Quasi-co-rotation curves given by Eq. (42)for different values of β, from top to bottom β = 1, 0.5, 0.25, and 0.1. The critical values L_c and n_c are indicated by vertical and horizontal black lines whose linestyle corresponds to the different values of β. The red vertical lines indicate the value of n_s, again with the linestyle corresponding to the different values of β. On each plot, the quasi-co-rotation condition corresponds to a pseudo-stable equilibrium for n<n_s (i.e. on the part of the curve on the left of the red line n = n_s), provided that the wind torque dominates the tidal torque. The numerical values correspond to a 1 M_⊙ star and a 1 M_J planet.