On the numerical treatment and dependence of thermohaline mixing in red giants

In recent years much interest has been shown in the process of thermohaline mixing in red giants. In low- and intermediate-mass stars this mechanism first activates at the position of the bump in the luminosity function, and has been identified as a likely candidate for driving the slow mixing inferred to occur in these stars. One particularly important consequence of this process, which is driven by a molecular weight inversion, is the destruction of lithium. We show that the degree of lithium destruction, or in some cases production, is extremely sensitive to the numerical details of the stellar models. Within the standard 1D diffusion approximation to thermohaline mixing, we find that different evolution codes, with their default numerical schemes, can produce lithium abundances that differ from one another by many orders of magnitude. This disagreement is worse for faster mixing. We perform experiments with four independent stellar evolution codes, and derive conditions for the spatial and temporal resolution required for a converged numerical solution. The results are extremely sensitive to the time-steps used. We find that predicted lithium abundances published in the literature until now should be treated with caution.