Rotation, Diffusion, and Overshoot in the Sun: Effects on the Oscillation Frequencies and the Neutrino Flux

Abstract

We have studied the importance of the combined effects of rotation, diffusion, and convective overshoot on the p-mode oscillation spectrum and the neutrino flux of the standard solar model. To isolate the various physical affects included in the new rotation plus diffusion models we also constructed solar models to test the significance of diffusion and of overshoot by themselves. In previous studies, models that include helium diffusion during solar evolution were found to improve the predicted p-mode frequencies for some modes and worsen the agreement for others (Guenther \ea 1993). Here we verify this result for both the Bahcall and Loeb (1990) formulation of diffusion and the Proffitt and Michaud (1991) formulation of diffusion. We find that the effects of rotation on the Sun's structure in the outer layers perturbs the $p$-mode frequencies only slightly when compared to the more substantial effects due to diffusion. In the thin overshoot layer (taken here to be $0.1\, H_p$), we have compared the effect of overmixing in a radiative layer versus convective (adiabatic) penetration. Neither radiative overmixing nor adiabatic penetration has any significant effect on the $p$-modes, probably in part because the overshoot layer is constrained to be thin. The predicted neutrino flux in our diffusion plus rotation model is 7.12 SNU for Cl detectors, 127 SNU for Ga detectors and $5.00\times 10^6\,{\rm erg \, cm^{-2} }$ for the $^8$B neutrinos; this is approximately half-way between the standard solar model without diffusion, and the standard solar model with diffusion alone.