We analyse the possibilities of detection of hypothetical exoplanets in co-orbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small-amplitude oscillations around the periodic solution, we generate a series of synthetic RV curves mimicking the stellar motion around the barycentre of the system. We then fit the data sets obtained assuming three possible different orbital architectures: (a) two planets in co-orbital motion, (b) two planets in a 2/1 mean-motion resonance (MMR) and (c) a single planet. We compare the resulting residuals and the estimated orbital parameters.
For synthetic data sets covering only a few orbital periods, we find that the discrete RV signal generated by a co-orbital configuration could be easily confused with other configurations/systems, and in many cases the best orbital fit corresponds to either a single planet or two bodies in a 2/1 resonance. However, most of the incorrect identifications are associated with dynamically unstable solutions.
We also compare the orbital parameters obtained with two different fitting strategies: a simultaneous fit of two planets and a nested multi-Keplerian model. We find that, even for data sets covering over 10 orbital periods, the nested models can yield incorrect orbital configurations (sometimes close to fictitious MMRs) that are nevertheless dynamically stable and with orbital eccentricities lower than the correct nominal solutions.
Finally, we discuss plausible mechanisms for the formation of co-orbital configurations, by the interaction between two giant planets and an inner cavity in the gas disc. For equal-mass planets, both Lagrangian and anti-Lagrangian configurations can be obtained from same initial condition depending on final time of integration.