Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 427
thorough statistical analyses. In their 1995 paper, Loredo and Lamb
have not studied neutrino mass limits which likely would change somewhat
because of corrections to their previous approach.
An analysis by Kernan and Krauss (1995) on the basis of a similar
method yields a limit 19.6 eV at 95% CL. Apparently, the reduction
of the limit is due to their inclusion of the 13% dead-time effect in
the IMB detector. The difference to the Loredo and Lamb (1989) limit
illustrates that changing a relatively fine point of the analysis procedure
can significantly change a so-called 95% CL limit. Therefore, instead
of quoting a specific confidence limit it is at present more realistic to
state qualitatively that a violation of the mass limit
m νe ∼ < 20 eV (11.10)
would have caused a significant and perhaps intolerable modification of
the SN 1987A signal.
This limit is weaker than the current bounds from the tritium β
decay endpoint spectrum (Sect. 7.1.3). Therefore, the above analysis
can be turned around in the sense that the observed neutrino signal
duration is probably representative of the duration of neutrino emission
at the source. The observed long time scale of Kelvin-Helmholtz cooling
which is indicated by the late IMB and Kamiokande events cannot be
blamed on neutrino dispersion effects. In this context it is interesting
to observe that Loredo and Lamb (1989) also performed a maximumlikelihood
analysis with m νe held fixed at their 95% CL upper limit
23 eV. The best-fit time scale in an exponential cooling model changed
from 4.15 to 2.96 s. Therefore, even assuming a large value for m νe did
not allow one to contemplate a significantly shorter Kelvin-Helmholtz
cooling phase than implied by massless neutrinos.
11.3.5 Anomalies in the Signal
The distribution of the Kamiokande and IMB events shows a number of
puzzling features. The least worrisome of them is a certain discrepancy
between the neutrino energies observed in the two detectors which point
to a harder spectrum at IMB. The maximum-likelihood analysis in the
exponential cooling model of Loredo and Lamb (1989) was also performed
for the two detectors separately. The 95% confidence volumes
projected on the T 0 -E b -plane are shown in Koshiba (1992); a similar result
is found in Janka and Hillebrandt (1989b). There is enough overlap
between the confidence contours to allow for a joint analysis. Still, the
best-fit value for Kamiokande lies outside the 95% CL volume of IMB.