Model-dependence of neutrino emissivities and neutrino luminosities of neutron stars from the direct Urca processes and the modified Urca processes

The neutrino emissivities in β-stable neutron star matter from the direct Urca (DU) processes and the modified Urca (MU) processes have been investigated by adopting 26 Skyrme interactions. Several physical quantities related to the MU processes and the DU processes have been calculated and discussed. The model-dependence of the neutrino emissivities from the DU processes is found to stem mainly from the model-dependence of the effective mass, while the neutrino emissivities from the MU processes are determined by the competition between the effects of the symmetry energy and the effective mass. Besides, we have investigated the total neutrino luminosities of neutron stars, with the masses of 1.2,1.4,1.6 and 1.8M⊙, from the DU processes and the MU processes. The neutrino luminosity of a neutron star is found to be primarily determined by whether the electron DU process is allowed or not. As long as the electron DU process can occur, the total luminosity turns out to be 5 to 8 orders of magnitude larger as compared with the case that the DU process is forbidden, which indicates that the strongest model-dependence of the neutrino luminosity comes from that of the symmetry energy and the equation of state (EOS) of neutron star matter. In the case that the DU processes are allowed, the discrepancy of the calculated neutrino luminosity using various Skyrme interactions remains noticeable, which is essentially attributed to the model-dependence of the symmetry energy, the EOS of NS matter and the effective masses.