The complementarity of astrometrie and radial velocity exoplanet observations: : Determining exoplanet mass with astrometric snapshots
Aims. It is commonly assumed that the two indirect exoplanet detection methods, the radial velocity method and astrometric method, require observational periods exceeding the orbital period to produce positive results. Here we test this assumption in detail. We also investigate the smallest ratio of observational timeline and orbital period required for positive detections. Methods. We obtain full information on the orbital parameters by combining radial-velocity and astrometric measurements by means of Bayesian inference, and sample the parameter probability densities of orbital and other model parameters with a Markov Chain Monte Carlo (MCMC) method in simulated observational scenarios to test the detectability of planets with orbital periods longer than the observational timelines. Results. We show that, when fitting model parameters simultaneously to measurements from both sources, it is possible to extract much more information from the measurements than when using either source alone. Currently available high-precision measurements of radial velocity (with 1 ms-1 precision) and astrometric measurements achievable with the SIM space telescope (with a precision of 1 μas) can be used together to detect a Jupiter analog 30 pc away with an observational timeline of only three years, approximately one fourth of the orbital period. Such measurements are sufficient for determining all its orbital parameters, including inclination and the true mass. Also, with accurate radial velocity measurements covering a timeline of 20 years, the true mass could be determined by astrometric observations within a single year. These case studies demonstrate the potential power of the Bayesian inference of multiple data sources in exoplanet observations. As an example, we show that using the currently available radial velocity measurements, the inclination of HD 154345b could be determined with SIM in a year.