Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 437
Fig. 11.19. Typical density profile for a SN model at 0.15 s after the core
bounce (Fuller et al. 1992). The right-hand scale is m res = ( √ 2G F n e 2E ν ) 1/2
which indicates the resonance value for (∆m 2 ν) 1/2 for E ν = 10 MeV, assuming
an electron number fraction of Y e = 0.5.
ing to the Landau-Zener formula Eq. (8.41) the swap probability is
1 − e −πγ/2 . It exceeds 86% if one requires γ > 4/π or
sin 2 2θ > 8 π
E ν
∆m 2 ν
|∇ ln n e | res , (11.13)
where the vacuum mixing angle θ was assumed to be small. For
(∆m 2 ν) 1/2 = 40 eV the density scale height at the resonance region is
|∇ ln n e | −1
res ≈ 50 km so that
sin 2 2θ ∼ > 10 −8 E ν /10 MeV. (11.14)
Therefore, unless the mixing angle with ν e is very small a cosmologically
interesting neutrino mass for, say, the ν τ may help to explode supernovae!
According to the discussion in Sect. 11.4.2 this would imply that
the prompt ν e burst would also oscillate. Then the first Kamiokande
event could not be associated with the prompt ν e burst.
11.4.5 R-Process Nucleosynthesis
a) Basic Picture
A partial swap of the ν e cooling flux with the more energetic ν µ or ν τ
flux can prevent the synthesis of heavy nuclei by the r-process neutron