A possible architecture of the planetary system HR 8799

HR 8799 is a nearby A-type star with a debris disk and three planetary candidates, which have been imaged directly. We undertake a coherent analysis of various observational data for all known components of the system, including the central star, imaged companions, and dust. Our goal is to elucidate the architecture and evolutionary status of the system. We try to further constrain the age and orientation of the system, the orbits and masses of the companions, and the location of dust. On the basis of the high luminosity of debris dust and dynamical constraints, we argue for a rather young system's age of $\la$50 Myr. The system must be seen nearly, but not exactly, pole-on. Our analysis of the stellar rotational velocity yields an inclination of 13–30°, whereas i $\ga$ 20° is needed for the system to be dynamically stable, which suggests a probable inclination range of 20–30°. The spectral energy distribution, including the Spitzer/IRS spectrum in the mid-infrared as well as IRAS, ISO, JCMT, and IRAM observations, is naturally reproduced by two dust rings associated with two planetesimal belts. The inner “asteroid belt” is located at ~10 AU inside the orbit of the innermost companion and a “Kuiper belt” at $\ga$100 AU is just exterior to the orbit of the outermost companion. The dust masses in the inner and outer ring are estimated to be ≈1 $\times$ 10-5 and 4 $\times$ 10-2 Earth masses, respectively. We show that all three planetary candidates may be stable in the mass range suggested in the discovery paper by Marois et al. (2008) (between 5 and 13 Jupiter masses), but only for some of all possible orientations. For (Mb, Mc, Md) = (5, 7, 7) Jupiter masses, an inclination i $\ga$ 20° is required and the line of nodes of the system's symmetry plane on the sky must lie within between 0° an 50° from north eastward. For higher masses Mb, Mc, Md from $(7, 10, 10)$ to $(11, 13, 13)$, the constraints on both angles are even more stringent. Stable orbits imply a double (4:2:1) mean-motion resonance between all three companions. We finally show that in the cases where the companions themselves are orbitally stable, the dust-producing planetesimal belts are also stable against planetary perturbations.