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Register a new userImproving the Accuracy of Planet Occurrence Rates from Kepler using Approximate Bayesian Computation
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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 2-D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1-Q16 planet candidates orbiting around solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates ($R_p<1.25 R_{oplus}$) at larger orbital periods ($P>80$d) compared to the rates estimated by the more common inverse detection efficiency method. Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is $1.6^{+1.2}_{-0.5}$ 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$R_{oplus}$ 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.
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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.
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.
The dynamical history of stars influences the formation and evolution of planets significantly. To explore the influence of dynamical history on planet formation and evolution from observations, we assume that stars who experienced significantly different dynamical histories tend to have different relative velocities. Utilizing the accurate Gaia-Kepler Stellar Properties Catalog, we select single main-sequence stars and divide these stars into three groups according to their relative velocities, i.e. high-V, medium-V, and low-V stars. After considering the known biases from Kepler data and adopting prior and posterior correction to minimize the influence of stellar properties on planet occurrence rate, we find that high-V stars have a lower occurrence rate of super-Earths and sub-Neptunes (1--4 R$_{rm oplus}$, P<100 days) and higher occurrence rate of sub-Earth (0.5--1 R$_{ oplus}$, P<30 days) than low-V stars. Additionally, high-V stars have a lower occurrence rate of hot Jupiter sized planets (4--20 R$_{oplus}$, P<10 days) and a slightly higher occurrence rate of warm or cold Jupiter sized planets (4--20 R$_{oplus}$, 10<P<400 days). After investigating the multiplicity and eccentricity, we find that high-V planet hosts prefer a higher fraction of multi-planets systems and lower average eccentricity, which is consistent with the eccentricity-multiplicity dichotomy of Kepler planetary systems. All these statistical results favor the scenario that the high-V stars with large relative velocity may experience fewer gravitational events, while the low-V stars may be influenced by stellar clustering significantly.
Our understanding of planetary systems different to our own has grown dramatically in the past 30 years. However, our efforts to ascertain the degree to which the Solar system is abnormal or unique have been hindered by the observational biases inherent to the methods that have yielded the greatest exoplanet hauls. On the basis of such surveys, one might consider our planetary system highly unusual - but the reality is that we are only now beginning to uncover the true picture. In this work, we use the full eighteen-year archive of data from the Anglo-Australian Planet Search to examine the abundance of Cool Jupiters - analogs to the Solar systems giant planets, Jupiter and Saturn. We find that such planets are intrinsically far more common through the cosmos than their siblings, the hot Jupiters. We find that the occurrence rate of such Cool Jupiters is $6.73^{+2.09}_{-1.13}$%, almost an order of magnitude higher than the occurrence of hot Jupiters (at $0.84^{+0.70}_{-0.20}$%). We also find that the occurrence rate of giant planets is essentially constant beyond orbital distances of $sim$1,au. Our results reinforce the importance of legacy radial velocity surveys for the understanding of the Solar systems place in the cosmos.
The CARMENES exoplanet survey of M dwarfs has obtained more than 18 000 spectra of 329 nearby M dwarfs over the past five years as part of its guaranteed time observations (GTO) program. We determine planet occurrence rates with the 71 stars from the GTO program for which we have more than 50 observations. We use injection-and-retrieval experiments on the radial-velocity (RV) time series to measure detection probabilities. We include 27 planets in 21 planetary systems in our analysis. We find 0.06+0.04-0.03 giant planets (100 M_Earth < M_pl sin i < 1000 M_Earth) per star in periods of up to 1000 d, but due to a selection bias this number could be up to a factor of five lower in the whole 329-star sample. The upper limit for hot Jupiters (orbital period of less than 10 d) is 0.03 planets per star, while the occurrence rate of planets with intermediate masses (10 M_Earth < M_pl sin i < 100 M_Earth) is 0.18+0.07-0.05 planets per star. Less massive planets with 1 M_Earth < M_pl sin i < 10 M_Earth are very abundant, with an estimated rate of 1.32+0.33-0.31 planets per star for periods of up to 100 d. When considering only late M dwarfs with masses M_star < 0.34 M_sol, planets more massive than 10 M_Earth become rare. Instead, low-mass planets with periods shorter than 10 d are significantly overabundant. For orbital periods shorter than 100 d, our results confirm the known stellar mass dependences from the Kepler survey: M dwarfs host fewer giant planets and at least two times more planets with M_pl sin i < 10 M_Earth than G-type stars. In contrast to previous results, planets around our sample of very low-mass stars have a higher occurrence rate in short-period orbits of less than 10 d. Our results demonstrate the need to take into account host star masses in planet formation models.
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