Photospheric stellar activity (i.e. dark spots or bright plages) might be an important source of noise and confusion in the radial-velocity (RV) measurements. Radial-velocimetry planet search surveys as well as follow-up of photometric transit surveys require a deeper understanding and characterization of the effects of stellar activities to disentangle it from planetary signals.
We simulate dark spots on a rotating stellar photosphere. The variations of the RV are characterized and analyzed according to the stellar inclination, the latitude and the number of spots. The Lomb-Scargle periodograms of the RV variations induced by activity present power at the rotational period Prot of the star and its two-first harmonics Prot/2 and Prot/3. Three adjusted sinusoids fixed at the fundamental period and its two-first harmonics allow to remove about 90% of the RV jitter amplitude. We apply and validate our approach on four known active planet-host stars: HD 189733, GJ 674, CoRoT-7 and ι Hor. We succeed in fitting simultaneously activity and planetary signals on GJ674 and CoRoT-7. We excluded short-period low-mass exoplanets around ι Hor. Our approach is efficient to disentangle reflex-motion due to a planetary companion and stellar-activity induced-RV variations provided that 1) the planetary orbital period is not close to that of the stellar rotation or one of its two-first harmonics, 2) the rotational period of the star is accurately known, 3) the data cover more than one stellar rotational period.