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