摘要：HR 8799 is a star accompanied by four massive planets on wide orbits. The observed planetary configuration has been shown to be unstable on a timescale much shorter than the estimated age of the system (~30 Myr) unless the planets are locked into mean motion resonances. This condition is characterised by small-amplitude libration of one or more resonant angles that stabilise the system by preventing close encounters. We simulate planetary systems similar to the HR 8799 planetary system, exploring the parameter space in separation between the orbits, planetary masses and distance from the Sun to the star. We find systems that look like HR 8799 and remain stable for longer than the estimated age of HR 8799. None of our systems are forced into resonances. We find, with nominal masses (Mb = 5 MJup and Mc,d,e = 7 MJup) and in a narrow range of orbit separations, that 5 of 100 systems match the observations and lifetime. Considering a broad range of orbit separations, we find 12 of 900 similar systems. The systems survive significantly longer because of their slightly increased initial orbit separations compared to assuming circular orbits from the observed positions. A small increase in separation leads to a significant increase in survival time. The low eccentricity the orbits develop from gravitational interaction is enough for the planets to match the observations. With lower masses, but still comfortably within the estimated planet mass uncertainty, we find 18 of 100 matching and long-lived systems in a narrow orbital separation range. In the broad separation range, we find 82 of 900 matching systems. Our results imply that the planets in the HR 8799 system do not have to be in strong mean motion resonances. We also investigate the future of wide-orbit planetary systems using our HR 8799 analogues. We find that 80% of the systems have two planets left after strong planet-planet scattering and these are on eccentric orbits with semi-major axes of a1 ~ 10 AU and a2 ~ 30−1000 AU. We speculate that other wide-orbit planetary systems, such as AB Pic and HD 106906, are the remnants of HR 8799 analogues that underwent close encounters and dynamical instability.
关键词：planets and satellites: dynamical evolution and stability
