Differences between Stable and Unstable Architectures of Compact Planetary Systems

We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by Kepler and K2. We propagated 21,400 simulated planetary systems up to 5 billion orbits of the innermost planet; approximately 13% of these simulations ended in a planet–planet collision within that time span. We examined trends in dynamical stability based on dynamical spacings, orbital period ratios, and mass ratios of nearest-neighbor planets as well as the system-wide planet mass distribution and the spectral fraction describing the system's short-term evolution. We find that instability is more likely in planetary systems with adjacent planet pairs that have period ratios less than 2 and in systems of greater variance of planet masses. Systems with planet pairs at very small dynamical spacings (less than ∼10–12 mutual Hill radii) are also prone to instabilities, but instabilities also occur at much larger planetary separations. We find that a large spectral fraction (calculated from short integrations) is a reasonable predictor of longer-term dynamical instability; systems that have a large number of Fourier components in their eccentricity vectors are prone to secular chaos and subsequent eccentricity growth and instabilities.