Figure 1: Artist’s impression of a multi-planet system seen from one of the planets.
Observations by Kepler have also turned up planetary systems that are sparsely populated, in particular, single or double planetary systems. These planets tend to have orbits that are more inclined and more eccentric. One hypothesis suggests that sparsely populated planetary systems could be the remnants of tightly-packed multi-planet systems that have undergone dynamic instability. Interactions during the period of dynamic instability can leave the remaining planets with more inclined and more eccentric orbits.
Simulations show that for a multi-planet system to remain stable for as long as a billion years, the required minimum spacing between adjacent planets is ~10 mutual Hill radii if all planets have orbits that are circular and lie on the same plane. However, if the orbits of the planets are slightly eccentric, then the required minimum spacing between adjacent planets is ~12 mutual Hill radii. The similarity between what is observed and what is theoretically predicted for tightly-packed multi-planet systems suggests that planetary systems tend to form with much tighter spacings between adjacent planets. Tightly-packed multi-planet systems with 5 or more planets are probably planetary systems that have remained stable since formation, while single or double planetary systems are the remnants of more tightly-packed multi-planet systems.
Figure 2: The observed K-distribution (i.e. distribution of the spacings between adjacent planets in units of mutual Hill radii) of multi-planet systems shown as solid histograms for the 4 planet and 5 planet + 6 planet systems. Pu & Wu (2015).
Pu & Wu (2015), “Spacing of Kepler Planets: Sculpting by Dynamical Instability”, arXiv:1502.05449 [astro-ph.EP]