Examples of initial conditions for Styx. Top row: time evolution of Styx’s semi-major axis (left) and eccentricity (right) during the tidal expansion of the PC binary. The initial conditions used in the simulations are a_C ∕R_P= 4, e_{s C} = 0.001, Ω_C ∕n_C = 2, A = 100, and Δt_P = 600 s. The final values of the orbital elements remain close to the current ones. Bottom row: time evolution of the mean-motion ratio (left) and Δϖ (right). We note that the mean value of n_C∕n is larger than 3. The secular angle, Δϖ, oscillates around 180°.