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Stellar activity induces apparent radial velocity (RV) variations inlate-type main-sequence stars that may hamper the detection of low-mass planetsand the measurement of their mass. We use simultaneous measurements of theactive planet host star HD189733 with high-precision optical photometry by theMOST satellite and high-resolution spectra by SOPHIE. We apply on this uniquedataset a spot model to predict the activity-induced RV variations and comparethem with the observed ones. The model is based on the rotational modulation ofthe stellar flux. A maximum entropy regularization is applied to find a uniqueand stable solution for the distribution of the active regions versus stellarlongitude. The RV variations are synthesized considering the effects on theline profiles of the brightness perturbations due to dark spots and brightfaculae and the reduction of the convective blueshifts in the active regions.The synthesized RV time series shows a remarkably good agreement with theobserved one although variations on timescales shorter than 4-5 days cannot bereproduced by our model. Persistent active longitudes are revealed by the spotmodelling. They rotate with slightly different periods yielding a minimumrelative amplitude of the differential rotation of \Delta \Omega / \Omega =0.23 \pm 0.10. The method proves capable of reducing the power of theactivity-induced RV variations by a factor from 2 to 10 at the rotationfrequency and its harmonics up to the third. Thanks to the high-precisionspace-borne photometry delivered by CoRoT, Kepler, or later PLATO, it ispossible to map the longitudinal distribution of active regions in late-typestars and apply the method presented in this paper to reduce remarkably theimpact of stellar activity on their RV jitter allowing us to confirm thedetection of low-mass planets or refine the measurement of their mass.

astronomy and astrophysics

Deriving the radial-velocity variations induced by stellar activity from  high-precision photometry - Test on HD189733 with simultaneous MOST/SOPHIE  data