Spacing of Kepler Planets: Sculpting by Dynamical Instability

Abstract

We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find that the observed spacings are tightly clustered around 12 mutual Hill radii, when transit geometry and sensitivity limits are accounted for. In comparison, dynamical integrations reveal that the minimum spacing required for systems of similar masses to survive dynamical instability for as long as a billion years is, ~10 if all orbits are circular and coplanar, and ~12 if planetary orbits have eccentricities ~0.02 (a value suggested by studies of planet transit-time-variations). This apparent coincidence, between the observed spacing and the theoretical stability threshold, leads us to propose that typical planetary systems were formed with even tighter spacing, but most, except for the widest ones, have undergone dynamical instability, and are pared down to a more anemic version of their former selves, with fewer planets and larger spacings. So while the high multiple systems (five or more transiting planets) are primordial systems that remain stable, the single or double planetary systems, abundantly discovered by the Kepler mission, may be the descendants of more closely packed high multiple systems. If this hypothesis is correct, we infer that the formation environment of Kepler systems should be different from that of the terrestrial planets.