# The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced

## TL;DR

This study analyzes 909 planets in 355 Kepler multi-planet systems, revealing that planets tend to be similar in size within a system and are regularly spaced, with patterns linked to formation and orbital dynamics.

## Contribution

It provides the first comprehensive analysis of size correlation and orbital spacing patterns in multi-planet systems, highlighting their regularities and potential formation mechanisms.

## Key findings

- Planets within a system are more likely to be similar in size.
- Adjacent planets tend to have regular orbital spacing.
- Most planet pairs are separated by at least 10 mutual Hill radii.

## Abstract

We have established precise planet radii, semimajor axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. In this sample, we find that planets within a single multi-planet system have correlated sizes: each planet is more likely to be the size of its neighbor than a size drawn at random from the distribution of observed planet sizes. In systems with three or more planets, the planets tend to have a regular spacing: the orbital period ratios of adjacent pairs of planets are correlated. Furthermore, the orbital period ratios are smaller in systems with smaller planets, suggesting that the patterns in planet sizes and spacing are linked through formation and/or subsequent orbital dynamics. Yet, we find that essentially no planets have orbital period ratios smaller than $1.2$, regardless of planet size. Using empirical mass-radius relationships, we estimate the mutual Hill separations of planet pairs. We find that $93\%$ of the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of $\sim20$ mutual Hill radii is most common. We also find that when comparing planet sizes, the outer planet is larger in $65 \pm 0.4\%$ of cases, and the typical ratio of the outer to inner planet size is positively correlated with the temperature difference between the planets. This could be the result of photo-evaporation.