No strong associations between eccentricity and orbital architecture in Kepler compact multis

TL;DR

This study investigates the relationship between orbital eccentricity and system architecture in Kepler's compact multi-planet systems, revealing tidal circularization effects and differences based on planetary multiplicity, with implications for planetary formation theories.

Contribution

It extends previous work by analyzing correlations between eccentricity and system architecture, providing new insights into the dynamical history of small, compact planetary systems.

Findings

Small planets on short orbits show evidence of tidal circularization.

Single-transiting systems have higher eccentricities than multi-transiting systems.

Systems with two transiting planets have higher eccentricities than those with three or more.

Abstract

The dynamical history of a planetary system is recorded in the present day architecture of its constituent planets' sizes, orbital periods, and eccentricities. Studying the relationships between these quantities for large populations provides a window into the processes by which planetary systems form and evolve. Recently, Gilbert, Petigura, and Entrican (2025) performed a hierarchical Bayesian analysis of 1626 planets from the Kepler census, demonstrating a strong relationship between planet radius $R_p$ and orbital eccentricity $e$. Here, we build upon that work to search for correlations between eccentricity and system architecture, focusing on compact systems of small planets. We find that small planets on short orbits ($P < 4$ days) show evidence of tidal circularization. This trend is well established for Jovian planets but a novel finding for super-Earths and sub-Neptunes. We reproduce the known wherein trend single-transiting systems possess elevated eccentricities relative to their multi-transiting counterparts. We further show that systems with two transiting planets have higher eccentricities than those with three or more transiting planets. When compared to population synthesis models, these multiplicity-eccentricity relationships imply that Kepler singles have intrinsic multiplicity ${\sim}3$ and Kepler multis have intrinsic multiplicity ${\sim}4{-}6$. We detect no statistically significant associations between eccentricity and planetary period ratios, gap complexity, size inequality, or size ordering. We interpret these findings as evidence either in favor of a quiescent formation history or against dynamical processes which excite eccentricity but not inclination. Sub-significant relationships between eccentricity and architecture imply that subtle, multi-factor trends may be detectable in the future using more sophisticated statistical techniques.