A Statistical Test on the Spatial Angular Distributions of Electrons from Neutrino Burst from SN 1987A of IMB and Kamiokande Groups

Using some statistical methods, many investigators have claimed on a basis of the polar angle "cos θ" distribution of neutrinos emitted from SN 1987A that the IMB data seem to be of a non-isotropic distribution, whereas the Kamiokande data show an isotropic distribution. It seems to be difficult to explain the distribution only by the capture process: ν^^-_e→n+e^+. They, however, haven't availed the method statistically tested on the spherical distributions in which both the polar and azimuthal angles must be utilized in polar co-ordinates. Also, the azimuthal angle distribution of the IMB burst has been affected by the lack of tracks due to the failure in the supply of high-voltage power to a part of the PMT's at the SN explosion time. Taking into account the effect of the lack of tracks and using the Rayleigh test on the spherical data, we find that the significance probability of 11. 8% is for an isotropic "cos θ" distribution. Accordingly, we conclude that both bursts observed by the IMB and Kamiokande groups are not in contradiction to the assumption that all events are due to ν^^-_e→n+e^+ in accordance with the standard model of a supernova explosion.