilibrium configurations of the magnetized stars obtained in this study are summarized as follows ; (1) For the non-rotating stars, the matter distribution of the stars is prolately distorted due to the toroidal magnetic fields. (2) For the rapidly rotating stars, the shape of the stellar surface becomes oblate because of the centrifugal force. But, the matter distribution deep inside the star is sufficiently prolate for the mean matter distribution of the star to be prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of the stars at the lower angular velocity. (4) For some equilibrium sequences of the constant baryon mass and magnetic flux, the stars can spin up as they lose angular momentum.