Multiple mean motion resonances in the HR 8799 planetary system

Abstract

HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in\nwide orbits up to ~70au, detected through the direct, high-contrast infrared\nimaging. Large companions and debris disks reported interior to ~10au, and\nexterior to ~100au indicate massive protoplanetary disc in the past. The\ndynamical state of the HR 8799 system is not yet fully resolved, due to limited\nastrometric data covering tiny orbital arcs. We construct a new, orbital model\nof the HR 8799 system, assuming rapid migration of the planets after their\nformation in wider orbits. We found that the HR 8799 planets are likely\ninvolved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary\norbits are coplanar with the stellar equator and inclined by ~25 degrees to the\nsky plane. This best-fit orbital configuration matches astrometry, debris disk\nmodels, and mass estimates from cooling models. The multiple MMR is stable for\nthe age of the star ~160Myr, for at least 1 Gyr unless significant\nperturbations to the N-body dynamics are present. We predict four\nconfigurations with the fifth hypothetical innermost planet HR 8799f in ~9.7au,\nor ~7.5au orbit, extending the MMR chain to triple Laplace resonance\n1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings\nmay establish strong boundary conditions for the system formation and its early\nhistory.\n