A semi-empirical stability criterion for real multi-planetary systems with eccentric orbits

Abstract

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom´s criterion of first order mean motion resonance overlap citep{Wisdom1980AJ}. We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocenter distance of the inner orbit is larger than the pericenter distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multi-planetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator.