An Exact, Generalized Laplace Resonance in the HR 8799 Planetary System

A system of four super-Jupiter planets around HR 8799 is the first multiplanet configuration discovered via the direct imaging technique. Despite over a decade of research, the system's architecture is still not fully resolved. The main difficulty comes from a still narrow observing window of ∼20 yr that covers small arcs of orbits with periods from roughly 50 to 500 yr. Soon after the discovery, it became clear that unconstrained best-fitting astrometric configurations self-disrupt rapidly due to strong mutual gravitational interactions between the companions of ≃10 Jupiter mass. Recently, we showed that the HR 8799 system may be long-term stable when locked in a generalized Laplace 8:4:2:1 mean-motion resonance (MMR) chain, and we constrained its orbits through the planetary migration. Here we qualitatively improve this approach by considering the MMR in terms of an exactly periodic configuration. This assumption enables us to construct for the first time the self-consistent N-body model of the long-term stable orbital architecture using only available astrometric positions of the planets relative to the star. We independently determine the planetary masses, which are consistent with thermodynamic evolution, and the parallax overlapping to 1σ with the most recent Gaia DR2 value. We also determine the global structure of the inner and outer debris disks in the [8, 600] au range, consistent with the updated orbital solution.