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Register a new userA Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates
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Exoplanet catalogs produced by surveys suffer from a lack of completeness (not every planet is detected) and less than perfect reliability (not every planet in the catalog is a true planet), particularly near the surveys detection limit. Exoplanet occurrence rate studies based on such a catalog must be corrected for completeness and reliability. The final Kepler data release, DR25, features a uniformly vetted planet candidate catalog and data products that facilitate corrections. We present a new probabilistic approach to the characterization of Kepler completeness and reliability, making full use of the Kepler DR25 products. We illustrate the impact of completeness and reliability corrections with a Poisson-likelihood occurrence rate method, using a recent stellar properties catalog that incorporates Gaia stellar radii and essentially uniform treatment of the stellar population. Correcting for reliability has a significant impact: the exoplanet occurrence rate for orbital period and radius within 20% of Earths around GK dwarf stars, corrected for reliability, is 0.015+0.011-0.007, whereas not correcting results in 0.034+0.018-0.012 - correcting for reliability reduces this occurrence rate by more than a factor of two. We further show that using Gaia-based vs. DR25 stellar properties impacts the same occurrence rate by a factor of two. We critically examine the the DR25 catalog and the assumptions behind our occurrence rate method. We propose several ways in which confidence in both the Kepler catalog and occurrence rate calculations can be improved. This work provides an example of how the community can use the DR25 completeness and reliability products.
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The Kepler DR25 planet candidate catalog was produced using an automated method of planet candidate identification based on various tests. These tests were tuned to obtain a reasonable but arbitrary balance between catalog completeness and reliability. We produce new catalogs with differing balances of completeness and reliability by varying these tests, and study the impact of these alternative catalogs on occurrence rates. We find that if there is no correction for reliability, different catalogs give statistically inconsistent occurrence rates, while if we correct for both completeness and reliability, we get statistically consistent occurrence rates. This is a strong indication that correction for completeness and reliability is critical for the accurate computation of occurrence rates. Additionally, we find that this result is the same whether using Bayesian Poisson likelihood MCMC or Approximate Bayesian Computation methods. We also examine the use of a Robovetter disposition score cut as an alternative to reliability correction, and find that while a score cut does increase the reliability of the catalog, it is not as accurate as performing a full reliability correction. We get the same result when performing a reliability correction with and without a score cut. Therefore removing low-score planets removes data without providing any advantage, and should be avoided when possible. We make our alternative catalogs publicly available, and propose that these should be used as a test of occurrence rate methods, with the requirement that a method should provide statistically consistent occurrence rates for all these catalogs.
We infer the number of planets-per-star as a function of orbital period and planet size using $Kepler$ archival data products with updated stellar properties from the $Gaia$ Data Release 2. Using hierarchical Bayesian modeling and Hamiltonian Monte Carlo, we incorporate planet radius uncertainties into an inhomogeneous Poisson point process model. We demonstrate that this model captures the general features of the outcome of the planet formation and evolution around GK stars, and provides an infrastructure to use the $Kepler$ results to constrain analytic planet distribution models. We report an increased mean and variance in the marginal posterior distributions for the number of planets per $GK$ star when including planet radius measurement uncertainties. We estimate the number of planets-per-$GK$ star between 0.75 and 2.5 $R_{oplus}$ and 50 to 300 day orbital periods to have a $68%$ credible interval of $0.49$ to $0.77$ and a posterior mean of $0.63$. This posterior has a smaller mean and a larger variance than the occurrence rate calculated in this work and in Burke et al. (2015) for the same parameter space using the $Q1-Q16$ (previous $Kepler$ planet candidate and stellar catalog). We attribute the smaller mean to many of the instrumental false positives at longer orbital periods being removed from the $DR25$ catalog. We find that the accuracy and precision of our hierarchical Bayesian model posterior distributions are less sensitive to the total number of planets in the sample, and more so on the characteristics of the catalog completeness and reliability and the span of the planet parameter space.
Correlations between the occurrence rate of exoplanets and their host star properties provide important clues about the planet formation processes. We studied the dependence of the observed properties of exoplanets (radius, mass, and orbital period) as a function of their host star metallicity. We analyzed the planetary radii and orbital periods of over 2800 $Kepler$ candidates from the latest $Kepler$ data release DR25 (Q1-Q17) with revised planetary radii based on $Gaia$~DR2 as a function of host star metallicity (from the Q1-Q17 (DR25) stellar and planet catalog). With a much larger sample and improved radius measurements, we are able to reconfirm previous results in the literature. We show that the average metallicity of the host star increases as the radius of the planet increases. We demonstrate this by first calculating the average host star metallicity for different radius bins and then supplementing these results by calculating the occurrence rate as a function of planetary radius and host star metallicity. We find a similar trend between host star metallicity and planet mass: the average host star metallicity increases with increasing planet mass. This trend, however, reverses for masses $> 4.0, M_mathrm{J}$: host star metallicity drops with increasing planetary mass. We further examined the correlation between the host star metallicity and the orbital period of the planet. We find that for planets with orbital periods less than 10 days, the average metallicity of the host star is higher than that for planets with periods greater than 10 days.
One core goal of the Kepler mission was to determine the frequency of Earth-like planets that orbit Sun-like stars. Accurately estimating this planet occurrence rate requires both a well-vetted list of planets and a clear understanding of the stars searched for planets. Previous ground-based follow-up observations have, through a variety of methods, sought to improve our knowledge of stars that are known to host planets. Kepler targets without detected planets, however, have not been subjected to the same intensity of follow-up observations. In this paper, we better constrain stellar multiplicity for stars around which Kepler could have theoretically detected a transiting Earth-sized planet in the habitable zone. We subsequently aim to improve estimates of the exoplanet search completeness -- the fraction of exoplanets that were detected by Kepler -- with our analysis. By obtaining adaptive optics observations of 71 Kepler target stars from the Shane 3-m telescope at Lick Observatory, we detected 14 candidate stellar companions within 4 of 13 target stars. Of these 14 candidate stellar companions, we determine through multiple independent methods that 3 are likely to be bound to their corresponding target star. We then assess the impact of our observations on exoplanet occurrence rate calculations, finding an increase in occurrence of 6% (0.9 $sigma$) for various estimates of the frequency of Earth-like planets and an increase of 26% (4.5 $sigma$) for super-Earths and sub-Neptunes. These occurrence increases are not entirely commensurate with theoretical predictions, though this discrepancy may be due to differences in the treatment of stellar binarity.
We have carried out an intensive study of photometric (Kepler Mission) and spectroscopic data on the system Kepler-2 (HAT-P-7A) using the dedicated software WinFitter. The mean individual data-point error of the normalized flux values for this system is 0.00015, leading to the models specification for the mean reference flux to an accuracy of $sim$0.5 ppm. This testifies to the remarkably high accuracy of the binned data-set, derived from over 1.8 million individual observations. Spectroscopic data are reported with the similarly high-accuracy radial velocity amplitude measure of $sim$2 m s$^{-1}$. The analysis includes discussion of the fitting quality and model adequacy. Our derived absolute parameters for Kepler-2 are as follows: $M_p$ (Jupiter) 1.80 $pm$ 0.13; $R_{star}$ 1.46 $pm 0.08 times 10^6$ km; $R_p$ 1.15 $pm 0.07 times 10^5$ km. These values imply somewhat larger and less condensed bodies than previously catalogued, but within reasonable error estimates of such literature parameters. We find also tidal, reflection and Doppler effect parameters, showing that the optimal model specification differs slightly from a `cleaned model that reduces the standard deviation of the $sim$3600 binned light curve points to less than 0.9 ppm. We consider these slight differences, making comparisons with the hot-jupiter systems Kepler-1 (TrES-2) and 13.
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