Comparison between the one-layer (blue) and the two-layer (orange) models. Secular evolution of a system formed by a 0.6 M_⊙ star with initial rotation period P_*,ini = 1.2 days and a 5 M_Jup planet initially orbiting at a distance a_ini = 0.024 AU. Top panel: semi-major axis (solid lines) and corotation radius of the star (dashed lines). Bottom panel: difference tothe rotation period in the case without the planet, as defined in Eq. (24).