Orbital Stability of Multi-Planet Systems: Behavior at High Masses

Abstract

In the coming years, high-contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR 8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that extrapolating to super-Jupiter masses can lead to up to an order of magnitude overestimate of stability for massive, tightly packed systems. We show that at both low and high planet masses, overlapping mean-motion resonances trigger chaotic orbital evolution, which leads to system instability. We attribute some of the difference in behavior as a function of mass to the increasing importance of second order resonances at high planet-star mass ratios. We use our tailored high mass planet results to estimate the maximum number of planets that might reside in double component debris disk systems, whose gaps may indicate the presence of massive bodies.

A Pluto–Charon Sonata: The Dynamical Architecture of the Circumbinary Satellite System

“…These results agree with expectations based on the Hill radius of each satellite. From previous calculations of multi-planet or multi-satellite systems orbiting single or binary central objects, stability requires K 8-10 (e.g., Wisdom 1980;Petit & Henon 1986;Gladman 1993;Chambers et al 1996;Deck et al 2013;Fang & Margot 2013;Fabrycky et al 2014;Mahajan & Wu 2014;Pu & Wu 2015;Morrison & Kratter 2016;Obertas et al 2017). With no stable tracers between the orbits of Styx and Hydra, our calculations support the more conservative K 10.…”

A Pluto–Charon Sonata: Dynamical Limits on the Masses of the Small Satellites

“…The Jupiter-Saturn system easily satisfies this constraint. For 3 or more satellites, the minimum K is sensitive to the masses of the satellites relative to each other and to the mass of the central object (Chambers et al 1996;Smith & Lissauer 2009;Fang & Margot 2013;Kratter & Shannon 2014;Fabrycky et al 2014;Mahajan & Wu 2014;Pu & Wu 2015;Morrison & Kratter 2016;Obertas et al 2017). K ≈ 10-12 is typical.…”

Planet scattering around binaries: ejections, not collisions

“…Note that in some regimes, β may not provide the best metric for planetary stability (see Morrison & Kratter (2016)). Previous works such as Chambers et al (1996), Faber & Quillen (2007), Smith & Lissauer (2009), Shikita et al (2010, Lissauer et al (2011), andPu &Wu (2015) have studied the impact of β on the dynamical "lifetime," meaning the timescale for planets to enter crossing orbits, for systems of three or more equal mass planets around a single star.…”