# Quantifying the uncertainties on spinodal instability in stellar matter through meta-modeling

## TL;DR

This paper investigates how uncertainties in nuclear matter parameters affect the crust-core transition in neutron stars using a meta-modeling approach, highlighting key parameters influencing the transition density and pressure.

## Contribution

It introduces a comprehensive meta-modeling framework that includes high-order empirical parameters and assesses their impact on the neutron star crust-core transition.

## Key findings

- Transition density estimated at 0.071 ± 0.011 fm^{-3}
- Transition pressure estimated at 0.294 ± 0.102 MeV fm^{-3}
- Key parameters like $K_{sym}$ and $Q_{sym}$ significantly influence the transition point.

## Abstract

The influence of the uncertainties of the equation of state empirical parameters on the neutron stars crust-core phase transition is explored within a meta-modeling approach, in which the energy per particle is expanded as a Taylor series in density and asymmetry around the saturation point. The phase transition point is estimated from the intersection of the spinodal instability region for dynamical fluctuations with the chemical equilibrium curve. Special attention is paid to the inclusion of high-order parameters of the Taylor series and their influence on the transition point. An uncorrelated prior distribution is considered for the empirical parameters, with bulk properties constrained through effective field theory predictions, while the surface parameters are controlled from a fit of nuclear masses using the extended Thomas Fermi approximation. The results show that the isovector compressibility $K_{sym}$ and skewness $Q_{sym}$ have the most significant correlations with the transition point, along with the previously observed influence of the $L_{sym}$ parameter. The estimated density and pressure of the crust-core transition are $n_t = (0.071 \pm 0.011) fm^{-3}$ and $P_t = (0.294 \pm 0.102) MeV fm^{-3}$.