Institution(s): 1. Yunnan Observatory, Chinese Academy of Sciences
When a low mass star evolves up along the red giant branch (RGB), it will develop much more extensive convection in its envelope. Such envelope convection penetrates rapidly inward into the stellar interior, and finally results in a composition discontinuity when it develops into the chemical gradient region. Subsequently, when the out-moving hydrogen burning-shell encounters the newly-formed composition discontinuity, the star will develops the so-called RGB bump on the HR diagram. Therefore, comparisons of characteristics of the RGB bump are crucial for the overshooting mixing below the base of the stellar convective envelope.
In order to treat overshooting convection below the base of the convective envelope, we used the k-omega model of Li (2012) in RGB models of a 1Msun star. We solved equations of the k-omega model in the stellar envelope, and then found that the turbulent kinetic energy and the frequency of turbulence decay in the overshooting region according approximately to power laws of pressure. The decaying indices are found to be sensitive to the parameters of the k-omega model. We adopted a modified overshooting mixing model of Zhang (2013) to investigate the overshooting mixing below the base of the convection zone. We found that the RGB bump appears at a significantly lower luminosity when using the k-omega model than when using the standard mixing-length theory, and its duration is also considerably reduced. Due to extra dredge-up effect of the overshooting mixing, we obtained a little hotter red giant branch using the k-omega model than the one using the standard MLT. We found that the position and duration of the RGB bump sensitively depend on the decaying law of turbulence in the overshooting region. These predictions could be good candidates for asteroseismology of RGB stars.