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Multiple mean motion resonances in the HR 8799 planetary system

HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in wide orbits up to ~70au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ~10au, and exterior to ~100au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ~25 degrees to the sky plane. This best-fit orbital configuration matches astrometry, debris disk models, and mass estimates from cooling models. The multiple MMR is stable for the age of the star ~160Myr, for at least 1 Gyr unless significant perturbations to the N-body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ~9.7au, or ~7.5au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.