Early tidal evolution of a circumbinary system. In all the panels, the black curve represents the results of our reference simulation (Table 1). Left: dynamical evolution of the binary, showing the spin rate (top), semimajor axis (middle) and eccentricity (bottom panel). The results depicted in blue consider initially slow-rotating stars with Ω₀ ∕ n₁ = Ω₁ ∕ n₁ = 0.1 (at t = 0), while those in black correspond to primordial fast rotators Ω₀ ∕ n₁ = Ω₁ ∕ n₁ = 10. Right: evolution of the planetary spin and orbit. Black (respectively green) curves correspond to initial super-synchronous (respectively sub-synchronous) planetary spin rates. Time variation of the semimajor axis a₂ and eccentricity e₂ are practically equal in both cases (middle and bottom panels).