A general stability-driven approach for the refinement of multi-planet systems

Context. Over recent years, the number of detected multi-planet systems has grown significantly. An important subclass of these are the compact configurations. Precise knowledge of this subclass is crucial for understanding the conditions in which planetary systems form and evolve. However, observations often leave these systems with large uncertainties, notably on the orbital eccentricities. This is especially prominent for systems with low-mass planets detected with radial velocities, and increasing numbers of these are being discovered in the exoplanet population. Refining these parameters with the help of orbital stability arguments is becoming a common approach. Aims. Such dynamical techniques can be computationally expensive. In this work, we use an alternative procedure that is orders of magnitude faster than classical N-body integration approaches, and has the potential to narrow down parameter uncertainties. Methods. We coupled a reliable exploration of the parameter space with the precision of the Numerical Analysis of Fundamental Frequencies (Laskar, J. 1990, Icarus, 88, 266) fast chaos indicator. We also propose a general procedure to calibrate the NAFF indicator on any multi-planet system without additional computational cost. This calibration strategy is illustrated using the compact multiplanet system HD 45364, in addition to yet-unpublished measurements obtained with the HARPS and CORALIE high-resolution spectrographs. We validate the calibration approach by a comparison with long integrations performed on HD 202696. We test the performances of this stability-driven approach on two systems with different architectures: first we study HD 37124, a three-planet system composed of planets in the Jovian regime; then, we analyse the stability constraints on HD 215152, a compact system of four low-mass planets. Results. We revise the planetary parameters for HD 45364, HD 202696, HD 37124, and HD 215152, and provide a comprehensive view of the dynamical state these systems are in. Conclusions. We demonstrate the potential of the NAFF stability-driven approach to refine the orbital parameters and planetary masses. We stress the importance of undertaking systematic global dynamical analyses on every new multi-planet system discovered.