Orbital and dynamical analysis of the system around HR 8799

Context. HR 8799 is a young planetary system composed of four planets and a double debris belt. Being the first multi-planetary system discovered with the direct imaging technique, it has been observed extensively since 1998. This wide baseline of astrometric measurements, counting over 50 observations in 20 years, permits a detailed orbital and dynamical analysis of the system. Aims. To explore the orbital parameters of the planets, their dynamical history, and the planet-to-disk interaction, we made follow-up observations of the system during the VLT/SPHERE guaranteed time observation program. We obtained 21 observations, most of them in favorable conditions. In addition, we observed HR 8799 with the instrument LUCI at the Large Binocular Telescope (LBT). Methods. All the observations were reduced with state-of-the-art algorithms implemented to apply the spectral and angular differential imaging method. We re-reduced the SPHERE data obtained during the commissioning of the instrument and in three open-time programs to have homogeneous astrometry. The precise position of the four planets with respect to the host star was calculated by exploiting the fake negative companions method. We obtained an astrometric precision of the order of 6 mas in the worst case and 1 mas in the best case. To improve the orbital fitting, we also took into account all of the astrometric data available in the literature. From the photometric measurements obtained in different wavelengths, we estimated the masses of the planets following the evolutionary models. Results. We obtained updated parameters for the orbits with the assumption of coplanarity, relatively small eccentricities, and periods very close to the 2:1 resonance. We also refined the dynamical mass of each planet and the parallax of the system (24.49 ± 0.07 mas), which overlap with the recent Gaia eDR3/DR3 estimate. Hydrodynamical simulations suggest that inward migration of the planets caused by the interaction with the disk might be responsible for the planets being locked in resonance. We also conducted detailed N-body simulations indicating possible positions of a putative fifth planet with a mass below the present detection limits of ≃3 MJup