LDEI stability diagram for synchronized celestial bodies in the optimal case for the instability, i.e. an optical libration (ϵ = 2e) for a quasi-equilibrium tide. All values are given in Table 5, and the horizontal axis represents the Ekman number E_k based on the thickness of the fluid layer. The label KM98 for Io calls that the point is placed with the values used by Kerswell & Malkus (1998). The zone below the black line, defined by the viscous surfacic damping coefficient α = 2.62, is the stable zone, whereas the black dashed lines represent the extremum values α = 1 and α = 10.