Comparison of statistical treatments for the equation of state for core-collapse supernovae

TL;DR

This paper evaluates the accuracy of the single-nucleus approximation in modeling stellar matter during core-collapse supernovae, revealing its limitations in predicting composition at higher temperatures and densities.

Contribution

It provides a detailed comparison of statistical treatments for the equation of state, highlighting the approximation's inaccuracies in composition predictions.

Findings

Single-nucleus approximation accurately predicts energy and pressure.

It overpredicts nuclear mass numbers at higher densities and temperatures.

It underestimates the presence of lighter nuclei in supernova matter.

Abstract

Neutrinos emitted during the collapse, bounce and subsequent explosion provide information about supernova dynamics. The neutrino spectra are determined by weak interactions with nuclei and nucleons in the inner regions of the star, and thus the neutrino spectra are determined by the composition of matter. The composition of stellar matter at temperature ranging from $T=1-3$ MeV and densities ranging from $10^{-5}$ to 0.1 times the saturation density is explored. We examine the single-nucleus approximation commonly used in describing dense matter in supernova simulations and show that, while the approximation is accurate for predicting the energy and pressure at most densities, it fails to predict the composition accurately. We find that as the temperature and density increase, the single nucleus approximation systematically overpredicts the mass number of nuclei that are actually present and underestimates the contribution from lighter nuclei which are present in significant amounts.