Population studies of Kepler's multiplanet systems have revealed a surprising degree of structure in their underlying architectures. Information from a detected transiting planet can be combined with a population model to make predictions about the presence and properties of additional planets in the system. Using a statistical model for the distribution of planetary systems, we compute the conditional occurrence of planets as a function of the period and radius of Kepler-detectable planets. About half (0.52 +/- 0.03) of the time, the detected planet is not the planet with the largest semi-amplitude (K) in the system, so efforts to measure the mass of the transiting planet with radial velocity (RV) follow up will have to contend with additional planetary signals in the data. We simulate RV observations to show that assuming a single-planet model to measure the K of the transiting planet often requires significantly more observations than in the ideal case with no additional planets, due to systematic errors from unseen planet companions. Our results show that planets around 10 day periods with K close to the single-measurement RV precision (sigma (1,obs)) typically require similar to 100 observations to measure their K to within 20% error. For a next generation RV instrument achieving sigma (1,obs) = 10 cm s(-1), about similar to 200 (600) observations are needed to measure the K of a transiting Venus in a Kepler-like system to better than 20% (10%) error, which is similar to 2.3 times as many as would be necessary for a Venus without any planetary companions.

Early analyses of exoplanet statistics from the Kepler mission revealed that a model population of multiplanet systems with low mutual inclinations (similar to 1 degrees-2 degrees) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a subpopulation of multiplanet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting transit duration variations (TDVs) of the Kepler planet population. When planetary orbits are mutually inclined, planet-planet interactions cause orbital precession, which can lead to detectable long-term changes in transit durations. These TDV signals are inclination sensitive and have been detected for roughly two dozen Kepler planets. We compare the properties of the Kepler-observed TDV detections to TDV detections of simulated planetary systems constructed from two population models with differing assumptions about the mutual inclination distribution. We find strong evidence for a continuous distribution of relatively low mutual inclinations that is well characterized by a power-law relationship between the median mutual inclination ((mu) over tilde (i,n)) and the intrinsic multiplicity (n):(mu) over tilde (i,n) = (mu) over tilde (i,5)(n/5)(alpha), where (mu) over tilde (i,5 )=1.10(-0.11)(+0.05) and alpha =-1.73(-0.08)(+0.09) These results suggest that late-stage planet assembly and possibly stellar oblateness are the dominant physical origins for the excitation of Kepler planet mutual inclinations.

Since the launch of the Kepler space telescope in 2009 and the subsequent K2 mission, hundreds of multiplanet systems have been discovered. The study of such systems, both as individual systems and as a population, leads to a better understanding of planetary formation and evolution. Kepler-80, a K dwarf hosting six super-Earths, was the first system known to have four planets in a chain of resonances, a repeated geometric configuration. Transiting planets in resonant chains can enable us to estimate not only the planets' orbits and sizes but also their masses. Since the original resonance analysis and TTV fitting of Kepler-80, a new planet has been discovered whose signal likely altered the measured masses of the other planets. Here, we determine masses and orbits for all six planets hosted by Kepler-80 by direct forward photodynamical modeling of the light curve of this system. We then explore the resonant behavior of the system. We find that the four middle planets are in a resonant chain, but that the outermost planet only dynamically interacts in similar to 14% of our solutions. We also find that the system and its dynamic behavior are consistent with in situ formation and compare our results to two other resonant chain systems, Kepler-60 and TRAPPIST-1.

The Kepler mission observed thousands of transiting exoplanet candidates around hundreds of thousands of FGK dwarf stars. He et al. applied forward modeling to infer the distribution of intrinsic architectures of planetary systems, developed a clustered Poisson point process model for exoplanetary systems (SysSim) to reproduce the marginal distributions of the observed Kepler population, and they showed that orbital periods and planet radii are clustered within a given planetary system. Here, we extend the clustered model to explore correlations between planetary systems and their host-star properties. We split the sample of Kepler FGK dwarfs into two halves and model the fraction of stars with planets (0.5–10R⊕ and 3–300 days), fswpa, as a linear function of the Gaia DR2 color. We confirm previous findings that the occurrence of these planetary systems rises significantly toward later-type (redder) stars. The fraction of stars with planets increases from  for F2V dwarfs to  for mid-K dwarfs. About half () of all solar-type (G2V) dwarfs harbor a planetary system between 3 and 300 days. This simple model can closely match the observed multiplicity distributions of both the bluer and redder halves in our sample, suggesting that the architectures of planetary systems around stars of different spectral types may be similar aside from a shift in the overall fraction of planet-hosting stars.

We present the occurrence rates for rocky planets in the habitable zones (HZs) of main-sequence dwarf stars based on the Kepler DR25 planet candidate catalog and Gaia-based stellar properties. We provide the first analysis in terms of star-dependent instellation flux, which allows us to track HZ planets. We define η⊕ as the HZ occurrence of planets with radii between 0.5 and 1.5 R⊕ orbiting stars with effective temperatures between 4800 and 6300 K. We find that η⊕ for the conservative HZ is between (errors reflect 68% credible intervals) and planets per star, while the optimistic HZ occurrence is between and planets per star. These bounds reflect two extreme assumptions about the extrapolation of completeness beyond orbital periods where DR25 completeness data are available. The large uncertainties are due to the small number of detected small HZ planets. We find similar occurrence rates between using Poisson likelihood Bayesian analysis and using Approximate Bayesian Computation. Our results are corrected for catalog completeness and reliability. Both completeness and the planet occurrence rate are dependent on stellar effective temperature. We also present occurrence rates for various stellar populations and planet size ranges. We estimate with 95% confidence that, on average, the nearest HZ planet around G and K dwarfs is ∼6 pc away and there are ∼4 HZ rocky planets around G and K dwarfs within 10 pc of the Sun.

The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criterion to constrain the orbital architectures for exoplanetary systems. Previously, He et al. showed through forward modeling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit can also match the observed Kepler population. We show that distributing a planetary system's maximum AMD among its planets results in a multiplicity-dependent distribution of eccentricities and mutual inclinations. Systems with intrinsically more planets have lower median eccentricities and mutual inclinations, and this trend is well described by power-law functions of the intrinsic planet multiplicity (n): ${\tilde{\mu }}_{e,n}\propto {n}^{-{1.74}_{-0.07}^{+0.11}}$ and ${\tilde{\mu }}_{i,n}\propto {n}^{-{1.73}_{-0.08}^{+0.09}}$, where ${\tilde{\mu }}_{e,n}$ and ${\tilde{\mu }}_{i,n}$ are the medians of the eccentricity and inclination distributions. We also find that intrinsic single planets have higher eccentricities (σ e,1 ~ 0.25) than multiplanet systems and that the trends with multiplicity appear in the observed distributions of period-normalized transit duration ratios. We show that the observed preferences for planet-size orderings and uniform spacings are more extreme than what can be produced by the detection biases of the Kepler mission alone. Finally, we find that for systems with detected transiting planets between 5 and 10 days, there is another planet with a greater radial velocity signal ~53% of the time.