Heating rates and dynamical timescales for the orbital evolution of the CoRoT-2 system as a function of the orbital eccentricity. The star and planet are assumed to have their present mass and orbital period, and tidal dissipation factors , . The blue curves refer to the star, the red curves to the planet. The planet is assumed to be either synchronously rotating (spin period=orbital period) (plain lines), or to rotate 10% faster than synchronous rotation (dashed lines). From top to bottom, the panels show various important quantities: a) heating rates due to tidal dissipation in the planet and in the star; b) migration timescale due to the star and the planet. Migration is inward except in the asynchronous case due to the planet’s spin down for eccentricities smaller than  ~0.12; c) spin-up timescale: the star is spun up by the planet in all cases. The planet is generally spun up, except in the asynchronous case (see text); d) Circularisation timescale: the evolution towards a circular orbit is due to both stellar and planetary tides.