STABILITY OF THE DIRECTLY IMAGED MULTIPLANET SYSTEM HR 8799: RESONANCE AND MASSES

A new era of directly imaged extrasolar planets has produced a three-planet system, where the masses of the planets have been estimated by untested cooling models. We point out that the nominal circular, face-on orbits of the planets lead to a dynamical instability in similar to 10(5) yr, a factor of at least 100 shorter than the estimated age of the star. Reduced planetary masses produce stability only for unreasonably small planets (less than or similar to 2 M(Jup)). Relaxing the face-on assumption, but still requiring circular orbits while fitting the observed positions, makes the instability time even shorter. A promising solution is that the inner two planets have a 2: 1 commensurability between their periods, and they avoid close encounters with each other through this resonance. The fact that the inner resonance has lasted until now, in spite of the perturbations of the outer planet, leads to a limit less than or similar to 10 M(Jup) on the masses unless the outer two planets are also engaged in a 2: 1 mean-motion resonance. In a double resonance, which is consistent with the current data, the system could survive until now even if the planets have masses of similar to 20 M(Jup). Apsidal alignment can further enhance the stability of a mean-motion resonant system. A completely different dynamical configuration, with large eccentricities and large mutual inclinations among the planets, is possible but finely tuned.