Résumé
Context. The high spot coverage of young active stars is responsible for distortions of spectral lines that hamper the detection of close-in planets through radial velocity methods. Aims: We aim to progress towards more efficient exoplanet detection around active stars by optimizing the use of Doppler imaging in radial velocity measurements. Methods: We propose a simple method to simultaneously extract a brightness map and a set of orbital parameters through a tomographic inversion technique derived from classical Doppler mapping. Based on the maximum entropy principle, the underlying idea is to determine the set of orbital parameters that minimizes the information content of the resulting Doppler map. We carry out a set of numerical simulations to perform a preliminary assessment of the robustness of our method, using an actual Doppler map of the very active star HR 1099 to produce a realistic synthetic data set for various sets of orbital parameters of a single planet in a circular orbit. Results: Using a simulated time series of 50 line profiles affected by a peak-to-peak activity jitter of 2.5 km s-1, in most cases we are able to recover the radial velocity amplitude, orbital phase, and orbital period of an artificial planet down to a radial velocity semi-amplitude of the order of the radial velocity scatter due to the photon noise alone (about 50 m s-1 in our case). One noticeable exception occurs when the planetary orbit is close to co-rotation, in which case significant biases are observed in the reconstructed radial velocity amplitude, while the orbital period and phase remain robustly recovered. Conclusions: The present method constitutes a very simple way to extract orbital parameters from heavily distorted line profiles of active stars, when more classical radial velocity detection methods generally fail. It is easily adaptable to most existing Doppler imaging codes, paving the way towards a systematic search for close-in planets orbiting young, rapidly-rotating stars.