Radial velocities of HD45364

In this work we use an alternative procedure faster by orders of magnitude than classical N-body integration approaches, and with the potential to narrow down the parameters uncertainties. We couple a reliable exploration of the parameter space with the precision of the Numerical Analysis of Fundamental Frequencies (NAFF, Laskar, 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This calibration strategy is illustrated on HD 45364, in addition to yet-unpublished measurements obtained with the HARPS and CORALIE high-resolution spectrographs.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 3-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. We revise the planetary parameters in HD 45364, HD 202696, HD 37124 and HD 215152, and provide a comprehensive view of the dynamical state these systems are in.

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.