Top panel: secular evolution of a star of mass 1 M_⊙ orbited by a planet of mass 1 M_Jup with initial semi-major axis a_ini = 0.025 AU. From light to dark blue: P_*,ini = 1.4, 5, 8 days. For each color, the solid line represents the rotation of the envelope, and the dashed line that of the core. Bottom panel: difference in rotation period between these simulations and the reference case of Fig. 5. The color scheme is the same as for the top panel.