Observed values of the gravity offset adapted from Mosser et al. (2018) as a function of ν_max in RGB stars (+ symbols). The color code indicates the seismic mass computed following Mosser et al. (2013). The error bars are also represented for each data point. The horizontal magenta dashed line corresponds to the asymptotic value expected from Eq. (32) for RGB stars in case a and in the low coupling hypothesis (see Sect. 4.1 for the definition of the cases a and b). This value is included in the dark gray rectangle that corresponds to the values predicted by Takata (2016a), considering typical structures of stars in the early RGB phase (see Sect. 5.2). The clear gray domain represents the asymptotic prediction that is expected from Eq. (39) for RGB stars in case b. Guided by stellar models, the transition is assumed to occur between ν_max ≈ 50 μHz (red solid line) and ν_max ≈ 110 μHz (blue solid line), depending on stellar mass (see main text). The prediction of the analytical model is plotted as a function of ν_max by assuming that the parameter 𝒩_b in Eq. (39) is constant. The black solid line shows the prediction for a transition at ν_max = 130 μHz. In contrast, the clear blue domain corresponds the prediction for a value at the transition of ν_max, t = 110 μHz, assuming that with x between 0 and 1 (see Sect. 4.3.3). The result with x = 1 is represented by the blue dashed line. The horizontal red dashed line indicates the lower limit predicted by the model for stars in case b. As an illustration, the predicted values of ε_g for the two 1.2 M_⊙ stellar models considered in Fig. 1 are represented by the cyan stars.