Bayesian analysis of the crust-core transition with a compressible liquid-drop model

The crust-core (CC) phase transition of neutron stars is studied within a unified meta-modeling of the nuclear Equation of State (EoS). The variational equations in the crust are solved within a Compressible Liquid-Drop (CLD) approach, with surface parameters consistently optimized for each EoS set on experimental nuclear mass data. When EoS parameters are taken from known Skyrme or RMF functionals, the transition point of those models is nicely reproduced as expected. The probability distribution of EoS parameters and of the transition density and pressure is determined with a Bayesian analysis, where the prior is given by an uncorrelated distribution of parameters considering the present empirical uncertainties, and constraints are applied both from neutron star physics and ab initio predictions. We show that the properties of the CC transition point are largely independent of the high density properties of the EoS, while ab initio EoS calculations of neutron and symmetric matter are far more constraining. The surface tension of extremely neutron rich matter, which remains poorly known, is the most influential parameter for the CC transition point. This explains the large dispersion of existing predictions of the CC transition point. Fixing the isospin dependence of the surface tension to a reasonable but somewhat arbitrary value, strong correlations with isovector EoS parameters (L${}_{sym}$, K${}_{sym}$ and Q${}_{sym}$) are recovered. Within the present experimental and theoretical uncertainties on those parameters, we estimate the transition density as n${}_t$= 0.072 $\pm$ 0.011 fm${}^{-3}$ and the transition pressure as P${}_t$=0.339 $\pm$ 0.115 MeV fm${}^{-3}$.