Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 347
10.2 Calculated Neutrino Spectrum
10.2.1 Individual Sources
A hydrogen-burning star like the Sun liberates nuclear binding energy
by helium fusion from hydrogen which proceeds by virtue of the pp
chains and the CNO cycle (Fig. 10.2). The energy-generation rate for
the CNO cycle is a much steeper function of temperature whence it
dominates in hot stars. For a 2% mass fraction of CN elements, typical
for population I stars like the Sun, the crossover temperature is at
about 1.8×10 7 K (Clayton 1968). The central temperature of the Sun
is about 1.56×10 7 K and so the CNO reactions contribute only about
1% to the total energy budget. In fact, of the CNO tri-cycle shown in
Fig. 10.2, in practice only the first loop (the CN cycle) is of importance
in the Sun as the branching rates into the second or even third loop are
extremely low.
In the Sun, the pp chains terminate in about 85% of all cases via
PPI, i.e. by the fusion of two 3 He nuclei. In this case the only neutrinoproducing
reactions are pp (pp → de + ν e ) and pep (pe − p → dν e ), the
latter occurring very rarely. In about 15% of all cases the termination
is via PPII where 7 Be is formed from 4 He + 3 He. Because of the
small energy difference between the ground states of the 7 Be and 7 Li
Reaction
Table 10.1. Source reactions for solar neutrinos.
Q ( a )
[MeV]
Flux at Earth b
[cm −2 s −1 ]
Uncertainty b
[ % ]
pp → 2 H e + ν e 0.420 c 5.9×10 10 +1 −1
pe − p → 2 H ν e 1.442 1.4×10 8 +1 −2
3 He p → 4 He e + ν e 18.77 c 1.2×10 3 Factor 6
7 Be e − → 7 Li ν e 0.862 4.6×10 9 +6 −7
7 Be e − → 7 Li ∗ ν e 0.384 5.2×10 8 +6 −7
8 B → 8 Be ∗ e + ν e ≈ 15 c 6.6×10 6 +14 −17
13 N → 13 C e + ν e 1.199 c 6.2×10 8 +17 −20
15 O → 15 N e + ν e 1.732 c 5.5×10 8 +19 −22
17 F → 17 O e + ν e 1.740 c 6.5×10 6 +15 −19
Total 6.5×10 10 +1 −1
a Maximum ν e energy for continuum (c) sources.
b Bahcall and Pinsonneault (1995).