Detecting multiple planets in Gaia data using Bayesian model selection

Gaia will soon provide a census of cold giant planets. However, an astrometric signal contains the superimposed reflex motion of all companions, so planetary signals cannot be treated individually. We therefore investigate Gaia's planet-detection capabilities for 1-planet and 2-planet systems, with special attention to systems near 2:1 mean-motion resonance. Gaia can detect 2-planet systems, although the lower-S/N planet requires a higher S/N threshold, especially when the outer planet is more massive and near 2:1 commensurability. When fitting a 1-planet model to a circular 2-planet resonant system, the resulting fit shows biases in eccentricity (up to e = 0.8), mass (up to 100%), and inclination (up to 50 deg). The bias is maximised when the planets' astrometric signatures are similar, since the combined orbital signal deviates most from a single Keplerian orbit. Many of these systems can be identified as having 2 planets using Bayesian model selection. Still, in some cases the second planet is hidden and undetectable due to its S/N, leading to these biases for the outer planet's orbital parameters. When the outer planet is roughly over three times as massive as the inner planet, orbital approximations allow us to recover the astrometric resoeccentric degeneracy from the bias. When the planets are in dynamical resonance, apsidal precession observed over a long enough baseline (e.g. DR5) can contribute to breaking the degeneracy at short orbital periods. Overall, these biases might significantly affect constraints on planet formation, migration, and evolution models from Gaia population-wide demographics.