EoS Dependence of the Relic Supernova Neutrino Spectrum

Understanding the mechanism of core-collapse supernova explosions requires knowledge of the nuclear equation of state (EoS). Recent multi-dimensional numerical simulations indicate that explosions are possible. Nevertheless, it is not yet fully understood which equation of state is realized in the proto-neutron star formed during SN explosions. We examine the EoS sensitivity of the relic supernova neutrino spectrum as a probe of the nuclear EoS. This sensitivity arises largely from the contribution to neutrino emission from failed supernovae. We consider a variety of astrophysical scenarios, which include different progenitor masses for a successful explosion, the cosmological star formation rate, starbursts, quiescent star formation, and the metallicity dependence of the initial mass function. We find that the EoS signature remains robust under a variety of conditions. We demonstrate the viability of future neutrino detectors to distinguish the nuclear EoS via the relic supernova neutrino spectrum.