Appearance of the prolate and the toroidal magnetic field dominated stars - Analytic approach

TL;DR

This paper presents an analytic approach to understanding the conditions under which magnetized stars develop prolate shapes and dominant toroidal magnetic fields, emphasizing the role of specific current density and Lorentz force relations.

Contribution

It introduces a new analytical framework identifying the necessary current density and Lorentz force conditions for prolate and toroidal magnetic field dominated stars.

Findings

Prolate stellar shapes require non force-free toroidal currents flowing opposite to the bulk current.

Special relations between current density and Lorentz force are essential for these configurations.

Analytic solutions support the existence of prolate, toroidal-dominated magnetized stars.

Abstract

We have analyzed magnetized equilibrium states and showed a condition for appearance of the prolate and the toroidal magnetic field dominated stars by analytic approaches. Both observations and numerical stability analysis support that the magnetized star would have the prolate and the large internal toroidal magnetic fields. In this context, many investigations concerning magnetized equilibrium states have tried to obtain the prolate and the toroidal dominant solutions, but many of them have failed to obtain such configurations. Since the Lorentz force is a cross product of current density and magnetic field, the prolate shaped configurations and the large toroidal magnetic fields in stars require a special relation between current density and the Lorentz force. We have analyzed simple analytical solutions and found that the prolate and the toroidal dominant configuration require non force-free toroidal current density that flows in the opposite direction with respect to the bulk current within the star. Such current density results in the Lorentz force which makes the stellar shape prolate. Satisfying this special relation between the current density and the Lorentz force is a key for appearance of the prolate and the toroidal magnetic field dominated magnetized star.