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

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.

Figures (9)

• Figure 1: The eccentricity of small planets in multi-planet systems for planets with vs without giant companions. The number of planets in each sub-population is indicated in parentheses in the figure legend. Left panel: Sub-population distributions $f(e)$. Dark solid lines indicate median retrieved distribution, and shaded regions indicate the 16th-84th percentile confidence interval. Right panel: Mean eccentricity ${\langle}e{\rangle}$ for each of the sub-populations.
• Figure 2: The eccentricity of small planets as a function of observed multiplicity. The number of planets in each sub-population is indicated in parentheses in the figure legend. Left panel: Sub-population distributions $f(e)$. Dark solid lines indicate median retrieved distribution, and shaded regions indicate the 16th-84th percentile confidence interval. Right panel: Mean eccentricity ${\langle}e{\rangle}$ for each of the sub-populations.
• Figure 3: The eccentricity of small planets as a function of orbital period, split between singles (top panel) and multis (bottom panel). The number of planets in each sub-population is indicated in parentheses in the figure legend. Planets in single-transiting systems with $P < 4$ days show evidence of circularization, and planets in multi-transiting systems at all periods have on average low-$e$ orbits.
• Figure 4: The eccentricity of small planets in two-planet systems as a function of orbital period ratio $P'/P$. The number of planets in each sub-population is indicated in parentheses in the figure legend. No statistically significant difference exists between ${\langle}e{\rangle}$ for various sub-populations.
• Figure 5: The eccentricity of small planets in high multiplicity ($N \geq 3)$ systems as a function of gap complexity $\mathcal{C}$. The number of planets in each sub-population is indicated in parentheses in the figure legend. No statistically significant difference exists between ${\langle}e{\rangle}$ and $\mathcal{C}$ for various sub-populations.