Equation of State of a Dense and Magnetized Fermion System

TL;DR

This paper derives the anisotropic equation of state for a dense fermion system in a magnetic field, highlighting pressure differences and thresholds relevant for astrophysical objects like stars.

Contribution

It introduces a method to calculate the anisotropic equation of state of magnetized fermions and identifies the magnetic field threshold where anisotropy becomes significant.

Findings

Pressure anisotropy due to magnetic field breaking rotational symmetry

Threshold magnetic field where matter and field contributions are comparable

Estimated upper magnetic field limits in self-bound and gravitational stars

Abstract

The equation of state of a system of fermions in a uniform magnetic field is obtained in terms of the thermodynamic quantities of the theory by using functional methods. It is shown that the breaking of the O(3) rotational symmetry by the magnetic field results in a pressure anisotropy, which leads to the distinction between longitudinal- and transverse-to-the-field pressures. A criterion to find the threshold field at which the asymmetric regime becomes significant is discussed. This threshold magnetic field is shown to be the same as the one required for the pure field contribution to the energy and pressures to be of the same order as the matter contribution. A graphical representation of the field-dependent anisotropic equation of state of the fermion system is given. Estimates of the upper limit for the inner magnetic field in self-bound stars, as well as in gravitationally bound stars with inhomogeneous distributions of mass and magnetic fields, are also found.