We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential ...importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (Rp < 1.25 R⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R⊕ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.
Accurately understanding the interior structure of extrasolar planets is critical for inferring their formation and evolution. The internal density distribution of a planet has a direct effect on the ...star-planet orbit through the gravitational quadrupole field created by the rotational and tidal bulges. These quadrupoles induce apsidal precession that is proportional to the planetary Love number (k 2p , twice the apsidal motion constant), a bulk physical characteristic of the planet that depends on the internal density distribution, including the presence or absence of a massive solid core. We find that the quadrupole of the planetary tidal bulge is the dominant source of apsidal precession for very hot Jupiters (a 0.025 AU), exceeding the effects of general relativity and the stellar quadrupole by more than an order of magnitude. For the shortest-period planets, the planetary interior induces precession of a few degrees per year. By investigating the full photometric signal of apsidal precession, we find that changes in transit shapes are much more important than transit timing variations. With its long baseline of ultra-precise photometry, the space-based Kepler mission can realistically detect apsidal precession with the accuracy necessary to infer the presence or absence of a massive core in very hot Jupiters with orbital eccentricities as low as e 0.003. The signal due to k 2p creates unique transit light-curve variations that are generally not degenerate with other parameters or phenomena. We discuss the plausibility of measuring k 2p in an effort to directly constrain the interior properties of extrasolar planets.
Abstract
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 (0.5–10
R
⊕
and 3–300 days),
f
swpa
, 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.
ABSTRACT During the planet formation process, billions of comets are created and ejected into interstellar space. The detection and characterization of such interstellar comets (ICs) (also known as ...extra-solar planetesimals or extra-solar comets) would give us in situ information about the efficiency and properties of planet formation throughout the galaxy. However, no ICs have ever been detected, despite the fact that their hyperbolic orbits would make them readily identifiable as unrelated to the solar system. Moro-Martín et al. have made a detailed and reasonable estimate of the properties of the IC population. We extend their estimates of detectability with a numerical model that allows us to consider "close" ICs, e.g., those that come within the orbit of Jupiter. We include several constraints on a "detectable" object that allow for realistic estimates of the frequency of detections expected from the Large Synoptic Survey Telescope (LSST) and other surveys. The influence of several of the assumed model parameters on the frequency of detections is explored in detail. Based on the expectation from Moro-Martín et al., we expect that LSST will detect 0.001-10 ICs during its nominal 10 year lifetime, with most of the uncertainty from the unknown number density of small (nuclei of ∼0.1-1 km) ICs. Both asteroid and comet cases are considered, where the latter includes various empirical prescriptions of brightening. Using simulated LSST-like astrometric data, we study the problem of orbit determination for these bodies, finding that LSST could identify their orbits as hyperbolic and determine an ephemeris sufficiently accurate for follow-up in about 4-7 days. We give the hyperbolic orbital parameters of the most detectable ICs. Taking the results into consideration, we give recommendations to future searches for ICs.
Abstract
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 (
σ
1,obs
) typically require ∼100 observations to measure their
K
to within 20% error. For a next generation RV instrument achieving
σ
1,obs
= 10 cm s
−1
, about ∼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 ∼2.3 times as many as would be necessary for a Venus without any planetary companions.
Abstract
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 ∼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.
We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. ...(2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass-radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ~96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1degrees.0-2degrees.2, for the packed systems of small planets probed by these observations.
Kepler-9, discovered by Holman et al. (2010), was the first system with multiple confirmed transiting planets and the first system to clearly show long-anticipated transit timing variations (TTVs). ...It was the first major novel exoplanet discovery of the Kepler Space Telescope mission. The Kepler pipeline identified two Saturn-radius candidates (called Kepler Objects of Interest or KOIs): KOI-377.01 with a 19-day period and KOI-377.02 with a 39-day period. Even with only 9 transits for KOI-377.01 and 6 of KOI-377.02, the transit times were completely inconsistent with a linear ephemeris and showed strongly anti-correlated variations in transit times. Holman et al. (2010) were able to readily show that these objects were planetary mass, confirming them as bona fide planets Kepler-9b and Kepler-9c. As a multi-transiting system exhibiting strong TTVs, the relative planetary properties (e.g., mass ratio, radius ratio) were strongly constrained, opening a new chapter in comparative planetology. KOI-377.03, a small planet with a 1.5-day period, was not initially discovered by the Kepler pipeline, but was identified during the analysis of the other planets and was later confirmed as Kepler-9d through the BLENDER technique by Torres et al. 2011. Holman et al. (2010) included significant dynamical analysis to characterize Kepler-9’s particular TTVs: planets near resonance show large amplitude anti-correlated TTVs with a period corresponding to the rotation of the line of conjunctions and an additional “chopping” signal due to the changing positions of the planets. We review the historical circumstances behind the discovery and characterization of these planets and the publication of Holman et al. (2010). We also review the updated properties of this system and propose ideas for future investigations.
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