About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of Their Intrinsic Architecture

Abstract

We constrain the intrinsic architecture of Kepler planetary systems by modeling the observed multiplicities of the transiting planets (tranets) and their transit timing variations (TTVs). We robustly determine that the fraction of Sun-like stars with Kepler -like planets, η Kepler , is 30 ± 3%. Here Kepler -like planets are planets that have radii R p R ⊕ and orbital periods P < 400 days. Our result thus significantly revises previous claims that more than 50% of Sun-like stars have such planets. Combining with the average number of Kepler planets per star (∼ 0.9), we obtain that on average each planetary system has 3.0 ± 0.3 planets within 400 days. We also find that the dispersion in orbital inclinations of planets within a given planetary system, σ i,k , is a steep function of its number of planets, k. This can be parameterized as σ i,k ∝ k α and we find that −4 < α < −2 at 2-σ level. Such a distribution well describes the observed multiplicities of both transits and TTVs with no excess of single-tranet systems. Therefore we do not find evidence supporting the so-called "Kepler dichotomy." Together with a previous study on orbital eccentricities, we now have a consistent picture: the fewer planets in a system, the hotter it is dynamically. We discuss briefly possible scenarios that lead to such a trend. Despite our Solar system not belonging to the Kepler club, it is interesting to notice that the Solar system also has three planets within 400 days and that the inclination dispersion is similar to Kepler systems of the same multiplicity.

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

“…Our model is based on the framework of Zhu et al (2018), but with many modifications and new ingredients. With the model, we generate tranet systems with model-expected tranet multiplicity function (N 1 ,N 2 ,N 3+ ) and TTV multiplicity function (M 1 ,M 2 ,M 3+ ).…”

“…With the model, we generate tranet systems with model-expected tranet multiplicity function (N 1 ,N 2 ,N 3+ ) and TTV multiplicity function (M 1 ,M 2 ,M 3+ ). Since we have already divided the sample into different temperature bins, we bin the tranets into three groups instead of six as in Zhu et al (2018) to avoid small number statistic. The simulated multi-plicity and TTV functions are compared to the observed ones (N 1 , N 2 , N 3+ and M 1 , M 2 , M 3+ ) and the likelihood is computed as…”

“…In Zhu et al (2018), the intrinsic multiplicities are modeled as six free parameters, i.e., f k , the fraction of stars with k Kepler -like planets, where 1 k 6. As found by Zhu et al (2018), individual f k were only loosely constrained, nevertheless, F Kep andN p could still be well constrained. For this reason, here in this work, we only consider F Kep andN p as the two free parameters in our model.…”

Energy optimization in extrasolar planetary systems: the transition from peas-in-a-pod to runaway growth

“…The goal of this paper is to generalize previous calculations of energy optimization during the planet assembly process by including the self-gravitational potential of the planetary bodies. The well-ordered planetary systems described above generally have super-earth masses (Zhu et al 2018). For systems that contain more massive Jovian planets, however, the masses, orbital spacing, and other properties are not nearly as uniform (Wang 2017).…”

Inner Super-Earths, Outer Gas Giants: How Pebble Isolation and Migration Feedback Keep Jupiters Cold

“…Inward of ∼100days, planets smaller than 4R ⊕ dominate, averaging to ∼0.6 planet per star around FGK stars, compared to ∼0.04 per star for larger planets (e.g., Fressin et al 2013;Christiansen et al 2015;Zhu et al 2018). The occurrence rate of Kepler super-Earths/mini-Neptunes (here defined as planets with radii 1-4R ⊕ ) rises toward orbital periods of ∼10 days and plateaus beyond (e.g., Mulders et al 2015).…”