Stars as Laboratories for Fundamental Physics - MPP Theory Group

Supernova Neutrinos 439
The approximate parameter range for which this effect is important
can be estimated from the density profile of a typical SN core a few
seconds after bounce (Fig. 11.20). Again, one expects resonant conversions
for the cosmologically interesting neutrino mass range as in the
above shock revival scenario. However, the present effect reaches down
to m ν of about 3 eV; for smaller masses the oscillations would occur at
radii too large to have an impact on nucleosynthesis.
With regard to the required mixing angle there is an important difference
to the previous case because the neutron star has already settled
so that the neutrino sphere is now at a radius of about 11 km rather
than at 50 km. Therefore, the relevant length scales in Fig. 11.20 are
reduced relative to Fig. 11.19 which corresponds to a postbounce but
preexplosion configuration. For example, at m res ≈ 40 eV the density
scale height is now |∇ ln n e | −1
res ≈ 0.3 km, about two orders of magnitude
smaller than before so that the lower limit on sin 2 2θ is about
two orders of magnitude larger than it was for the shock revival scenario.
From a more detailed analysis Qian et al. (1993) found the
hatched area in Fig. 11.21 where Y e would be driven beyond 0.5 and so
this area would be in conflict with r-process nucleosynthesis in supernovae.
Fig. 11.21. Mass difference and mixing angle of ν e with ν µ or ν τ where a spectral
swap would be efficient enough to help explode supernovae (schematically
after Fuller et al. 1992), and where it would prevent r-process nucleosynthesis
(schematically after Qian et al. 1993; Qian and Fuller 1994).