Evolution of the gravity offset of mixed modes in RGB stars

Context. Observations of mixed modes in evolved low-mass stars enable us to probe the properties of not only the outer envelope of these stars, but also their deep layers. Among the seismic parameters associated with mixed modes, the gravity offset, denoted with epsilon(g), is expected to reveal information on the boundaries of the inner buoyancy resonant cavity. This parameter was recently measured for hundreds of stars observed by the Kepler satellite and its value was shown to change during evolution. Aims. In this article, we theoretically investigate the reasons for such a variation in terms of structure properties, focusing only on the red giant branch. Methods. Using available asymptotic analyses and a simple model of the Brunt-Vaisala and Lamb frequencies in the upper part of the radiative zone, we derived an analytical expression of epsilon(g) for dipolar modes and compared its predictions to observations. Results. First, we show that the asymptotic value of epsilon(g) well agrees with the mean value observed at the beginning of the ascent of the red giant branch, which results from the high density contrast between the helium core and the base of the convective envelope. Second, we demonstrate that the predicted value also explains the sharp decrease in e g observed for the more luminous red giant stars of the sample. This rapid drop turns out to occur just before the luminosity bump and results from the kink of the Brunt-Vaisala frequency near the upper turning point associated with the buoyancy cavity as stars evolve and this latter nears the base of the convective envelope. The potential of epsilon(g) to probe the value and slope of the Brunt-Vaisala frequency below the base of the convective region is clearly highlighted. Conclusions. The observed variation in e g and its link with the internal properties on the red giant branch are now globally understood. This work motivates further analyses of the potential of this parameter as a seismic diagnosis of the region located between the hydrogen-burning shell and the base of the convective envelope, and of the local dynamical processes associated for instance with core contraction, the migration of the convective boundary, or overshooting.