\dot{E}_{\mathrm{tides}}&=&\,2\,\Kp\ \times\ &\nonumber\\  
&\times&\Bigg[N_a(e)-2&N(e)\,x_\mathrm{p}+\left(\frac{1+x_\mathrm{p}^2}{2}\right)\Omega(e)\Bigg] ;\ (\op=n)\ .\end{aligned}$$ This equation fully agrees with Eq.(30) of @Wis08 who calculated it for a homogeneous, incompressible with a radial displacement Love number $h_2 =5k_2/3$. Note that our derivation does not require such an hypothesis and all the uncertainties in the radial distribution of material and its physical properties (e.g., density, compressibility, elasticity) are lumped into the $k_2$ parameter [@Lev08].

Relationship between the time lag $\Delta t$ and the quality factor ($Q$) {#sec:q}
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The aforedescribed tidal model, which leads to [*exact*]{} tidal evolution equations in the viscous approximation, implies a [*constant time lag*]{} $\Delta t$. Neither the tidal quality factor ($Q$), or its counterpart, the phase lag ($\epsilon$) [@Gol63; @GS66] enter the dynamical evolution equations. Instead, the model is characterized by the time lag between the maximum of the tidal potential and the tidal bulge in each body, $\Delta t_\ii$, considered to be constant during the evolution. As shown e.g. by @Dar08 (see also @Gre09), this model is equivalent to considering a body whose rheology entails $Q^{-1}(\sigma)\approx \epsilon(\sigma)\propto \sigma$, where $\sigma/2\pi$ is the frequency of the tidal forcing. The actual rheology of giant gaseous planets being poorly constrained, this arbitrary choice based on the 