Temporal evolution of the frequency-averaged imaginary part of the potential Love number corresponding to components of degree l = 2, m = 1 (top panel) and l = m = 2 (bottom panel) along the tidal evolution of the systems shown in Fig. 6 of a 1M_Jup planet orbiting 1 M_⊙ mass star starting at a(t₀) = 0.1 AU. The line styles and colours correspond to those of the tracks shown in Fig. 6. The dissipation starts with the value expected from the dissipation of inertial waves and assumes the equilibrium tide constant Q′ value only after the first Gyr for most orbital configurations.