Motivated by the trends found in the observed sample of extrasolar planets, this paper determines tidal equilibrium states for forming planetary systems --- subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low-mass limit, valid for superearth-class planets with masses of order $m_{\rm p}\sim10M_\oplus$, previous work showed that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. The present treatment generalizes previous results by including the self-gravity of the planetary bodies. For systems with sufficiently large total mass $m_{\scriptstyle T}$ in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately $m_{\scriptstyle T} \ge m_{\scriptstyle C}\sim40M_\oplus$ (where the value depends on the semimajor axes of the planetary orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the collection of moons orbiting the giant planets in our solar system.
Peas and USPs: Can Stellar Spindown and Peas in a Pod Replicate Ultra-Short-Period Planet Characteristics?
Center for Astrophysics — Harvard and Smithsonian（哈佛-史密森天体物理中心）；Department of Astronomy, University of Wisconsin-Madison（威斯康星大学麦迪逊分校天文系）；Wisconsin Center for Origins Research, University of Wisconsin–Madison（威斯康星大学麦迪逊分校起源研究中心）
\Kepler\ planets around a given star have similar sizes to each other and regular orbital spacing, like "peas in a pod." Several studies have tested whether detection bias could produce this apparent pattern by resampling planet radii at random and applying a sensitivity function analogous to that of the Kepler spacecraft. However, \citet{Zhu2019} argues that this pattern is not astrophysical but an artifact of Kepler's discovery efficiency at the detection threshold. To support this claim, their new analysis samples the transit signal-to-noise ratio (SNR) to derive a synthetic population of b…
Recent studies have shown that the radii and masses of adjacent planets within a planetary system are correlated. It is unknown how this 'peas-in-a-pod' phenomenon originates, whether it is in place at birth or requires evolution, and whether it (initially) applies only to neighboring planets or to all planets within a system. Here we address these questions by making use of the recent discovery that planetary system architectures strongly depend on ambient stellar clustering. Based on Gaia's second data release, we divide the sample of planetary systems hosting multiple planets into those res…
The planets within compact multi-planet systems tend to have similar sizes, masses, and orbital period ratios, like "peas in a pod". This pattern was detected when considering planets with radii between 1 and 4 $R_\oplus$. However, these same planets show a bimodal radius distribution, with few planets between 1.5 and 2 $R_{\oplus}$. The smaller "super-Earths" are consistent with being stripped rocky cores, while the larger "sub-Neptunes" likely have gaseous H/He envelopes. Given these distinct structures, it is worthwhile to test for intra-system uniformity separately within each category of …
We address the claim of Weiss et al. (2018) that the radii of adjacent planets in Kepler multi-planet systems are correlated. We explore two simple toy models---in the first the radii of the planets are chosen at random from a single universal distribution, and in the second we postulate several types of system with distinct radius distributions. We show that an apparent correlation between the radii of adjacent planets similar to the one reported by Weiss et al. (2018) can arise in both models. In addition the second model fits the radius and signal-to-noise distribution of the observed plane…
It has been demonstrated that planets belonging to the same close-in, compact multiple-planet system tend to exhibit a striking degree of uniformity in their sizes. A similar trend has also been found to hold for the masses of such planets, but considerations of such intra-system mass uniformity have generally been limited to statistical samples wherein a majority of systems have constituent planetary mass measurements obtained via analysis of transit timing variations (TTVs). Since systems with strong TTV signals typically lie in or near mean motion resonance, it remains to be seen whether in…
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 small…
(abridged) Observations of exoplanets indicate the existence of several correlations in the architecture of planetary systems. Exoplanets within a system tend to be of similar size and mass, evenly spaced, and are often ordered in size and mass. Small planets are frequently packed in tight configurations, while large planets often have wider orbital spacing. Together, these correlations are called the peas in a pod trends in the architecture of planetary systems. In this paper these trends are investigated in theoretically simulated planetary systems and compared with observations. Whether the…
Although the architectures of compact multiple-planet systems are well-characterized, there has been little examination of their "outer edges", or the locations of their outermost planets. Here we present evidence that the observed high-multiplicity Kepler systems truncate at smaller orbital periods than can be explained by geometric and detection biases alone. To show this, we considered the existence of hypothetical planets orbiting beyond the observed transiting planets with properties dictated by the "peas-in-a-pod" patterns of intra-system radius and period ratio uniformity. We evaluated …
Previous studies using Kepler data suggest that planets orbiting the same star tend to have similar sizes. However, due to the faintness of the stars, only a few of the planets were also detected with radial velocity follow-ups, and therefore the planetary masses were mostly unknown. It therefore yet to be determined whether planetary systems indeed behave as "peas in a pod". Follow-up programs of TESS targets significantly increased the number of confirmed planets with mass measurements, allowing for a more detailed statistical analysis of multi-planet systems. In this work we explore the sim…
The size frequency distribution of exoplanet radii between 1 and 4$R_{\oplus}$ is bimodal with peaks at $\sim$1.4 $R_{\oplus}$ and $\sim$2.4 $R_{\oplus}$, and a valley at $\sim$1.8$R_{\oplus}$. This radius valley separates two classes of planets -- usually referred to as "super-Earths" and "mini-Neptunes" -- and its origin remains debated. One model proposes that super-Earths are the outcome of photo-evaporation or core-powered mass-loss stripping the primordial atmospheres of the mini-Neptunes. A contrasting model interprets the radius valley as a dichotomy in the bulk compositions, where sup…
Planetary Architectures of Kepler Compact Multis with Binary Star Companions
University of California Santa Cruz（加州大学圣克鲁兹分校）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德空间科学实验室）；California Institute of Technology（加州理工学院）
The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed predictions as to where habitable worlds exist within the galaxy. In this paper, we examine using N-body simulations how the properties of planetary systems are determined during the final stages of assembly. While accretion is a chaotic process, trends in the ensemble properties of planetary systems provide a memory of the initial distribution of solid mass around a …
