Stars as Laboratories for Fundamental Physics - MPP Theory Group

458 Chapter 12
12.3 Particles from the Sun
12.3.1 Electron Neutrinos
Like a terrestrial power reactor, the Sun is a prolific neutrino source except
that it emits ν e ’s rather than ν e ’s. The expected spectrum as well
as the relevant measurements were discussed in Chapter 10. Suffice
it to recall that the solar neutrino flux is now experimentally established
without a shred of doubt. There remain significant discrepancies
between the predicted and measured spectral shape of the spectrum
which may be explained by neutrino oscillations. However, the solar
neutrino problem is a fine point in the context of the present discussion
because the following results depend mostly on the low-energy
pp flux.
One may proceed exactly as in the previous section in order to translate
the solar neutrino spectrum shown in Fig. 10.1 into an expected
flux of x- and γ-rays from the Sun. In Fig. 12.4 I show this flux at Earth
for τ γ /m νe = 10 s/eV (about the laboratory lifetime limit) and for the
values ±1 for the “anisotropy parameter” α. The spectrum as shown is
based on the calculated neutrino flux. The shoulders corresponding to
other than the pp neutrinos likely would have to be reduced somewhat.
The magnitude of the photon flux is enormous because the decay path
d γ is the entire distance to the Sun of 1.5×10 13 cm = 500 s.
The quiet Sun is a significant source of soft x-rays from the quasithermal
emission of the hot corona at T ≈ 4.5×10 6 K. The flux measurements
of Chodil et al. (1965) are marked as open diamonds in
Fig. 12.4. The flux of decay photons in Fig. 12.4 would outshine the
solar corona by some 4 orders of magnitude! Moreover, the corona
spectrum falls off sharply at larger energies. In the hard x- and soft
γ-ray band very restrictive upper limits exist on the emission of the
quiet Sun that are shown in Fig. 12.4. They are based on balloonborne
detectors flown many years ago (Frost et al. 1966; Peterson et al.
1966). These upper limits are still far above the estimated albedo (radiation
from cosmic rays hitting the surface of the Sun), leaving much
room for improvement. Alas, the quiet Sun is not an object of great
interest to γ-ray astronomers and so more recent measurements do not
seem to exist.
In order to respect these measured upper limit photon fluxes one
must shift the decay spectrum in Fig. 12.4 down by about 8 orders of
magnitude (thin solid line in Fig. 12.4). This yields a lower radiative
liftime limit for ν e of τ γ /m > νe ∼ 7×10 9 s/eV (Cowsik 1977; Raffelt 1985).