SUPERNOVA RELIC NEUTRINOS AND THE SUPERNOVA RATE PROBLEM: ANALYSIS OF UNCERTAINTIES AND DETECTABILITY OF ONeMg AND FAILED SUPERNOVAE

Direct measurements of the core collapse supernova rate (R-SN) in the redshift range 0 <= z <= 1 appear to be about a factor of two smaller than the rate inferred from the measured cosmic massive star formation rate (SFR). This discrepancy would imply that about one-half of the massive stars that have been born in the local observed comoving volume did not explode as luminous supernovae. In this work, we explore the possibility that one could clarify the source of this supernova rate problem by detecting the energy spectrum of supernova relic neutrinos with a next generation 10(6) ton water C. erenkov detector like Hyper-Kamiokande. First, we re-examine the supernova rate problem. We make a conservative alternative compilation of the measured SFR data over the redshift range 0 <= z <= 7. We show that by only including published SFR data for which the dust obscuration has been directly determined, the ratio of the observed massive SFR to the observed supernova rate R-SN has large uncertainties similar to 1.8(-0.6)(+1.6) and is statistically consistent with no supernova rate problem. If we further consider that a significant fraction of massive stars will end their lives as faint ONeMg SNe or as failed SNe leading to a black hole remnant, then the ratio reduces to similar to 1.1(-0.4)(+1.0) and the rate problem is essentially solved. We next examine the prospects for detecting this solution to the supernova rate problem. We first study the sources of uncertainty involved in the theoretical estimates of the neutrino detection rate and analyze whether the spectrum of relic neutrinos can be used to independently identify the existence of a supernova rate problem and its source. We consider an ensemble of published and unpublished core collapse supernova simulation models to estimate the uncertainties in the anticipated neutrino luminosities and temperatures. We illustrate how the spectrum of detector events might be used to establish the average neutrino temperature and constrain SN models. We also consider supernova nu-process nucleosynthesis to deduce constraints on the temperature of the various neutrino flavors. We study the effects of neutrino oscillations on the detected neutrino energy spectrum and also show that one might distinguish the equation of state (EoS) as well as the cause of the possible missing luminous supernovae from the detection of supernova relic neutrinos. We also analyze a possible enhanced contribution from failed supernovae leading to a black hole remnant as a solution to the supernova rate problem. We conclude that indeed it might be possible (though difficult) to measure the neutrino temperature, neutrino oscillations, and the EoS and confirm this source of missing luminous supernovae by the detection of the spectrum of relic neutrinos.