Astrometry and exoplanets in the Gaia era: a Bayesian approach to detection and parameter recovery

(abridged) We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the in-flight properties of Gaia. Limiting ourselves to one-planet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the delta chi^2. For the delta chi^2, the effective number of degrees of freedom depends on the mission length. We find that the choice of the Markov chain starting point can affect the quality of the results; we therefore consider two limit possibilities: an ideal case, and a very simple method that finds the starting point assuming circular orbits. Using Jeffreys' scale of evidence, the fraction of false positives passing a strong evidence criterion is < ~0.2% (0.6%) when considering a 5 yr (10 yr) mission and using the Akaike information criterion or the Watanabe-Akaike information criterion, and
18 pages, 11 figures. New version accepted by A&A for publication