Magnetic activity in the photosphere of CoRoT-Exo-2a. Active longitudes and short-term spot cycle in

Context. The space experiment CoRoT has recently detected transits by a hot Jupiter across the disk of an active G7V star (CoRoTExo-2a) that can be considered as a good proxy for the Sun at an age of approximately 0.5 Gyr. Aims. We present a spot modelling of the optical variability of the star during 142 days of uninterrupted observations performed by CoRoT with unprecedented photometric precision. Methods. We apply spot modelling approaches previously tested in the case of the Sun by modelling total solar irradiance variatio ns, a good proxy for the optical flux variations of the Sun as a star . The best results in terms of mapping of the surface brightness inhomogeneities are obtained by means of maximum entropy regularized models. To model the light curve of CoRoT-Exo-2a, we take into account both the photometric effects of cool spots as well as those of solar-like faculae, ado pting solar analogy. Results. Two active longitudes initially on opposite hemispheres are found on the photosphere of CoRoT-Exo-2a with a rotation period of 4.522± 0.024 days. Their separation changes by≈ 80 ◦ during the time span of the observations. From this variation, a relative amplitude of the surface differential rotation lower than ∼ 1 percent is estimated. Individual spots form within the act ive longitudes and show an angular velocity about∼ 1 percent smaller than that of the longitude pattern. The tot al spotted area shows a cyclic oscillation with a period of 28.9± 4.3 days, which is close to 10 times the synodic period of the planet as seen by the rotating active longitudes. We discuss the effects of solar-like faculae on our models, finding indication of a facular contribution to the optical flux variations of CoRoT-Exo-2a being significantly smaller than in the present Sun. Conclusions. The implications of such results for the internal rotation o f CoRoT-Exo-2a are discussed on the basis of solar analogy. A possible magnetic star-planet interaction is suggested by the cyclic variation of the spotted area. Alternatively, t he 28.9-d cycle may be related to Rossby-type waves propagating in the subphotospheric layers of the star.