  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 (~< 1 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 occured in the
years since the detections in both our understanding of the supernova mechanism
and our ability to analyze sparse data. As a result there are substantial
differences between our inferences and those found in earlier studies. We find
that two-component models for the neutrino signal make the data >100 times more
probable than single-component models. In addition, the radius and binding
energy of the nascent neutron star implied by single-component models deviates
significantly from the values predicted by current neutron star models, whereas
those implied by models with an accretion component are in complete agreement
with the predictions. As a result, two-component models are hundreds to
thousands of times more probable than single-component models. The neutrino
data thus provide the first direct observational evidence in favor of the
delayed supernova scenario over the prompt scenario. (Abridged abstract)
