Finite temperature effects on anisotropic pressure and equation of state of dense neutron matter in an ultrastrong magnetic field

TL;DR

This study investigates how intense magnetic fields and finite temperatures influence the anisotropic pressure and equation of state of dense neutron matter, revealing instability thresholds and entropy behavior relevant for magnetar interiors.

Contribution

It provides a detailed analysis of finite temperature effects on anisotropic pressure and stability in neutron matter under ultrastrong magnetic fields using a Skyrme interaction model.

Findings

Pressure anisotropy becomes significant above 10^{18} G.

Longitudinal pressure vanishes at 10^{18} to 10^{19} G, causing instability.

Entropy increases with magnetic field due to effective mass differences.

Abstract

Spin polarized states in dense neutron matter with recently developed Skyrme effective interaction (BSk20 parametrization) are considered in the magnetic fields $H$ up to $10^{20}$ G at finite temperature. In a strong magnetic field, the total pressure in neutron matter is anisotropic, and the difference between the pressures parallel and perpendicular to the field direction becomes significant at $H>H_{th}\sim10^{18}$ G. The longitudinal pressure decreases with the magnetic field and vanishes in the critical field $10^{18}<H_c\lesssim10^{19}$ G, resulting in the longitudinal instability of neutron matter. With increasing the temperature, the threshold $H_{th}$ and critical $H_c$ magnetic fields also increase. The appearance of the longitudinal instability prevents the formation of a fully spin polarized state in neutron matter and only the states with moderate spin polarization are accessible. The anisotropic equation of state is determined at densities and temperatures relevant for the interiors of magnetars. The entropy of strongly magnetized neutron matter turns out to be larger than the entropy of the nonpolarized matter. This is caused by some specific details in the dependence of the entropy on the effective masses of neutrons with spin up and spin down in a polarized state.