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

The Gaia mission is expected to make a significant contribution to the knowledge of exoplanet systems, both in terms of their number and of their physical properties. 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. We use 6644 and 4402 simulations to assess the fraction of false positive detections in a 5 yr and in a 10 yr mission, respectively; and 4968 and 4706 simulations to assess the detection rate and how the parameters are recovered. Using Jeffreys' scale of evidence, the fraction of false positives passing a strong evidence criterion is less than or similar to 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 <0.02% (<0.06%) when using the Bayesian information criterion. We find that there is a 50% chance of detecting a planet with a minimum S/N = 2.3 (1.7). This sets the maximum distance to which a planet is detectable to similar to 70 pc and similar to 3.5 pc for a Jupiter-mass and Neptune-mass planets, respectively, assuming a 10 yr mission, a 4 au semi-major axis, and a 1 M-circle dot star. We show the distribution of the accuracy and precision with which orbital parameters are recovered. The period is the orbital parameter that can be determined with the best accuracy, with a median relative difference between input and output periods of 4.2% (2.9%) assuming a 5 yr (10 yr) mission. The median accuracy of the semi-major axis of the orbit can be recovered with a median relative error of 7% (6%). The eccentricity can also be recovered with a median absolute accuracy of 0.07 (0.06).