Maximum mass of magnetic white dwarfs

TL;DR

This paper investigates the maximum mass of magnetized white dwarfs, showing that strong magnetic fields destabilize these stars and prevent stable super-Chandrasekhar mass white dwarfs from existing.

Contribution

The study derives stability bounds for magnetic white dwarfs considering anisotropic pressures and demonstrates the impossibility of stable super-Chandrasekhar mass white dwarfs with magnetic fields exceeding 10^{13} G.

Findings

Stable solutions vanish for magnetic fields above 10^{13} G.

Super-Chandrasekhar mass white dwarfs are not stable with strong magnetic fields.

Magnetic field limits constrain white dwarf mass and stability.

Abstract

We revisit in this work the problem of the maximum masses of magnetized White Dwarfs (WD). The impact of a strong magnetic field onto the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into a parallel and perpendicular components. We first construct stable solutions of TOV equations for the parallel pressures, and found that physical solutions vanish for the perpendicular pressure when $B \gtrsim 10^{13}$ G. This fact establishes an upper bound for a magnetic field and the stability of the configurations in the (quasi) spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WD with super Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we derived structure equations appropriated for a cylindrical metric with anisotropic pressures. From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for $B \sim 10^{13} $ G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WD, with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.