Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Figure 3.2: Solid (S100 = 0.5), dashed (S100 = 1), and dotted (S100=1.5) lines corresponds
to matter density profiles (upper panel), and temperature profiles (lower panel)
based on heuristic description. The thick band in the upper panel is matter density
profile from numerical supernova models for tPB ≈ 4 s (taken from [25]).
3.2.2 The neutrino fluxes at the neutrino spheres
Processes that occur during the cooling stage thermalize the neutrinos which
bounce back and forth before being finally emitted, within a sphere called the
neutrino sphere, whose size is much larger than the collapsed core radius. Since νe
interact more strongly with matter than the other species, their effective neutrino
sphere is outside the neutrino spheres of the other species and hence they have a
lower average energy than ¯νe and νx. The ¯νe also interact via charged current, but
the cross section is smaller and the matter contains more neutrons than protons
so their average energy is more than that of the νe, but less than that of νx. We
therefore expect a hierarchy of average energies, for the different neutrino species
as: 6 .
〈Eνe〉 < 〈E¯νe〉 < 〈Eνx〉 . (3.21)
Estimates of the neutrino luminosity and average energy have been obtained with
the numerical simulations: 〈Eνe〉 ≈ 10-12 MeV, 〈E¯νe〉 ≈ 15-18 MeV, 〈Eνx〉 ≈ 20-
24 MeV. Note that how much such hierarchies are pronounced is currently under
debate.
Since the neutrinos emitted at their respective neutrino-sphere are almost in thermal
equilibrium we can assume that their corresponding differential flux follow a
Fermi-Dirac distribution. Actually the spectra of neutrinos from the cooling stage
6 Note that this theoretical expectations has not been tested yet because a water Cerenkov
detector can only detect indistinctively fast electrons and positrons, whereas the νµ and the ντ
can only interact with the detector via neutral current interactions such as
νx + N → νx + N (3.20)
where x describes the flavour of the scattering neutrino whether µ or τ.
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