The Exoplanet Census: A General Method, Applied to Kepler

Abstract

We develop a general method to fit the planetary distribution function (PLDF) to exoplanet survey data. This maximum likelihood method accommodates more than one planet per star and any number of planet or target star properties. Application to \Kepler data relies on estimates of the efficiency of discovering transits around Solar type stars by Howard et al. (2011). These estimates are shown to agree with theoretical predictions for an ideal transit survey. Using announced \Kepler planet candidates, we fit the PLDF as a joint powerlaw in planet radius, down to 0.5 R_Eart, and orbital period, up to 50 days. The estimated number of planets per star in this sample is ~ 0.7 --- 1.4, where the broad range covers systematic uncertainties in the detection efficiency. To analyze trends in the PLDF we consider four planet samples, divided between shorter and longer periods at 7 days and between large and small radii at 3 R_Earth. At longer periods, the size distribution of the small planets, with index α= -1.2 \pm 0.2 steepens to α= -2.0 \pm 0.2 for the larger planet sample. For shorter periods, the opposite is seen: smaller planets follow a steep powerlaw, α= -1.9 \pm 0.2 that is much shallower, α= -0.7 \pm 0.2 at large radii. The observed deficit of intermediate-sized planets at the shortest periods may arise from the evaporation and sublimation of Neptune and Saturn-like planets. If the trend and explanation hold, it would be spectacular observational confirmation of the core accretion and migration hypotheses, and allow refinement of these theories.

Submitted to ApJ

References in corpus (6)

• A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
• The Occurrence and Mass Distribution of Close-in Super-Earths, Neptunes, and Jupiters
• On the Low False Positive Probabilities of Kepler Planet Candidates
• Mass-loss rates for transiting exoplanets
• Impact of Orbital Eccentricity on the Detection of Transiting Extrasolar Planets
• Using Stellar Densities to Evaluate Transiting Exoplanetary Candidates

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• The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets
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• Planetary Candidates Observed by Kepler, III: Analysis of the First 16 Months of Data
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• The Occurrence Rate of Small Planets around Small Stars
• A Technique for Extracting Highly Precise Photometry for the Two-Wheeled Kepler Mission
• The Role of Core Mass in Controlling Evaporation: the Kepler Radius Distribution and the Kepler-36 Density Dichotomy
• The Minimum-Mass Extrasolar Nebula: In-Situ Formation of Close-In Super-Earths
• Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25
• Extracting distribution parameters from multiple uncertain observations with selection biases
• Identifying Exoplanets with Deep Learning: A Five Planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90
• Terrestrial Planet Occurrence Rates for the Kepler GK Dwarf Sample
• The California-Kepler Survey. IV. Metal-rich Stars Host a Greater Diversity of Planets
• A stellar-mass-dependent drop in planet occurrence rates
• A Framework for Characterizing the Atmospheres of Low-Mass Low-Density Transiting Planets
• The K2 Ecliptic Plane Input Catalog (EPIC) and Stellar Classifications of 138,600 Targets in Campaigns 1-8
• Migration then assembly: Formation of Neptune mass planets inside 1 AU
• A Revised Exoplanet Yield from the Transiting Exoplanet Survey Satellite (TESS)
• Atmospheric Escape and the Evolution of Close-in Exoplanets
• Characterization of exoplanets from their formation II: The planetary mass-radius relationship
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• Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months)
• About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of their Intrinsic Architecture
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• A Plateau in the Planet Population Below Twice the Size of Earth
• The Exoplanet Population Observation Simulator. I - The Inner Edges of Planetary Systems
• Architecture of Planetary Systems Based on Kepler Data: Number of Planets and Coplanarity
• Planetary Candidates Observed by Kepler. VII. The First Fully Uniform Catalog Based on The Entire 48 Month Dataset (Q1-Q17 DR24)
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• Planetary Candidates Observed by Kepler IV: Planet Sample From Q1-Q8 (22 Months)
• Giant planets orbiting metal-rich stars show signatures of planet-planet interactions
• Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference
• Revealing A Universal Planet-Metallicity Correlation For Planets of Different Sizes Around Solar-Type Stars
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• The New Generation Planetary Population Synthesis (NGPPS). I. Bern global model of planet formation and evolution, model tests, and emerging planetary systems
• Emerging Trends in a Period-Radius Distribution of Close-in Planets
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• No universal minimum-mass extrasolar nebula: Evidence against in-situ accretion of systems of hot super-Earths
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