Equation of state for magnetized Coulomb plasmas

TL;DR

This paper presents a comprehensive analytical equation of state for magnetized Coulomb plasmas, applicable across a wide range of conditions relevant to white dwarfs and neutron stars, including effects of magnetic quantization and electron screening.

Contribution

It introduces new analytical expressions for thermodynamic functions of magnetized Coulomb plasmas and provides a publicly available numerical code for their evaluation.

Findings

Effects of magnetic quantization on melting points analyzed

Electron screening impacts on plasma thermodynamics quantified

The EOS is applicable to modeling white dwarf and neutron star structures

Abstract

We develop an analytical equation of state (EOS) for magnetized fully ionized plasmas, which cover a wide range of temperatures and densities, from low-density classical plasmas to relativistic, quantum plasma conditions. This EOS directly applies to calculations of structure and evolution of strongly magnetized white dwarfs and neutron stars. We review available analytical and numerical results for thermodynamic functions of the nonmagnetized and magnetized Coulomb gases, liquids, and solids. We propose a new analytical expression for the free energy of solid Coulomb mixtures. Based on recent numerical results, we construct analytical approximations for the thermodynamic functions of harmonic Coulomb crystals in quantizing magnetic fields. The analytical description ensures a consistent evaluation of all astrophysically important thermodynamic functions based on the first, second, and mixed derivatives of the free energy. Our numerical code for calculation of thermodynamic functions based on these approximations is made publicly available. Using this code, we calculate and discuss the effects of electron screening and magnetic quantization on the position of the melting point in a range of densities and magnetic fields relevant to white dwarfs and outer envelopes of neutron stars. We consider also the thermal and mechanical structure of a magnetar envelope and argue that it can have a frozen surface which covers the liquid ocean above the solid crust.