Inner crust of neutron stars: Polymorphism and superconductivity in the liquid drop model

TL;DR

This paper investigates the complex phases and superconductivity in the inner crust of neutron stars using a liquid drop model based on chiral effective field theory, revealing phase coexistence, effects of curvature, and magnetic properties.

Contribution

It introduces a detailed numerical analysis of nuclear pasta phases, including the impact of curvature corrections and superconductivity crossover, within the liquid drop model framework.

Findings

Coexistence of multiple nuclear phases at relevant pressures.

Curvature correction significantly alters phase transition densities.

Identifies a crossover in superconductivity regimes in lasagna phase.

Abstract

Within the liquid drop model built up with the nuclear interaction parametrization Sk$\chi$450, which is based on the chiral effective field theory, we calculate numerically the internal energy density for each of nuclear pasta phases and for the uniform nuclear matter. We provide quantitative arguments in favor of coexistence of various nuclear matter phases at a significant range of total pressure within the inner crust of neutron stars, a concept known as crystal polymorphism. Specifically, we find that differences of the internal energy per baryon for various phases are typically less than the thermal energy per a freedom degree at temperature about $10^8$--$10^9$ K, which sets the energetic scale for thermal fluctuations of state of Fermi liquid from the ground state. The nuclear energy contributions are described using the same parametrization Sk$\chi$450 for the bulk, plain surface and curvature terms. We find that the introduction of the curvature correction changes the ground state in a relevant way. This may be understood as a consequence of the corresponding change in size of the nucleus, which significantly modifies the phase transition densities. Using the calculated structural parameters from liquid drop model, we explore the physical consequences of the expected Cooper pairing of protons in lasagna phase. In this case, we find a crossover between the discreet layered and the three-dimensional anisotropic regimes of superconductivity. Additionally, we study the magnetic stress in lasagna accounting for a rotational lag between superfluid neutrons and the crystal lattice, which is believed to develop naturally in pulsars and magnetars. Our results offer a preliminary insight into rich magnetic properties of the inner crust of neutron stars.