  (abridged) We study the low energy events observed by Kamiokande-II. We focus
on the event 6 of 6.3 MeV and also on the other events that at 1 sigma fall
below the energy threshold: events 3,4,10,12. The volume distribution is not a
uniform distribution at 3 sigma, that suggests the presence of background
events close or at the border of the volume used for the analysis, including
the events 3,4,10. We checked the expected energy distribution assuming that
the signal is due to nubar(e)p-->e+n and that the average antineutrino energy
is 14 MeV. The agreement with the observations is not perfect but it is
acceptable at the 11 % confidence level if we include the peak of low energy
background events; otherwise, we face a 2.9 sigma problem. The expected energy
distribution implies that the evidence for supernova neutrinos is at 10 sigma
and that 1-3 background events are plausible. This conclusion does not change
strongly when we model the time distribution of the signal taking into account
the presence of an initial luminous phase of neutrino emission. This suggests
however that some of the early events are due to supernova neutrinos and not to
background. In summary, we formulate the hypothesis that some of the observed
low energy events are due to background and that some among them belong to a
peculiar phase of emission, that could be further characterized by low energy
neutrinos. Such an interpretation diminishes to a minimum the postulated number
of background events and thus improves the agreement between the a priori and
the a posteriori expectations on the number of background events. We argue on
these grounds that there is no significant disagreement between the average
energy of the supernova neutrinos seen in Kamiokande-II and the conventional
expectations.
