Abstract
To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically ...motivated set of solutions in the Circular Restricted Three-Body Problem (CR3BP). We applied Floquet theory to characterize the linear dynamical behavior—static, oscillatory, or exponential—surrounding planar circumbinary periodic trajectories (limit cycles). We computed prograde and retrograde limit cycles and analyzed their geometries, stability bifurcations, and dynamical structures. Orbit and stability calculations are exact computations in the CR3BP and reproducible through the open-source Python package
pyraa
. The periodic trajectories (doi.org/10.5281/zenodo.7532982) produce a set of noncrossing, dynamically cool circumbinary orbits conducive to planetesimal growth. For mass ratios
μ
∈ 0.01, 0.50, we found recurring features in the prograde families. These features include (1) an innermost near-circular trajectory, inside which solutions have resonant geometries, (2) an innermost stable trajectory (
a
c
≈ 1.61 − 1.85
a
bin
) characterized by a tangent bifurcating limit cycle, and (3) a region of dynamical instability (
a
≈ 2.1
a
bin
; Δ
a
≈ 0.1
a
bin
), the exclusion zone, bounded by a pair of critically stable trajectories bifurcating limit cycles. The exterior boundary of the exclusion zone is consistent with prior determinations of
a
c
around a circular binary. We validate our analytic results with
N
-body simulations and apply them to the Pluto–Charon system. The absence of detected CBPs in the inner stable region, between the prograde exclusion zone and
a
c
, suggests that the exclusion zone may inhibit the inward migration of CBPs.
Studies of exoplanet demographics require large samples and precise constraints on exoplanet host stars. Using the homogeneous Kepler stellar properties derived using the Gaia Data Release 2 by ...Berger et al., we recompute Kepler planet radii and incident fluxes and investigate their distributions with stellar mass and age. We measure the stellar mass dependence of the planet radius valley to be / = , consistent with the slope predicted by a planet mass dependence on stellar mass (0.24-0.35) and core-powered mass loss (0.33). We also find the first evidence of a stellar age dependence of the planet populations straddling the radius valley. Specifically, we determine that the fraction of super-Earths (1-1.8 ) to sub-Neptunes (1.8-3.5 ) increases from 0.61 0.09 at young ages (<1 Gyr) to 1.00 0.10 at old ages (>1 Gyr), consistent with the prediction by core-powered mass loss that the mechanism shaping the radius valley operates over Gyr timescales. Additionally, we find a tentative decrease in the radii of relatively cool (Fp < 150 ) sub-Neptunes over Gyr timescales, which suggests that these planets may possess H/He envelopes instead of higher mean molecular weight atmospheres. We confirm the existence of planets within the hot sub-Neptunian "desert" (2.2 R⊕ < Rp < 3.8 , Fp > 650 ) and show that these planets are preferentially orbiting more evolved stars compared to other planets at similar incident fluxes. In addition, we identify candidates for cool (Fp < 20 ) inflated Jupiters, present a revised list of habitable zone candidates, and find that the ages of single and multiple transiting planet systems are statistically indistinguishable.
We study the masses and radii of 65 exoplanets smaller than 4 R sub(+ in circle) with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 R sub(+ ...in circle) and identify a density maximum of 7.6 g cm super(-3) at 1.4 R sub(+ in circle). On average, planets with radii up to R sub(P) = 1.5 R sub(+ in circle) increase in density with increasing radius. Above 1.5 R sub(+ in circle), the average planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Including the solar system terrestrial planets with the exoplanets below 1.5 R sub(+ in circle), we find rho sub(P) = 2.43 + 3.39 (R sub(P)/R sub(+ in circle)) g cm super(-3) for R sub(P) < 1.5 R sub(+ in circle), which is consistent with rocky compositions. For 1.5 < or =, slant R sub(P)/R sub(+ in circle) < 4, we find M sub(P)/M sub(+ in circle) = 2.69(R sub(P)/R sub(+ in circle)) super(0.93). The rms of planet masses to the fit between 1.5 and 4 R sub(+ in circle) is 4.3 M sub(+ in circle) with reduced chi super(2) = 6.2. The large scatter indicates a diversity in planet composition at a given radius. The compositional diversity can be due to planets of a given volume (as determined by their large H/He envelopes) containing rocky cores of different masses or compositions.
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, Zhu 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 (S/N) to derive a synthetic population of bootstrapped planet radii. Here, we examine the procedure of sampling transit S/N and demonstrate it is not applicable. Sampling transit S/N does not set up random, independent planet radii, and so it is unsuitable for corroborating (or falsifying) detection bias as the origin of apparent patterns in planet radius. By sampling the planet radii directly and using a simple model for Kepler's sensitivity, we rule out detection bias as the source of the peas-in-a-pod pattern with >10 confidence.
Abstract
The size of a planet is an observable property directly connected to the physics of its formation and evolution. We used precise radius measurements from the California-
Kepler
Survey to ...study the size distribution of 2025
Kepler
planets in fine detail. We detect a factor of ≥2 deficit in the occurrence rate distribution at 1.5–2.0
. This gap splits the population of close-in (
P
< 100 days) small planets into two size regimes:
and
, with few planets in between. Planets in these two regimes have nearly the same intrinsic frequency based on occurrence measurements that account for planet detection efficiencies. The paucity of planets between 1.5 and 2.0
supports the emerging picture that close-in planets smaller than Neptune are composed of rocky cores measuring 1.5
or smaller with varying amounts of low-density gas that determine their total sizes.
Probing the connection between a star's metallicity and the presence and properties of any associated planets offers an observational link between conditions during the epoch of planet formation and ...mature planetary systems. We explore this connection by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets. After correcting for survey incompleteness, we measure planet occurrence: the number of planets per 100 stars with a given metallicity M. Planet occurrence correlates with metallicity for some, but not all, planet sizes and orbital periods. For warm super-Earths having P = 10-100 days and = 1.0-1.7 , planet occurrence is nearly constant over metallicities spanning −0.4 to +0.4 dex. We find 20 warm super-Earths per 100 stars, regardless of metallicity. In contrast, the occurrence of warm sub-Neptunes ( = 1.7-4.0 ) doubles over that same metallicity interval, from 20 to 40 planets per 100 stars. We model the distribution of planets as , where β characterizes the strength of any metallicity correlation. This correlation steepens with decreasing orbital period and increasing planet size. For warm super-Earths β = , while for hot Jupiters β = . High metallicities in protoplanetary disks may increase the mass of the largest rocky cores or the speed at which they are assembled, enhancing the production of planets larger than 1.7 . The association between high metallicity and short-period planets may reflect disk density profiles that facilitate the inward migration of solids or higher rates of planet-planet scattering.
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.
Abstract
In 2017, the California-Kepler Survey (CKS) published its first data release (DR1) of high-resolution optical spectra of 1305 planet hosts. Refined CKS planet radii revealed that small ...planets are bifurcated into two distinct populations, super-Earths (smaller than 1.5
R
⊕
) and sub-Neptunes (between 2.0 and 4.0
R
⊕
), with few planets in between (the “radius gap”). Several theoretical models of the radius gap predict variation with stellar mass, but testing these predictions is challenging with CKS DR1 due to its limited
M
⋆
range of 0.8–1.4
M
⊙
. Here we present CKS DR2 with 411 additional spectra and derived properties focusing on stars of 0.5–0.8
M
⊙
. We found that the radius gap follows
R
p
∝
P
m
with
m
= −0.10 ± 0.03, consistent with predictions of X-ray and ultraviolet- and core-powered mass-loss mechanisms. We found no evidence that
m
varies with
M
⋆
. We observed a correlation between the average sub-Neptune size and
M
⋆
. Over 0.5–1.4
M
⊙
, the average sub-Neptune grows from 2.1 to 2.6
R
⊕
, following
R
p
∝
M
⋆
α
with
α
= 0.25 ± 0.03. In contrast, there is no detectable change for super-Earths. These
M
⋆
–
R
p
trends suggest that protoplanetary disks can efficiently produce cores up to a threshold mass of
M
c
, which grows linearly with stellar mass according to
M
c
≈ 10
M
⊕
(
M
⋆
/
M
⊙
). There is no significant correlation between sub-Neptune size and stellar metallicity (over −0.5 to +0.5 dex), suggesting a weak relationship between planet envelope opacity and stellar metallicity. Finally, there is no significant variation in sub-Neptune size with stellar age (over 1–10 Gyr), which suggests that the majority of envelope contraction concludes after ∼1 Gyr.
Abstract
The California-
Kepler
Survey (CKS) is an observational program developed to improve our knowledge of the properties of stars found to host transiting planets by NASA’s
Kepler
Mission. The ...improvement stems from new high-resolution optical spectra obtained using HIRES at the W. M. Keck Observatory. The CKS stellar sample comprises 1305 stars classified as
Kepler
objects of interest, hosting a total of 2075 transiting planets. The primary sample is magnitude-limited (
) and contains 960 stars with 1385 planets. The sample was extended to include some fainter stars that host multiple planets, ultra-short period planets, or habitable zone planets. The spectroscopic parameters were determined with two different codes, one based on template matching and the other on direct spectral synthesis using radiative transfer. We demonstrate a precision of 60 K in
, 0.10 dex in
, 0.04 dex in
, and 1.0
in
. In this paper, we describe the CKS project and present a uniform catalog of spectroscopic parameters. Subsequent papers in this series present catalogs of derived stellar properties such as mass, radius, and age; revised planet properties; and statistical explorations of the ensemble. CKS is the largest survey to determine the properties of
Kepler
stars using a uniform set of high-resolution, high signal-to-noise ratio spectra. The HIRES spectra are available to the community for independent analyses.
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