Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismology provides a powerful tool to explore the deep interior of the Sun. Measurements of solar interior quantities are provided with unprecedented accuracy: for example, the adiabatic sound speed c can be inferred with an accuracy of a few parts in 10⁴. 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 the theory. This paper focuses on our own current calculations but is also a review paper summarizing the latest calculations of other authors. We find that the largest uncertainty in the sound speed c in the solar interior, namely, three parts in 10³, arises from uncertainties in the observed photospheric abundances of the elements: C, N, O, and Ne have uncertainties of ~15%, leading to an uncertainty of ~10% in the photospheric Z/X ratio. Uncertainties of one part in 10³ in the sound speed c arise, in each case, from (1) the ~4% uncertainty in the OPAL opacities, (2) the ~5% uncertainty in the basic p-p 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.) In the convective envelope only, uncertainties in c of order one part in 10³ arise from the uncertainty of a few parts in 10⁴ in the solar radius and from uncertainties in the low-temperature equation of state. Other current uncertainties, namely, in the solar age and luminosity, in nuclear rates other than the p-p reaction, and in the low-temperature molecular opacities, have no significant effect on the quantities that can be inferred from helioseismic observations. Significant uncertainty in the convective envelope position R_ce (of up to 3 times the observational uncertainty of +/-0.001 R_solar) arises only from uncertainties in Z/X, opacities, the p-p rate, and helium diffusion constants; the envelope helium abundance Y_e is significantly affected (+/-0.005) only by extreme variations in Z/X, opacities, or diffusion constants and is always consistent with the ``observed'' range of helioseismically inferred Y_e values. Our predicted pre-main-sequence solar lithium depletion is a factor of ~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 ³⁷Cl experiment and by ~3% for the ⁷¹Ga experiments (not including uncertainties in the capture cross sections), while the ⁸B neutrino flux is uncertain by ~30%.