Stars as Laboratories for Fundamental Physics - MPP Theory Group

438 Chapter 11
capture. As discussed in Sect. 11.1.4, the hot bubble between the settled
protoneutron star and the escaping shock wave at a few seconds
after core bounce might be an ideal high-entropy environment for this
process for which no other site is currently known that could reproduce
the observed galactic heavy element abundance and isotope distribution.
Naturally, the r-process can only occur in a neutron-rich medium
(Y e < 1 ). The p/n ratio in the hot bubble is governed by the β reactions
ν e n ↔ pe − and ν e p ↔ ne + . Because the neutrino number density
2
is much larger than the ambient e + e − population the proton/neutron
fraction is governed by the neutrino spectra and fluxes. The system
is driven to a neutron-rich phase because normally the ν e ’s are more
energetic than the ν e ’s. They emerge from deeper and hotter regions of
the star because their opacity is governed by the same reactions, and
because the core is neutron rich, yielding a larger opacity for ν e .
If an exchange ν e ↔ ν µ,τ occurs outside of the neutrino sphere the
subsequent ν e flux is more energetic than the ν e flux which did not
undergo a swap. (A normal mass hierarchy has been assumed.) Even
a partial swap of a few 10% is enough to shift the medium to a protonrich
state, i.e. to Y e > 1 , to be compared with the standard values of
2
0.35−0.46. Therefore, the occurrence of such oscillations would be in
conflict with r-process nucleosynthesis in supernovae (Qian et al. 1993).
Fig. 11.20. Density profile for a SN model at 6 s after the core bounce,
typical for the “hot bubble phase” (Qian et al. 1993). 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 Y e = 0.5. (Note that out to a few km above the
neutrino sphere Y e ≪ 0.5.)