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

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 ∼20 mutual Hill radii is most common. We also find that when comparing planet sizes, the outer planet is larger in 65%±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.

Occurrence and Architecture of Kepler Planetary Systems as Functions of Stellar Mass and Effective Temperature

“…Above planet system generating processes assume the planets are randomly paired. In order to better match the observed period ratio (pr; Fabrycky et al 2014;Brakensiek & Ragozzine 2016) and radius ratio (rr) distributions (Ciardi et al 2013;Weiss et al 2018), we further adjust the orbit ratios and rrs of the generated planet systems. Before the adjustment, we first debias the observed pr and rr distributions.…”

Fingerprints of giant planets in the composition of solar twins

“…Since the radii of planets within the same system are known to be mildly correlated (e.g. Weiss et al 2018) we have tested the influence of correlated sizes by examining the two most extreme scenarios: where the sizes of each planet in a system are independent or identical. Finally, to convert the planet radii to masses we use forecaster (Chen & Kipping 2017), which we sum to generate the total mass in a given system.…”

Unified Simulations of Planetary Formation and Atmospheric Evolution: Effects of Pebble Accretion, Giant Impacts, and Stellar Irradiation on Super-Earth Formation

“…Owing to the late orbital instability, the observed period ratio distribution is well reproduced. In addition, other orbital properties such as similar sizes and regular spacing (e.g., Weiss et al 2018) are naturally explained.…”

“…The late instability is observed in all five simulations for high pebble flux, while the instability is not seen in two simulations out of five for low pebble flux. Weiss et al (2018) pointed out that Kepler multi-planet systems have remarkable properties; they are similar in size and regularly spaced (e.g. Lissauer et al 2011).…”