Inferring the nuclear symmetry energy at supra saturation density from neutrino cooling

An ambitious goal of the astrophysical community is not only to constrain the equation of state (EOS) of neutron star (NS) matter by confronting it with astrophysics observations, but ultimately also to infer the NS composition. Nevertheless, the composition of the NS core is likely to remain uncertain unless we have an accurate determination of the nuclear symmetry energy at supra saturation density ($\rho>\rho_0$). We investigate how the nucleonic direct Urca (dUrca) processes can be used as an effective probe to constraint the high density nuclear symmetry energy. A large number of minimally constrained EOSs has been constructed by applying a Bayesian approach to study the correlations of the symmetry energy at different densities with a few selected properties of a NS. The nuclear symmetry energy above the baryon density 0.5 fm$^{-3}$ ($\sim 3 \rho_0$) is found to be strongly correlated with NS mass at which the onset of nucleonic dUrca neutrino cooling takes place in the core. This allows us to constrain the high density behavior of nuclear symmetry energy within narrow bounds. {The pure neutron matter pressure constraint from chiral effective field theory rules out the onset of nucleonic dUrca in stars with a mass $\lesssim$ 1.4 $M_\odot$.} The onset of dUrca inside 1.6 M$_\odot$ to 1.8 M$_\odot$ NS implies a slope of the symmetry energy $L$ at $\sim 2.5~\rho_0$, respectively, between 54 and 48 MeV.