Stars as Laboratories for Fundamental Physics - MPP Theory Group

442 Chapter 11
linear equations of motion for the neutrino density matrix which causes
an “off-diagonal refractive index” as discussed in Sect. 9.3.2. Qian and
Fuller (1995) have performed an approximately self-consistent analysis
of this problem. All told, they found that the neutrino-neutrino interactions
have a relatively small impact on the parameter space where flavor
conversion disturbs the r-process. Within the overall precision of these
arguments and calculations, their final exclusion plot is nearly identical
with the schematic picture shown in Fig. 11.21. Qian and Fuller’s
findings are corroborated by a study performed by Sigl (1995a).
c) Summary
In summary, there remains a large range of mixing angles where neutrino
oscillations between ν e and ν µ or ν τ with a cosmologically interesting
mass could help to explode supernovae, and yet not disturb
r-process nucleosynthesis. If one assumes a mass hierarchy with ν e
dominated by the lightest, ν τ by the heaviest mass eigenstate, the cosmologically
relevant neutrino would be identified with ν τ . It is interesting
that the relevant range of mixing angles, 3×10 −4 < ∼ θ < ∼ 3×10 −3 ,
overlaps with the mixing angle among the first and third family quarks
which is in the range 0.002−0.005 (Eq. 7.6). Therefore, a scenario
where a massive ν τ plays a cosmologically important role, helps to explode
supernovae, and leaves r-process nucleosynthesis unscathed does
not appear to be entirely far-fetched. This scenario leaves the possibility
open that the MSW effect solves the solar neutrino problem by
ν e -ν µ oscillations.
11.4.6 A Caveat
All existing discussions of neutrino flavor oscillations in SNe were based
on spherically symmetric, smooth density profiles. However, there
can be significant density variations, convection, turbulence, and so
forth. Therefore, it is clear that many of my statements about mediuminduced
oscillation effects are provisional. Further studies will be required
to develop a more complete picture of SNe and their neutrino
oscillations as 3-dimensional events.
A first study of SN neutrino oscillations with an inhomogeneous density
profile was recently performed by Loreti et al. (1995). They added
a random density field to the standard smooth profile and studied the
impact on neutrino oscillations. They found that the shock-revival scenario
involving MSW oscillations can be significantly affected in the