  We propose a new parameterization of the antineutrino flux from core collapse
supernovae, that allows an interpretation of its astrophysical parameters
within the Bethe and Wilson scenario for the explosion, and that leads to a
reasonable (smooth) behavior of the average energy and of the luminosity curve.
We apply it to analyze the events observed by Kamiokande-II, IMB and Baksan
detectors in correlation with SN1987A. For the first time, we consider in the
same analysis all data characteristics: times, energies and angles of the
observed events. We account for the presence of background and evaluate the
impact of neutrino oscillations. The hypothesis that the initial luminous phase
of emission (accretion) is absent can be rejected at the 2 % significance
level. Without the need to impose external priors in the likelihood analysis,
the best-fit values of the astrophysical parameters are found to be in
remarkable agreement with the expectations of the standard core-collapse
scenario; in particular, the electron antineutrino-sphere radius is 16 km, the
duration of the accretion phase is found to be 0.55 s, and the initial
accreting mass is 0.22 M(sun). Similarly the total energy emitted in neutrinos
is 2.2*10^{53} erg, again close to the expectations. The errors on the
parameters are evaluated and found to be relatively large, consistently with
the limited number of detected events; the two dimensional confidence regions,
that demonstrate the main correlations between the parameters, are also given.
