The diffusive overshooting approach on Li abundance in clusters

Abstract

The helioseimic investigation shows that the convective overshooting can penetrate $0.37H_P$ to the location where the temperature is $2.5\times10^6 K$ which is the typical temperature of the reaction $Li^7(p,\alpha)He^4$. This indicates that the overshooting mixing should be involved in investigating the solar Li abundance problem. Observations of Li abundance of solar-twins show that the sun is not very peculiar. The overshooting mixing should be also involved in investigating Li abundance in clusters. However, the fully overshooting mixing with the length of $0.37H_P$ results in too much Li depletion to fit the observation in the solar case. Therefore, using the diffusive process to describe the overshooting is more suitable. The diffusive overshooting approach requires the turbulent r.m.s. velocity in the overshooting region to calculate the diffusion coefficient. Turbulent convection models(TCMs), which are suggested by helioseimic investigation, can provide the turbulent properties in the overshooting region. However, TCMs are often too complex to be applied in the calculations of the stellar evolution. It is an easier way to use the asymptotic solution of TCMs. In this paper, I use the asymptotic solution of Li & Yang's TCM, which results in agreements in both solar sound speed and solar Li abundance, to investigate Li abundance in clusters(Hyades, Praesepe, NGC6633, NGC752, NGC3680 & M67). It is found that the overshooting mixing leads to significant Li depletion in the old clusters($t>1Gyr$) and little effect in the young clusters($t<1Gyr$).