Simple fits for the neutrino luminosities from protoneutron star cooling

We propose a simple fit function, $L_{\nu_i}(t) = C\, t^{-\alpha}\, e^{-(t/\tau)^{n}}$, to parametrize the luminosities of neutrinos and antineutrinos of all flavors during the protoneutron star (PNS) cooling phase at post-bounce times $t \gtrsim 1$ s. This fit is based on results from a set of neutrino-hydrodynamics simulations of core-collapse supernovae in spherical symmetry. The simulations were performed with an energy-dependent transport for six neutrino species and took into account the effects of convection and muons in the dense and hot PNS interior. We provide values of the fit parameters $C$, $\alpha$, $\tau$, and $n$ for different neutron star masses and equations of state as well as correlations between these fit parameters. Our functional description is useful for analytic supernova modeling, for characterizing the neutrino light curves in large underground neutrino detectors, and as a tool to extract information from measured signals on the mass and equation of state of the PNS and on secondary signal components on top of the PNS's neutrino emission.