Modelling the photosphere of active stars for planet detection and characterization

Context. Stellar activity patterns are responsible for jitter effects that are observed at different timescales and amplitudes in the measurements obtained from photometric and spectroscopic time series observations. These effects are currently in the focus of many exoplanet search projects, since the lack of a well-defined characterization and correction strategy hampers the detection of the signals associated with small exoplanets. Aims. Accurate simulations of the stellar photosphere based on the most recent available models for main-sequence stars can provide synthetic photometric and spectroscopic time series data. These may help to investigate the relation between activity jitter and stellar parameters when considering different active region patterns. Moreover, jitters can be analysed at different wavelength scales (defined by the passbands of given instruments or space missions) to design strategies to remove or minimize them. Methods. We present the StarSim tool, which is based on a model for a spotted rotating photosphere built from the integration of the spectral contribution of a fine grid of surface elements. The model includes all significant effects affecting the flux intensities and the wavelength of spectral features produced by active regions and planets. The resulting synthetic time series data generated with this simulator were used to characterize the effects of activity jitter in extrasolar planet measurements from photometric and spectroscopic observations. Results. Several cases of synthetic data series for Sun-like stars are presented to illustrate the capabilities of the methodology. A specific application for characterizing and modelling the spectral signature of active regions is considered, showing that the chromatic effects of faculae are dominant for low-temperature contrasts of spots. Synthetic multi-band photometry and radial velocity time series are modelled for HD 189733 by adopting the known system parameters and fitting for the map of active regions with StarSim. Our algorithm reproduces both the photometry and the radial velocity (RV) curves to good precision, generally better than the studies published to date. We evaluate the RV signature of the activity in HD 189733 by exploring a grid of solutions from the photometry. We find that the use of RV data in the inverse problem could break degeneracies and allow for a better determination of some stellar and activity parameters, for example, the configuration of active regions, the temperature contrast of spots, and the amount of faculae. In addition, the effects of spots are studied for a set of simulated transit photometry, showing that these can introduce variations in Rp/R∗ measurements with a spectral signature and amplitude that are very similar to the signal of an atmosphere dominated by dust