Our Sun IV: The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters
Helioseismic frequency observations provide an extremely accurate window into the solar interior; frequencies from the Michaelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft, enable the adiabatic sound speed and adiabatic index to be inferred with an accuracy of a few parts in 10(exp 4) and the density with an accuracy of a few parts in 10(exp 3). This has become a Serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of the sources of uncertainties in the standard solar models. We found that the largest effect on the interior structure arises from the observational uncertainties in the photospheric abundances of the elements, which affect the sound speed profile at the level of 3 parts in 10(exp 3). The estimated 4% uncertainty in the OPAL opacities could lead to effects of 1 part in 10(exp 3); the approximately 5%, uncertainty in the basic pp nuclear reaction rate would have a similar effect, as would uncertainties of approximately 15% in the diffusion constants for the gravitational settling of helium. The approximately 50% uncertainties in diffusion constants for the heavier elements would have nearly as large an effect. Different observational methods for determining the solar radius yield results differing by as much as 7 parts in 10(exp 4); we found that this leads to uncertainties of a few parts in 10(exp 3) in the sound speed int the solar convective envelope, but has negligible effect on the interior. Our reference standard solar model yielded a convective envelope position of 0.7135 solar radius, in excellent agreement with the observed value of 0.713 +/- 0.001 solar radius and was significantly affected only by Z/X, the pp rate, and the uncertainties in helium diffusion constants. Our reference model also yielded envelope helium abundance of 0.2424, in good agreement with the approximate range of 0.24 to 0.25 inferred from helioseismic observations; only extreme Z/X values yielded envelope helium abundance outside this range. We found that other current uncertainties, namely, in the solar age and luminosity, in nuclear rates other than the pp reaction, in the low-temperature molecular opacities, and in the low-density equation of state, have no significant effect on the quantities that can be inferred from helioseismic observations. The predicted pre-main-sequence lithium depletion is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by approximately 30% for the Cl-27 experiment and by approximately 3% for Ga-71 experiments, while the B-8 neutrino flux is uncertain by approximately 30%.