Bayesian analysis of neutrinos observed from supernova SN-1987A

We present a Bayesian analysis of the energies and arrival times of the neutrinos from supernova SN 1987A detected by the Kamiokande II, IMB, and Baksan detectors, and find strong evidence for two components in the neutrino signal: a long time scale component from thermal Kelvin-Helmholtz cooling of the nascent neutron star, and a brief $(\ensuremath{\sim}1 \mathrm{s}),$ softer component similar to that expected from emission by accreting material in the delayed supernova scenario. In the context of this model, we show that the data constrain the electron antineutrino rest mass to be less than 5.7 eV with 95% probability. Our analysis takes advantage of significant advances that have occurred in the years since the detections in both our understanding of the supernova mechanism and our ability to analyze sparse data. This has led to significant improvement over previous studies in two important respects. First, our comparison of the data with parametrized models of the neutrino emission uses a consistent and straightforward Bayesian statistical methodology. This methodology helps us distinguish the complementary tasks of parameter estimation and model assessment, and fully accounts for the strong, nonlinear correlations between inferred values of neutrino emission model parameters. It also clarifies and improves the derivation of the likelihood function (the probability for the data), improving on earlier derivations in two ways: more consistent accounting for the energy-dependent efficiencies of the detectors; and inclusion of the empirically measured detector background spectra. These improvements lead to significant differences between our inferences and those found in earlier studies. Inclusion of detector background spectra proves crucial for proper analysis of the Baksan data and for demonstrating its consistency with data from other detectors. Second, we compare the data with a much wider variety of neutrino emission models than was explored previously, several of them inspired by recent numerical calculations of collapse and explosion based on the delayed supernova mechanism. This allows us to compare predictions of both the prompt and delayed mechanisms with the data, and ensures that our conclusions are robust. We find that two-component models for the neutrino signal are $\ensuremath{\sim}100$ times more probable than single-component models. Moreover, single-component models imply a radius and binding energy for the nascent neutron star significantly larger than those implied by even the stiffest acceptable equations of state for neutron star matter. In contrast, the radius and binding energy implied by two-component models are in agreement with predictions. Taking this agreement with prior expectations into account increases the odds in favor of two-component models by more than an order of magnitude. The inferred characteristics of the neutrino emission are in spectacular agreement with the salient features of the theory of stellar collapse and neutron star formation that had developed over several decades in the absence of direct observational data. We compare our work with previous work that used more conventional ``frequentist'' methods (including our own previous maximum likelihood analysis). We identify several methodological and technical weaknesses in earlier analyses, and show how these are overcome in our Bayesian analysis.