A combined study of thermohaline mixing and envelope overshooting with PARSEC: Calibration to NGC 6397 and M4

Thermohaline mixing is one of the main processes in low-mass red giant stars that affect the transport of chemicals and, thus, the surface abundances along the evolution. The interplay of thermohaline mixing with other processes, such as the downward overshooting from the convective envelope, should be carefully investigated. This study aims to understand the combined effects of thermohaline mixing and envelope overshooting. After implementing the thermohaline mixing process in the \textsc{parsec} stellar evolutionary code, we compute tracks and isochrones (with \textsc{trilegal} code) and compare them with observational data. To constrain the efficiencies of both processes, we perform a detailed modelling that is suitable for globular clusters NGC 6397 and M4. Our results indicate that an envelope overshooting efficiency parameter, $\Lambda_\mathrm{e}=0.6$, and a thermohaline efficiency parameter, $\alpha_\mathrm{th}=50$, are necessary to reproduce the RGB bump magnitudes and lithium abundances observed in these clusters. We find that both envelope overshooting and thermohaline mixing have a significant impact on the variation of $^7$Li abundances. Additionally, we also explore the effects of adopting solar-scaled or $\alpha$-enhanced mixtures on our models. The $^{12}$C and the $^{12}$C/$^{13}$C ratio are also effective indicators to probe extra mixing in RGB stars. Although, their usefulness is currently limited by the lack of precise and accurate C-isotopes abundances.