Improving the Accuracy of Planet Occurrence Rates from Kepler using Approximate Bayesian Computation

Abstract

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 ($R_p<1.25R_{\oplus }$) 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 $1.6_{-0.5}^{+1.2}$ 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.

Accepted by AJ; 27 pages, 8 figures

References in corpus (7)

• An asteroseismic view of the radius valley: stripped cores, not born rocky
• Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs
• Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months)
• Exploring Exoplanet Populations with NASA's Kepler Mission
• A Statistical Reconstruction of the Planet Population Around Kepler Solar-Type Stars
• Constraining the thick disc formation scenario of the Milky Way
• Transit Light Curves with Finite Integration Time: Fisher Information Analysis

Cited by in corpus (54)

• The California Kepler Survey VII. Precise Planet Radii Leveraging Gaia DR2 Reveal the Stellar Mass Dependence of the Planet Radius Gap
• A Revised Exoplanet Yield from the Transiting Exoplanet Survey Satellite (TESS)
• Exoplanet Statistics and Theoretical Implications
• Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference
• The Occurrence of Rocky Habitable Zone Planets Around Solar-Like Stars from Kepler Data
• Vetting of 384 TESS Objects of Interest with TRICERATOPS and Statistical Validation of 12 Planet Candidates
• The California-Kepler Survey. X. The Radius Gap as a Function of Stellar Mass, Metallicity, and Age
• Searching the Entirety of Kepler Data. II. Occurrence Rate Estimates for FGK Stars
• Architectures of Exoplanetary Systems. I: A Clustered Forward Model for Exoplanetary Systems around Kepler's FGK Stars
• Occurrence Rates of Planets Orbiting M Stars: Applying ABC to Kepler DR25, Gaia DR2, and 2MASS Data
• Architectures of Exoplanetary Systems. III: Eccentricity and Mutual Inclination Distributions of AMD-stable Planetary Systems
• The New Generation Planetary Population Synthesis (NGPPS). III. Warm super-Earths and cold Jupiters: A weak occurrence correlation, but with a strong architecture-composition link
• Accounting for Incompleteness due to Transit Multiplicity in Kepler Planet Occurrence Rates
• A Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates
• Predicted Number, Multiplicity, and Orbital Dynamics of TESS M Dwarf Exoplanets
• Properties and occurrence rates of $Kepler$ exoplanet candidates as a function of host star metallicity from the DR25 catalog
• The Compositional Diversity of Low-Mass Exoplanets
• An information theoretic framework for classifying exoplanetary system architectures
• Predicting Exoplanets Mass and Radius: A Nonparametric Approach
• Giant planet occurrence within 0.2 AU of low-luminosity red giant branch stars with K2
• The New Generation Planetary Population Synthesis (NGPPS). V. Predetermination of planet types in global core accretion models
• A Joint Mass-Radius-Period Distribution of Exoplanets
• The Case for Technosignatures: Why They May Be Abundant, Long-lived, Highly Detectable, and Unambiguous
• Mapping the exo-Neptunian landscape. A ridge between the desert and savanna
• A Closer Look at Exoplanet Occurrence Rates: Considering the Multiplicity of Stars Without Detected Planets
• The New Generation Planetary Population Synthesis (NGPPS). VI. Introducing KOBE: Kepler Observes Bern Exoplanets. Theoretical perspectives on the architecture of planetary systems: Peas in a pod
• Exoplanet Validation with Machine Learning: 50 new validated Kepler planets
• The multiplicity distribution of Kepler's exoplanets
• EXPRES I. HD~3651 an Ideal RV Benchmark
• Architectures of Exoplanetary Systems. II: An Increase in Inner Planetary System Occurrence Toward Later Spectral Types for Kepler's FGK Dwarfs
• Setting the Stage: Planet formation and Volatile Delivery
• Exoplanets in the Galactic context: Planet occurrence rates in the thin disk, thick disk and stellar halo of Kepler stars
• Diffuser-assisted Photometric Follow-up Observations of the Neptune-sized Planets K2-28b and K2-100b
• Sculpting the sub-Saturn Occurrence Rate via Atmospheric Mass Loss
• Edge-of-the-Multis: Evidence for a Transition in the Outer Architectures of Compact Multi-Planet Systems
• An ablating super-Earth in an eccentric binary from the Dispersed Matter Planet Project
• Occurrence rates of small planets from HARPS: Focus on the Galactic context
• CKS IX: Revisiting the Minimum-Mass Extrasolar Nebula with Precise Stellar Parameters
• The PAU Survey: Measurement of Narrow-band galaxy properties with Approximate Bayesian Computation
• 21st Century Statistical and Computational Challenges in Astrophysics
• On the role of resonances in polluting white dwarfs by asteroids
• Planet occurrence rate density models including stellar effective temperature
• The Demographics of Wide-Separation Planets
• Sensitivity Analyses of Exoplanet Occurrence Rates from Kepler and Gaia
• Unveiling the Planet Population at Birth
• Comparing Approximate Bayesian Computation with the Poisson-Likelihood Method for Exoplanet Occurrence Rates
• Combining Transit and RV: A Synthesized Population Model
• Stacked Periodograms as a Probe of Exoplanetary Populations
• Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations
• Mass Upper Bounds for Over 50 Kepler Planets Using Low-S/N Transit Timing Variations
• Trans-Neptunian Space and the Post-Pluto Paradigm
• Detecting false positives with PLATO using double-aperture photometry and centroid shifts
• Exploring Long-period Architectures: Four New Planet Candidates from Kepler with Periods >342 days
• Friends and Foes: Conditional Occurrence Rates of Exoplanet Companions and their Impact on Radial Velocity Follow-up Surveys