# Thermodynamics of Neutrons in a Magnetic Field and its Implications for Neutron Stars

## TL;DR

This paper explores how strong magnetic fields influence neutron star physics, revealing that magnetic effects are limited in magnitude, but impact properties like susceptibility and specific heat, with implications for understanding magnetars.

## Contribution

It provides a detailed analysis of magnetic field effects on neutron star thermodynamics, especially regarding pressure anisotropy and maximum magnetic field strength consistent with equilibrium.

## Key findings

- Maximum magnetic field in neutron stars is about 10^{17} G.
- Magnetic field has negligible impact on the neutron matter equation of state.
- Magnetic susceptibility increases with temperature.

## Abstract

We investigate the effects of a magnetic field on the thermodynamics of a neutron system at finite density and temperature. Our main motivation is to deepen the understanding of the physics of a class of neutron stars known as magnetars, which exhibit extremely strong magnetic fields. Taking into account two facts, (i) the existence of a pressure anisotropy in the presence of a magnetic field and (ii) that the quantum field theory contribution to the pressure is non-negligible, we show that the maximum value that the inner magnetic field of a star can reach while being in agreement with the magnetohydrostatic equilibrium between the gravitational and matter pressures becomes $10^{17}$ G, an order of magnitude smaller than the previous value obtained through the scalar virial theorem; that the magnetic field has a negligible effect on the neutron system's equation of state; that the system's magnetic susceptibility increases with the temperature; and that the specific heat $C_V$ does not significantly change with the magnetic field in the range of temperatures characteristic of protoneutron stars.