Spherical statistical tests on the angular distributions of electrons of the IMB events associated with SN 1987A

Details Spherical statistical tests on the angular distributions of electrons of the IMB events associated with SN 1987A Spherical statistical tests on the angular distributions of electrons of the IMB events associated with SN 1987A

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvd..47.5228k&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 47, Issue 12, 15 June 1993, pp.5228-5232

Mathematics

Probability

1

Supernovae, Probability Theory

Scientific paper

Using various statistical methods, many investigators have claimed on the basis of the polar angle ``cosθ'' distribution of electrons from neutrinos emitted from SN 1987A that the IMB data seem to have a nonisotropic distribution, whereas the Kamiokande data show an isotropic distribution. They assert that it is difficult to explain the distribution only by the capture process ν¯e+p-->n+e+. However, they do not seem to have succeeded in testing spherical distributions using both the polar and azimuthal angles because they calculate using only the polar angle while keeping the azimuthal angle uniform a priori. Also, the azimuthal angle distribution of the IMB events has been affected by the lack of tracks due to the failure at the high-voltage supply to a part of the photomultiplier tubes at the time of the supernova explosion. Taking into account the effect of the lack of tracks, and using a test for the mean direction of the spherical data, we found a significance probability of 12.2% for an isotropic cosθ distribution. In addition to this, the expected distribution from scattering off electrons for antineutrino+proton absorption may not be perflectly isotropic, although the deviation is small. For the expected distribution with the approximate form 1+0.13 cosθ which peaks slightly forward at the typical energies of the IMB events (~30 MeV), we obtained a significance probability of 25.5% by the similar test for the mean direction on the sphere using Rz (z component of the resultant length for the data of events), whereas the IMB group has given only few % significance using the Smirnov-Cramer-von Mises test. The significance shows that the IMB data can be accepted with such a nonuniform distribution. The energy dependence of the expected distribution shows the IMB events to peak slightly forward and the Kamiokande events with a mean energy of ~20 MeV to be distributed uniformly. We can therefore conclude that both angular distributions observed by the IMB and Kamiokande groups do not contradict the assumption that all events are due to ν¯e+p-->n+e+ in accordance with the standard model of a supernova explosion.

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