The Search For Hidden Mixing; Analysis of the Collective and Intrusive Instabilities for Low Prandtl Number and Diffusivity Ratio Systems
Abstract
Low mass stars on the red giant branch (RGB) experience more mixing in their outer convection zone than what is predicted by stellar evolution theory. If there exists an inverse composition gradient on the external wing of the HBS shell after the first `dredge- up', then an unstable composition stratification along with the stable stratification played by entropy implies that double diffusive mixing processes should occur in stellar interiors and that some of the hidden mixing might be a result of double diffusive convection. We explore double diffusive modes in the case where there exists a lateral gradient in composition and entropy, in addition to a vertical gradient in order to understand their mixing rates. We find that under these circumstances, the mixing rates of laminar fingering modes and oscillatory modes may be able to address the missing mixing problem. In addition, we find that the `collective instability', oscillatory modes with no lateral gradients cannot explain the missing mixing on the RGB.