0.07. As expected, in this low eccentricity limit both models yield very similar tracks: the eccentricity is damped to zero in a few Gyr and the semi-major axis decreases until the planet reaches the Roche limit and merges with the star, because the system does not have enough angular momentum to reach a stable equilibrium [@Hut80; @LWC09]. In this case, tidal heating is not sufficient to significantly affect the radius of the planet which keeps shrinking steadily as it cools. Note, however, that, although the qualitative behavior of the evolution is the same, the hypothesis made on the rheology of the body can influence the age at which the merging occurs.

Calculations at high eccentricity {#sec:comp2}
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In the moderately to highly eccentric regime, the tidal dissipation rate can no longer be approximated by Eq.(\[tidal\_energye2\]) (see §\[sec:edot\_2ndOrder\]). Instead, Eq.(\[tidal\_energy\]) must be used and yields - as shown by Fig.\[fig:edot\] - a much more important dissipation rate. As a result, tidal evolution takes place on a much shorter time scale, and both the eccentricity damping and the merging with the star occur earlier in the evolution of the planet. For illustration, Fig.\[fig:xo4\] portrays the possible thermal/tidal evolution (for given initial 