Statistical analysis of the time structure of the neutrinos from supernova 1987A

We perform a maximum likelihood analysis of all the Kamiokande-IMB neutrino events in order to determine most likely values for the parameters describing the cooling neutron star. The best fit, rapid cooling from an initial temperature T_s_= 42 +/- 0.5 MeV down to 3.3 MeV in 2 s followed by slow cooling thereafter, is approximately that of a degenerate ν_e_ gas diffusing out of a collapsed neutronized core. This cooling model fits the decrease in average event rate and neutrino energy and the 7 s gap in the Kamiokande data better than any constant temperature or exponential cooling model. The total number of (1.3 +/- 0.4) x 10_58nu^bar^_e_ released with (9 +/- 3) x 10^52^ ergs is consistent with the binding energy released in the collapse of a massive core. The best fit parameters imply an effective neutrinosphere radius of 35 +/- 10 km. Minimum residual analysis and power spectrum analysis shows no significant periods on any time scale. The neutrino data therefore confirm the general features of the neutrino transport model of Type II supernovae but is too sparse to test particular theories. Optically weak or invisible collapses to neutron stars, expected every decade in our Galaxy, will test dynamical details of particular theories.