Indeed, in this approach, one must first separate the forcing potential in terms with a defined frequency before lagging them with the chosen $\epsilon(\sigma)$ (See @FRH08 [@Gre09]). As a result they can only be used in the $e\ll1$ and $\varepsilon_\ii\ll1$ limit.

The time lag $\Delta t$ can be linked to the reduced quality factor $Q'\equiv 3Q/2k_2$, chosen so that $Q'=Q$ for an homogeneous sphere ($k_2=3/2$). Indeed, one must remember that the [*phase lag*]{}, $\epsilon(\sigma)$, induced by the tidal dissipative effects, is twice the geometrical lag angle, $\delta(\sigma)$, between the maximum of the deforming potential and the tidal bulge: $\epsilon(\sigma)=2\delta(\sigma)=\sigma\Delta t $. Moreover, for an incompressible body, a reasonable assumption for giant planets, the tidal dissipation function is given by [@Gol63; @EW09]: $$Q^{-1}(\sigma)=-\frac{\Delta_{\mathrm{cycle}} E(\sigma)}{2\pi E_{\mathrm{peak}}(\sigma)}=\frac{\tan\epsilon(\sigma)}{1-(\frac{\pi}{2}-\epsilon(\sigma))\tan\epsilon(\sigma)},
\label{Qfunc}$$ where $\Delta_{\mathrm{cycle}}E(\sigma)$ is the energy dissipated by the body at the frequency $\sigma$ during one tidal period and $E_{\mathrm{peak}}(\sigma)$ the maximum energy stored in the perturbation. In the cases of interest in the present study, where $Q\gg1$, and for non-synchronized circular orbits, semi-diurnal tides dominate and one can equal the average tidal quality factor to the one given by Eq.(\[Qfunc\]) for the relevant frequency $$\label{QforJ}
Q'^{-1}\approx \frac{4}{3} k_2\Delta t |\omega-n|.$$ This formula can be used 