The constrained results for the crust-core transition density of neutron stars from the radii of neutron stars and neutron skin data

The crust-core transition density of neutron stars is inferred based upon the neutron-star radius and the neutron-skin thickness data. A thermodynamical method is used to calculate the transition density and a Bayesian approach is employed to simulate the posterior probability distribution functions.It has a larger probability to have values higher than 0.1 fm$^{-3}$ for $\rho_t$ as the uniform prior and the neutron-star radius data are used. The obtained $\rho_t$ is 0.075$^{+0.005}_{-0.01}$ fm$^{-3}$ at 68\% confidence level when both the neutron-star radius and the neutron-skin thickness data are taken into account. The strongly anti-correlations between $\rho_t$ and the slope $L$, curvature of the nuclear symmetry energy are observed. The dependence of the three $L$-$K_{\rm{sym}}$ correlationspredicted in the literature on the crust-core density and pressure is quantitatively investigated. The most probable value of 0.08 fm$^{-3}$ for $\rho_t$ is obtained from the $L$-$K_{\rm{sym}}$ relation raised by Holt \textit{et al}. and the larger values are preferred by the other two relations.