Temporal evolution of the obliquity (top panel), semi-major axis (middle panel), and rotation frequency of the envelope (bottom panel) for a 1M_Jup planet orbiting a 1 M_⊙ star starting at a(t₀) = 0.1 AU. The line colours indicate the value of the initial obliquity as indicated on the colour scale in the middle panel. The solid, dotted, and dashed lines correspond to a star initially rotating with Ω (t₀) = 3, 8.5, and 25Ω_⊙, respectively.The solid blue line in the middle panel indicates the Roche limit, where our evolution is stopped.