Helioseismology provides a powerful tool to explore the deep interior of the
Sun: for example, the adiabatic sound speed can be inferred with an accuracy of
a few parts in 10,000. This has become a serious challenge to theoretical
models of the Sun. Therefore, we have undertaken a self-consistent, systematic
study of sources of uncertainties in the standard solar model, which must be
understood before the helioseismic observations can be used as constraints on
theory. We find that the largest uncertainty in the sound speed in the solar
interior, namely, 3 parts in 1000, arises from uncertainties in the observed
photospheric abundances of the elements; uncertainties of 1 part in 1000 arise
from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in
the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion
constants for the gravitational settling of helium, and (4) the 50%
uncertainties in diffusion constants for the heavier elements. (Other
investigators have shown that similar uncertainties arise from uncertainties in
the interior equation of state and in rotation-induced turbulent mixing.) The
predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an
order of magnitude larger than that predicted by earlier models that neglected
gravitational settling and used older opacities), and is uncertain by a factor
of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37
experiment and by 3% for the Ga-71 experiments (not including uncertainties in
the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.Comment: LaTeX, 38 pages (including 8 figures); ApJ, in press. Added
figures/color figurea available at
http://www.cita.utoronto.ca/~boothroy/sun4.htm