Relativistic mean-field predictions for dense matter equation of state and application to neutron stars

Relativistic mean-field models (RMF) based on the exchange of $\sigma$, $\omega$, and $\rho$ mesons including non-linear nucleon-$\sigma$ couplings and density-dependent $\rho$ coupling, are considered. A large set of models is generated using the Markov chain Monte Carlo approach and Bayesian statistics to reproduce nuclear physics knowledge encoded in terms of the nuclear empirical parameters and $\chi$EFT predictions for low-density neutron matter. These models are filtered, in a second step, using astrophysical constraints: the tidal deformability obtained from GW170817 parameter estimation and the observational masses deduced from radio-astronomy. We then obtain a set of selected RMF models that are compatible with present nuclear and astrophysical constraints and that can be employed to make predictions and to quantity their uncertainties. Predictions for masses and radii are compared to NICER masses-radii analyses for PSR J0030+0451 and PSR J0740+6620. We find that RMF models can be made soft enough to predict low values for neutron star radii compatible with GW170817 and, at larger densities, stiff enough to be compatible with NICER analyses for massive neutron stars. Our models can also reach large values for the maximum mass, up to 2.6$M_\odot$. In addition, for the core composition, we obtain a large distribution of the proton fraction for canonical mass neutron stars, some of them allowing the direct URCA fast cooling process. For massive neutron stars, however, most of our models suggest a large proton fraction in the core allowing direct URCA fast cooling process.