SOLAR MODELS WITH HELIUM AND HEAVY-ELEMENT DIFFUSION

Helium and heavy-element diffusion are both included in precise calcul ations of solar models. In addition, improvements in the input data fo r solar interior models are described for nuclear reaction rates, the solar luminosity, the solar age, heavy-element abundances, radiative o pacities, helium and metal diffusion rates, and neutrino interaction c ross sections. The effects on the neutrino fluxes of each change in th e input physics are evaluated separately by constructing a series of s olar models with one additional improvement added at each stage. The e ffective 1 sigma uncertainties in the individual input quantities are estimated and used to evaluate the uncertainties in the calculated neu trino fluxes and the calculated event rates for solar neutrino experim ents. The calculated neutrino event rates, including all of the improv ements, are 9.3(-1.4)(+1.2) SNU for the Cl-37 experiment and 137(-7)(8) SNU for the Ga-71 experiments. The calculated flux of Be-7 neutrino s is 5.1 1.00(-0.07)(+0.06)) X 10(9) cm(-2) s(-1) and the flux of B-8 neutrinos is 6.6(1.00(-0.17)(+0.14) X 10(6) cm(-2) s(-1). The primordi al helium abundance found for this model is Y=0.278. The present-day s urface abundance of the model is Y-s=0.247, in agreement with the heli oseismological measurement of Y-s=0.242+/-0.003 determined by Hernande z and Christensen-Dalsgaard (1994). The computed depth of the convecti ve zone is R=0.712R(circle dot) , in agreement with the observed value determined from p-mode oscillation data of R=0.713+/-0.003R(circle do t) found by Christensen-Dalsgaard et al. (1991). Although the present results increase the predicted event rate in the four operating solar neutrino experiments by almost 1 sigma (theoretical uncertainty), they only slightly increase the difficulty of explaining the existing expe riments with standard physics (i.e., by assuming that nothing happens to the neutrinos after they are created in the center of the sun). For an extreme model in which all diffusion (helium and heavy-element dif fusion) is neglected, the event rates are 7.0(-1.0)(+0.9) SNU for the Cl-37 experiment and 126(-6)(+6) SNU for the Ga-71 experiments, while the Be-7 and B-8 neutrino fluxes are, respectively, 4.5(1.00(-0.07)(+0 .06)) X 10(9) cm(-2) s(-1) and 4.9(1.00(-0.17)(+0.14)) X 10(6) cm(-2) S-1. For the no-diffusion model, the computed value of the depth of th e convective zone is R = 0.726R(circle dot), which disagrees with the observed helioseismological value. The calculated surface abundance of helium, Y-s=0.268, is also in disagreement with the p-mode measuremen t. The authors conclude that helioseismology provides strong evidence for element diffusion and therefore for the somewhat larger solar neut rino event rates calculated in this paper.