Neutrino oscillations and the supernova 1987A signal

We study the impact of neutrino oscillations on the interpretation of the supernova (SN) 1987A neutrino signal by means of a maximum-likelihood analysis. We focus on oscillations between ${\overline{\nu }}_e$ with ${\overline{\nu }}_{\mu }$ or ${\overline{\nu }}_{\tau }$ with those mixing parameters that would solve the solar neutrino problem. For the small-angle MSW solution ($\Delta m^2\approx {10}^{-5\mathrm{}}$ e${\mathrm{V}}^2$, ${{sin}^{2}2\Theta }_0\approx 0.007$), there are no significant oscillation effects on the Kelvin-Helmholtz cooling signal; we confirm previous best-fit values for the neutron-star binding energy and average spectral ${\overline{\nu }}_e$ temperature. There is only marginal overlap between the upper end of the 95.4% C.L. inferred range of $〈E_{{\overline{\nu }}_e}〉$ and the lower end of the range of theoretical predictions. Any admixture of the stiffer ${\overline{\nu }}_{\mu }$ spectrum by oscillations aggravates the conflict between experimentally inferred and theoretically predicted spectral properties. For mixing parameters in the neighborhood of the large-angle MSW solution ($\Delta m^2\approx {10}^{-5\mathrm{}}$ e${\mathrm{V}}^2$, ${{sin}^{2}2\Theta }_0\approx 0.7$) the oscillations in the SN are adiabatic, but one needs to include the regeneration effect in the Earth which causes the Kamiokande and IMB detectors to observe different ${\overline{\nu }}_e$ spectra. For the solar vacuum solution ($\Delta m^2\approx {10}^{-10\mathrm{}}$ e${\mathrm{V}}^2$, ${{sin}^{2}2\Theta }_0\approx 1$) the oscillations in the SN are nonadiabatic; vacuum oscillations take place between the SN and the detector. If one of the two large-angle solutions were borne out by the upcoming round of solar neutrino experiments, one would have to conclude that the SN 1987 A ${\overline{\nu }}_{\mu }$ and/or ${\overline{\nu }}_e$ spectra had been much softer than predicted by current treatments of neutrino transport.