Stars as Laboratories for Fundamental Physics - MPP Theory Group

434 Chapter 11
Fig. 11.17. MSW triangle for the prompt ν e burst from a stellar collapse. In
the shaded area the conversion probability exceeds 50% for E ν = 20 MeV,
assuming the electron density profile of Eq. (11.11). The MSW solutions
to the solar neutrino problem and the Kamiokande allowed range for solar
neutrinos are indicated (see Fig. 10.19).
11.4.3 Cooling-Phase ν e ’s
Neutrino oscillations would cause a partial swap ν e ↔ ν µ,τ and ν e ↔
ν µ,τ so that the measured ν e flux at Earth could be a mixture of the
original ν e and ν µ or ν τ source spectra (Wolfenstein 1987). The energy
spectra of the neutrinos emitted during the Kelvin-Helmholtz cooling
phase are flavor dependent (Eq. 11.4); typically, one finds ⟨E νµ ⟩ =
(1.3 − 1.7) × ⟨E νe ⟩. From the SN 1987A measurements one infers a low
value of roughly ⟨E νe ⟩ ≈ 10 MeV. While the lowest typical predictions
are about 14 MeV, this discrepancy is not a serious problem. However,
it is probably not tolerable that a significant fraction of the observed
events were due to oscillated ν µ ’s.
One may contemplate an “inverted” mass hierarchy where the predominant
mass component of ν e is larger than that of, say, ν τ . In this
case one would obtain resonant oscillations and thus a complete spectral
swap in the shaded triangle of mixing parameters shown in Fig. 11.17.
Even if ⟨E ντ ⟩ is only 1.3×⟨E νe ⟩ this would be in contradiction with the
soft ν e energies observed from SN 1987A. Therefore, an inverted mass
scheme looks excluded for a large range of masses and mixings.