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We used a sample of Kepler candidate planets with orbital periods less than200 days and radii between 1.5 and 30 Earth radii to determine the typicaldynamical spacing of neighboring planets. To derive the intrinsic (i.e., freeof observational bias) dynamical spacing of neighboring planets, we generatedpopulations of planetary systems following various dynamical spacingdistributions, subjected them to synthetic observations by the Keplerspacecraft, and compared the properties of observed planets in our simulationswith actual Kepler detections. We found that, on average, neighboring planetsare spaced 21.7 mutual Hill radii apart with a standard deviation of 9.5. Thisdynamical spacing distribution is consistent with that of adjacent planets inthe Solar System. To test the packed planetary systems hypothesis, the ideathat all planetary systems are dynamically packed or filled to capacity, wedetermined the fraction of systems that are dynamically packed by performinglong-term (10^8 years) numerical simulations. In each simulation, we integrateda system with planets spaced according to our best-fit dynamical spacingdistribution but containing an additional planet on an intermediate orbit. Thefraction of simulations exhibiting signs of instability provides an approximatelower bound on the fraction of systems that are dynamically packed; we foundthat >31%, >35%, and >45% of 2-planet, 3-planet, and 4-planet systems aredynamically packed, respectively. Such sizeable fractions suggest that manyplanetary systems are indeed filled to capacity. This feature of planetarysystems is another profound constraint that formation and evolution models mustsatisfy.

Are Planetary Systems Filled to Capacity? A Study Based on Kepler Results