Magnetohydrodynamic equilibria in barotropic stars

TL;DR

This paper constructs barotropic magnetohydrodynamic equilibria using a new numerical code to test their stability, contributing to understanding magnetic star models despite their idealized nature.

Contribution

It develops a finite-difference numerical code to solve the Grad-Shafranov equation for barotropic equilibria with mixed magnetic field components.

Findings

Constructed a set of barotropic equilibria.

Developed a new numerical solver for the Grad-Shafranov equation.

Discussed properties of the equilibria obtained.

Abstract

Although barotropic matter does not constitute a realistic model for magnetic stars, it would be interesting to confirm a recent conjecture that states that magnetized stars with a barotropic equation of state would be dynamically unstable (Reisenegger 2009). In this work we construct a set of barotropic equilibria, which can eventually be tested using a stability criterion. A general description of the ideal MHD equations governing these equilibria is summarized, allowing for both poloidal and toroidal magnetic field components. A new finite-difference numerical code is developed in order to solve the so-called Grad-Shafranov equation describing the equilibrium of these configurations, and some properties of the equilibria obtained are briefly discussed.