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

**Authors:** Gregory J. Gilbert, Erik A. Petigura, Paige M. Entrican  
**arXiv:** [2603.23644](https://arxiv.org/abs/2603.23644)  
**Date:** 2026-03-24  
**Summary page:** https://www.summarizepaper.com/en/paper/2603.23644v1/

## Key points

- Strong correlation between planet radius ($R_p$) and orbital eccentricity ($e)
- Small planets on short orbits (<4 days) show signs 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
- Kepler singles likely have an intrinsic multiplicity around 3, while Kepler multis may range from 4 to 6
- No statistically significant associations found between eccentricity and planetary period ratios, gap complexity, size inequality, or size ordering within these planetary systems

## Summary

A hierarchical Bayesian analysis of 1626 planets from the Kepler census by Gilbert, Petigura, and Entrican (2025) revealed a strong correlation between planet radius ($R_p$) and orbital eccentricity ($e). Building upon this work, the researchers delved deeper into the relationships between eccentricity and system architecture within compact systems of small planets. They observed that small planets on short orbits (with periods less than 4 days) exhibited signs of tidal circularization. This phenomenon was previously well-documented for Jovian planets but has now also been identified in super-Earths and sub-Neptunes. The study also highlighted an intriguing trend where single-transiting systems displayed higher eccentricities compared to multi-transiting counterparts. Additionally, systems with two transiting planets demonstrated elevated eccentricities relative to those with three or more transiting planets. By comparing their findings to population synthesis models, Gilbert et al. inferred that Kepler singles likely have an intrinsic multiplicity around 3 while Kepler multis may possess an intrinsic multiplicity ranging from 4 to 6. Interestingly, the researchers did not find statistically significant associations between eccentricity and planetary period ratios, gap complexity, size inequality, or size ordering within these planetary systems. This led them to interpret their results as suggestive of either a relatively calm formation history or as evidence against dynamical processes that solely excite eccentricity without affecting inclination. Overall, the study's nuanced exploration of eccentricity and architectural relationships in compact multis provides valuable insights into the formation and evolution of planetary systems. While no definitive conclusions were drawn regarding the underlying mechanisms shaping these systems' architectures, the researchers hinted at the potential for future discoveries through more advanced statistical techniques capable of detecting subtle multi-factor trends in similar studies.