Comparison of simulated neutrino emission models with data on Supernova 1987A

We compare models of supernova (SN) neutrino emission with the Kamiokande II data on SN 1987A using the Bayesian approach. These models are taken from simulations and are representative of current one-dimensional SN models. We find that models with a brief accretion phase of neutrino emission are the most favored. This result is not affected by varying the overall flux normalization or considering neutrino oscillations. We also check the compatibility of the best-fit models with the data.

Figure 1

The luminosity $L_{\nu }$, average energy $⟨E_{\nu }⟩$, and spectral parameter ${\alpha }_{\nu }$ are shown as functions of time for ${\overline{\nu }}_e$ and ${\overline{\nu }}_x$ for the baseline models A, B, and C. Note the change of the time scale at $t=1\mathrm{s}$.

Figure 2

The best-fit values (plus) and the 68% (dashed curve) and 95% (solid curve) credible regions for $d$ and $t_{\mathrm{off}}$ are shown for models A, B, and C including three cases of neutrino oscillations.

Figure 3

The best-fit values (plus) and the 68% (dashed curve) and 95% (solid curve) credible regions for $K$ and $t_{\mathrm{off}}$ are shown for models ${\mathrm{A}}^{\prime }$, ${\mathrm{B}}^{\prime }$, and ${\mathrm{C}}^{\prime }$ including three cases of neutrino oscillations.

Figure 4

The contours expected to enclose 68% (dashed curve) and 95% (solid curve) of the events for the best-fit models A, B, and C including three cases of neutrino oscillations are compared with the SN 1987A data (filled circles).

Figure 5

Same as Fig. 4, but for the best-fit models ${\mathrm{A}}^{\prime }$, ${\mathrm{B}}^{\prime }$, and ${\mathrm{C}}^{\prime }$.

Figure 6

Histograms of the statistic $\ln \lambda$ are shown for samples of the best-fit models ${\mathrm{A}}^{\prime }$, ${\mathrm{B}}^{\prime }$, and ${\mathrm{C}}^{\prime }$ including three cases of neutrino oscillations. A total of ${10}^6$ samples are simulated for each model. The red lines denote the corresponding values of $\ln \lambda$ for the SN 1987A data.