Run of Π and characteristic timescales of convection in the most external layers of a low-mass star. Left panel: profile of Π across the atmosphere of the MS model of the 1.0 M_⊙ star with chemical composition [X = 0.703,  Y = 0.280,  Z = 0.017]. We note the fall of Π to the minimum value followed by the rapid increase to Π = 1 at increasing pressure. Right panel: run of the asymptotic time t_asy and convective time t_cnv as a function of log P in the atmosphere of the 1.0 M_⊙ at the Sun’s position (log L/L_⊙ = 0 and log T_eff = 3.762). The asymptotic time has a minimum at the position log P ≃ 5.4, roughly coincident with the adiabatic fall layer. This trend is the remote cause of the minimum in the ratio Π of the left panel, and it is related to the mathematical behavior of the real solutions of the quintic equation in the outermost layer of the external convection (see Fig. 3 of Pasetto et al. 2016). Data are from Pasetto et al. (2016).