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

Abstract

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 isospinasymmetric
nuclear matter (ANM) on its isoscalar and isovector saturation properties, and on the
β-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 (Imax) reached for bound ANM. The density-slope (L) of the
symmetry energy is found to correlate directly with the stiffness of ANM, meanwhile the symmetryenergy
curvature (Ksym) and the quadratic isovector incompressibility coefficient (Kτ ) are found
to correlate with it inversely. We found also that the stiffer EOS indicates larger neutron-rich
npeμ NS matter under β-equilibrium. Only the CDM3Y-Paris EOSs of isoscalar incompressibility
K0 up to 270 MeV and that of CDM3Y-Reid with K0 = 200 MeV indicate allowed direct URCA
(DU) cooling process in β-stable NS matter, at densities greater than 3.5 ρ0, 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 β-stable npe matter at
ρ ≥ 0.85 ρ0 (0.79 ρ0), which slightly decreases both the neutron richness at NS core and the DU
threshold density.