$Ab~initio$ thermodynamics of one-component plasma for astrophysics of white dwarfs and neutron stars

TL;DR

This paper uses path-integral Monte Carlo simulations to calculate thermodynamic properties of a one-component plasma relevant to white dwarfs and neutron stars, providing analytic formulas and insights into anharmonic effects and melting parameters.

Contribution

It introduces new PIMC-based thermodynamic calculations for dense plasma in stellar objects, including analytic approximations and analysis of anharmonic effects and melting behavior.

Findings

Total crystal specific heat exceeds harmonic lattice predictions by 50% due to anharmonicity.

Derived density-dependent melting parameters such as Coulomb coupling strength and latent heat.

Provided analytic formulas for thermodynamic functions applicable to stellar plasma modeling.

Abstract

Using path-integral Monte Carlo (PIMC) simulations, we have calculated energy of a crystal composed of atomic nuclei and uniform incompressible electron background in the temperature and density range, covering fully ionized layers of compact stellar objects, white dwarfs and neutron stars, including the high-density regime, where ion quantization is important. We have approximated the results by convenient analytic formulae, which allowed us to integrate and differentiate the energy with respect to temperature and density to obtain various thermodynamic functions such as Helmholtz free energy, specific heat, pressure, entropy etc. In particular, we have demonstrated, that the total crystal specific heat can exceed the well-known harmonic lattice contribution by a factor of 1.5 due to anharmonic effects. By combining our results with the PIMC thermodynamics of a quantum Coulomb liquid, updated in the present work, we were able to determine density dependences of such melting parameters as the Coulomb coupling strength at melting, latent heat, and a specific heat jump. Our results are necessary for realistic modelling of thermal evolution of compact degenerate stars.