Larger mutual inclinations for the shortest-period planets

TL;DR

This study analyzes Kepler data to show that the closest-in planets in multi-planet systems tend to have larger mutual inclinations and larger period ratios, indicating inclination excitation and orbital shrinkage effects.

Contribution

It provides the first empirical measurement of mutual inclination differences as a function of orbital distance for short-period planets.

Findings

Inner planets with a/R*<5 have a mutual inclination dispersion of 6.7±0.6 degrees.

Planets with 5<a/R*<12 have a dispersion of 2.0±0.1 degrees.

Higher mutual inclinations correlate with larger period ratios.

Abstract

The {\it 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 {\it Kepler} and {\it K2} multi-planet systems, we measure the minimum difference $\Delta I$ 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 $\Delta I$ 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 $a/R_\star$<5 have a dispersion in $\Delta I$ of $6.7\pm 0.6$~degrees, while planets with $5 < a/R_\star < 12$ have a dispersion of $2.0\pm 0.1$~degrees. 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.