SIMBAD references

The Kepler mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 Kepler and K2 multiple-planet systems, we measure the minimum difference ΔI between the orbital inclinations, as a function of the orbital distance of the innermost planet. This is accomplished by fitting all the planetary signals simultaneously, constrained by an external estimate of the stellar mean density. We find ΔI to be larger when the inner orbit is smaller, a trend that does not appear to be a selection effect. We find that planets with a/R_* < 5 have a dispersion in ΔI of 6.°7 ± 0.°6, while planets with 5 < a/R_* < 12 have a dispersion of 2.°0 ± 0.°1. The planetary pairs with higher mutual inclinations also tend to have larger period ratios. These trends suggest that the shortest-period planets have experienced both inclination excitation and orbital shrinkage.