Impact of the stiffness of equation of state on saturation properties of asymmetric nuclear matter and Urca cooling in neutron stars

We consider nuclear equation of state (EoS) based on the semi-realistic M3Y-Paris and M3Y-Reid effective nucleon-nucleon (NN) interactions to assess the influence of the stiffness of the isospin-asymmetric nuclear matter (ANM) on its isoscalar and isovector saturation properties, and on the beta-stable proton fraction in neutron star (NS) matter. Two parameterizations schemes of the CDM3Y isovector density dependence of the NN interaction are adopted, one is scaled to the isoscalar density dependence and the other (IVF1) is developed independently of it. We found that the stiffer EoS yields larger binding saturation density that decreases with the isospin asymmetry (I), and slightly decreases the maximum asymmetry (I (max)) reached for bound ANM. The density-slope (L) of the symmetry energy is found to correlate directly with the stiffness of ANM, meanwhile the symmetry-energy curvature (K-sym) and the quadratic isovector incompressibility coefficient (K-tau) are found to correlate with it inversely. We found also that the stiffer EoS indicates larger neutron-rich npe mu NS matter under beta-equilibrium. Only the CDM3Y-Paris EoSs of isoscalar incompressibility K-0 up to 270 MeV and that of CDM3Y-Reid with K-0 = 200 MeV indicate allowed direct Urca (DU) cooling process in beta-stable NS matter, at densities greater than 3.5 rho(0), based on the IVF1 density dependence. The stiffer EoS proposes a narrower density range for DU process in NS. According to the considered Paris (Reid) forces, muons can emerge in cold beta-stable npe matter at rho >= 0.85 rho(0)(0.79 rho(0)), which slightly decreases both the neutron richness at NS core and the DU threshold density.