Statistical description of complex nuclear phases in supernovae and proto-neutron stars

TL;DR

This paper introduces a statistical model for dilute star matter at finite temperature, revealing a continuous crust-core transition and highlighting differences from traditional models in the composition and thermodynamics of supernovae and proto-neutron stars.

Contribution

It presents a novel phenomenological model that describes the continuous nature of the crust-core transition and the composition of baryonic matter in supernovae environments.

Findings

Crust-core transition is not first order, but a continuous fluid mixture.

Model predicts larger medium nuclei mass fractions at high density and temperature.

Good agreement with existing EOS at low temperatures and homogeneous phases.

Abstract

We develop a phenomenological statistical model for dilute star matter at finite temperature, in which free nucleons are treated within a mean-field approximation and nuclei are considered to form a loosely interacting cluster gas. Its domain of applicability, that is baryonic densities ranging from about $\rho>10^8$ g $\cdot$ cm$^{-3}$ to normal nuclear density, temperatures between 1 and 20 MeV and proton fractions between 0.5 and 0, make it suitable for the description of baryonic matter produced in supernovae explosions and proto-neutron stars. The first finding is that, contrary to the common belief, the crust-core transition is not first order, and for all subsaturation densities matter can be viewed as a continuous fluid mixture between free nucleons and massive nuclei. As a consequence, the equations of state and the associated observables do not present any discontinuity over the whole thermodynamic range. We further investigate the nuclear matter composition over a wide range of densities and temperatures. At high density and temperature our model accounts for a much larger mass fraction bound in medium nuclei with respect to traditional approaches as Lattimer-Swesty, with sizeable consequences on the thermodynamic quantities. The equations of state agree well with the presently used EOS only at low temperatures and in the homogeneous matter phase, while important differences are present in the crust-core transition region. The correlation among the composition of baryonic matter and neutrino opacity is finally discussed, and we show that the two problems can be effectively decoupled.