Stars as Laboratories for Fundamental Physics - MPP Theory Group

354 Chapter 10
correlation between T c and the neutrino fluxes which allows one to understand
the impact of certain modifications of a solar model on the
neutrino fluxes via their impact on T c . Bahcall (1989) found
⎧
⎪⎨
Neutrino Flux ∝
⎪⎩
T −1.2
c
T 8 c
for pp,
for 7 Be,
T 18
c for 8 B.
(10.5)
It is noteworthy that the pp flux decreases with increasing T c because
of the constraint imposed by the solar luminosity. One concludes that
a 1% uncertainty in T c translates roughly into a 20% uncertainty of the
boron flux.
There are two sources of uncertainty for the opacity. First, for an
assumed chemical composition, the actual opacity calculation which involves
complicated details of atomic and plasma physics. Second, there
is the uncertain metal content in the central region of the Sun (Z/X).
Because iron retains several bound electrons even for the conditions
at the solar center it contributes substantially to the Rosseland mean
opacity; removing iron entirely would reduce it by 25−30%.
For a recent calculation and detailed discussion of solar opacities see
Iglesias and Rogers (1991a). In view of the relatively small deviations
between different opacity calculations for the relevant conditions Turck-
Chièze and Lopes (1993) as well as Bahcall and Pinsonneault (1992)
agree that the radiative opacities are likely calculated with a precision
of better than a few percent. 53
The actual amount of heavy elements in the Sun, notably iron, is
determined by spectroscopic measurements in the photosphere, and by
the abundance in meteorites which are assumed to represent the presolar
material. The results from both methods seem to agree essentially
on a common value—see Bahcall and Pinsonneault (1995) for a summary
of the recent status. They believe that the uncertainty in the
8 B flux caused by the uncertainty of Z/X is about 8%. Of course, in
the central regions of the Sun the metal abundance is also determined
by gravitational settling as discussed above. The uncertainty of the 8 B
flux inherent in the treatment of gravitational settling is thought to
be 8% as well.
53 However, most recently Tsytovich et al. (1995) have claimed that relativistic
corrections to the electron free-free opacity as well as a number of other hitherto
ignored effects reduce the standard total opacity by as much as 5%.