The shape of the red giant branch bump as a diagnostic of partial mixing processes in low-mass stars

We suggest the use of the shape of the red giant branch (RGB) bump in metal-rich globular clusters as a diagnostic of partial mixing processes between the base of the convective envelope and the H-burning shell. The bump located along the differential luminosity function of cluster RGB stars is a key observable to constrain the H-profile inside these structures. In fact, standard evolutionary models that account for complete mixing in the convective unstable layers and radiative equilibrium in the innermost regions do predict that the first dredge-up produces a very sharp H-discontinuity at the bottom of the convective region. Interestingly enough, we found that both atomic diffusion and a moderate convective overshooting at the base of the convective region marginally affects the shape of the RGB bump in the differential luminosity function (LF). As a consequence, we performed several numerical experiments to estimate whether plausible assumptions concerning the smoothing of the H-discontinuity due to the possible occurrence of extra mixing below the convective boundary affect the shape of the RGB bump. We found that the difference between the shape of RGB bump predicted by standard and by smoothed models can be detected if the H-discontinuity is smoothed over an envelope region whose thickness is equal or larger than 0.5 pressure scale heights. Finally, we briefly discuss the comparison between theoretical predictions and empirical data in metal-rich, reddening-free galactic globular clusters (GGCs) to constrain the sharpness of the H-profile inside RGB stars.