The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced (1706.06204v3)

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.

• The paper shows that planets in the same Kepler system exhibit a strong size correlation with their neighbors.
• It reveals that adjacent planets maintain regular orbital spacing, with period ratios rarely dropping below 1.2, indicating a stability boundary.
• Mutual Hill radii analysis indicates most planet pairs are spaced by 10 to 20 radii apart, supporting dynamical stability theories.

An Overview of the California-Kepler Survey Paper: Planetary Similarity and Spacing in Multi-Planet Systems

The paper, "The California-Kepler Survey. V. Peas in a Pod: Planets in a Kepler multi-planet System are Similar in Size and Regularly Spaced," presents a comprehensive paper of 909 planets in 355 multi-planet systems discovered by Kepler. This paper takes advantage of improved stellar and planetary characterizations made possible by the California Kepler Survey (CKS).

Key Findings

1. Planetary Correlation in Size: A prominent discovery is that planets within the same multi-planet system exhibit a remarkable similarity in size. The size of a planet is often correlated with the size of its immediate neighbor, as opposed to resembling a size drawn randomly from the general distribution of observed planet sizes. This correlation remains robust even after correcting for potential detection biases through bootstrap testing.
2. Regular Orbital Spacing: Another significant finding is that the spacing between planets in multi-planet systems is not arbitrary. The orbital period ratios of adjacent planet pairs exhibit correlation, leading to a pattern of regular spacing. Notably, these ratios are smaller in systems composed of smaller planets, indicative of a linked relationship between planet size and spacing, potentially through formation dynamics or subsequent orbital interactions.
3. Minimum Orbital Period Ratio: The paper identifies that practically no planets have orbital period ratios less than 1.2, regardless of their size. This consistent threshold reinforces the possibility of a dynamical stability boundary at this ratio, likely influenced by resonance overlap and resulting in Lagrange instability.
4. Mutual Hill Radii Evaluation: Using empirically derived mass-radius relationships, the paper estimates that most planet pairs are at least 10 mutual Hill radii apart, with a prevalent spacing of approximately 20 mutual Hill radii. This finding aligns with theoretical models that suggest dynamical stability concerns dictate planetary spacing.
5. Temperature-Size Relationship: It is observed that in 65% of cases, the outer planet is larger than the inner one, and this inclination correlates with the temperature differential between the planets. Such correlations suggest influences like photo-evaporation may play a significant role in shaping these planetary systems.

Implications and Speculations

The findings offer substantial contributions to the understanding of planetary formation and system architecture. The similarity in planetary sizes within systems and the regularity of their spacing highlight underlying processes that govern planetary formation and migration. These processes may include co-formation in situ or gradual migration while avoiding resonant capture unless specific mass and eccentricity conditions are met.

The association of planet size with spacing and the correlation with temperature differences provide essential insights into the physical and dynamical interactions within these systems. This could propose new avenues of research in understanding how different formation pathways—whether in situ accretion or migration—shape system architectures.

Future Directions in Exoplanet Research

Continued advancements in observational capabilities, such as those anticipated from TESS and subsequent missions, will allow further refinement of planet characterization. This, alongside radial velocity methods and next-generation telescopes, will enhance the understanding and detection of additional planets within multi-planet systems, possibly including those in long-period orbits.

Conclusively, these findings from the California-Kepler Survey illuminate critical facets of planetary system formation and dynamics, offering a remarkable glimpse into the diverse architectures of exoplanetary systems compared to our own solar system. Further scrutiny into the Kepler multi-planet systems promises to unravel more nuances of planet formation and migration theories, clarifying how typical our solar system's architecture is in the grand scheme of the Milky Way galaxy.