EXOPLANET POPULATION INFERENCE AND THE ABUNDANCE OF EARTH ANALOGS FROM NOISY, INCOMPLETE CATALOGS

By Daniel Foreman-Mackey, David W. Hogg, Timothy Morton. 2014

194 citations recorded by the source corpus.

No true extrasolar Earth analog is known. Hundreds of planets have been found around Sun-like stars that are either Earth-sized but on shorter periods, or else on year-long orbits but somewhat larger. Under strong assumptions, exoplanet catalogs have been used to make an extrapolated estimate of the rate at which Sun-like stars host Earth analogs. These studies are complicated by the fact that every catalog is censored by non-trivial selection effects and detection efficiencies, and every property (period, radius, etc.) is measured noisily. Here we present a general hierarchical probabilistic framework for making justified inferences about the population of exoplanets, taking into account survey completeness and, for the first time, observational uncertainties. We are able to make fewer assumptions about the distribution than previous studies; we only require that the occurrence rate density be a smooth function of period and radius (employing a Gaussian process). By applying our method to synthetic catalogs, we demonstrate that it produces more accurate estimates of the whole population than standard procedures based on weighting by inverse detection efficiency. We apply the method to an existing catalog of small planet candidates around G dwarf stars. We confirm a previous result that the radius distribution changes slope near Earth's radius. We find that the rate density of Earth analogs is about 0.02 (per star per natural logarithmic bin in period and radius) with large uncertainty. This number is much smaller than previous estimates made with the same data but stronger assumptions.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

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Citations in the corpus

A SYSTEMATIC SEARCH FOR TRANSITING PLANETS IN THE K2 DATA (2015, background): “They will also deliver input data for next-generation population inferences (Foreman-Mackey et al. 2014), especially for the population of planets around cool stars (for example, Dressing & Charbonneau 2015).”
Habitable Moist Atmospheres on Terrestrial Planets near the Inner Edge of the Habitable Zone around M Dwarfs (2017, background): “…(HZ) by both the Kepler mission and ground-based surveys (Anglada-Escudé et al. 2016; Kane et al. 2016; Gillon et al. 2017) have shown that potentially habitable planets are common in our Galaxy (Petigura et al. 2013; Foreman-Mackey et al. 2014; Dressing & Charbonneau 2015; Silburt et al. 2015).”
THE OCCURRENCE OF POTENTIALLY HABITABLE PLANETS ORBITING M DWARFS ESTIMATED FROM THE FULL KEPLER DATASET AND AN EMPIRICAL MEASUREMENT OF THE DETECTION SENSITIVITY (2015, methodology): “As a result, Foreman-Mackey et al. (2014) found an occurrence rate of potentially habitable Earth-size planets 3.6 times lower than the Petigura et al. (2013a) estimate.”
PROBABILISTIC FORECASTING OF THE MASSES AND RADII OF OTHER WORLDS (2016, methodology): “Indeed, by our definition three of the eight solar system planets are Neptunian worlds, which are the most common type of planet around other Sun-like stars (Foreman-Mackey et al. 2014).”
FALSE POSITIVE PROBABILITIES FOR ALL KEPLER OBJECTS OF INTEREST: 1284 NEWLY VALIDATED PLANETS AND 428 LIKELY FALSE POSITIVES (2016, background): “And perhaps most notably, it has enabled for the first time estimates of the occurrence rates of small planets (&1 R⊕) out to orbits of about one year (e.g. Petigura et al. 2013; Foreman-Mackey et al. 2014; Burke et al. 2015).”
Inferring probabilistic stellar rotation periods using Gaussian processes (2017, methodology): “celerite, a new method for rapid computation of the ‘solve’ and determinant calculations of covariance matrices necessary for GP inference has recently been developed (Foreman-Mackey et al. 2017). celerite scales with the number of data points, O(N) rather than the N log(N)2 scaling of the HODLR alg”
Extracting distribution parameters from multiple uncertain observations with selection biases (2018, background): “…the observed population will have a Malmquist bias (Malmquist 1922, 1925) whereby the loudest or brightest sources are most likely to be detected, and it is necessary to correct for this bias in order to extract the true source population (e.g., Foreman-Mackey et al. 2014; Farr et al. 2014).”
Calibrating gyrochronology using Kepler asteroseismic targets (2015, methodology): “(8) We used hierarchical inference to account for observational uncertainties, following the method of Hogg et al. (2010), also c© 0000 RAS, MNRAS 000, 000–000 used by Foreman-Mackey et al. (2014), Rogers (2014), Morton & Winn (2014) and Demory (2014).”
PLANETARY CANDIDATES OBSERVED BY KEPLER. VI. PLANET SAMPLE FROM Q1–Q16 (47 MONTHS) (2015, background): “Independent groups have constructed their own catalogs (Petigura et al. 2013; Schmitt et al. 2014; Sanchis-Ojeda et al. 2014), and derive their own occurrence rates (Foreman-Mackey et al. 2014).”
Binary Companions of Evolved Stars in APOGEE DR14: Search Method and Catalog of ∼5000 Companions (2018, methodology): “This trick has been used in other hierarchical inferences as a way to marginalize over the per-object parameters to infer population-level parameters (Hogg et al. 2010; Foreman-Mackey et al. 2014); we describe how to compute the marginal likelihood in detail in the Appendix.”
Identifying Exoplanets with Deep Learning: A Five-planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90 (2017, background): “As the Kepler mission matured and the list of planet candidates grew, the focus of the community shifted towards population-level studies (Fressin et al. 2013; Petigura et al. 2013a,b; Foreman-Mackey et al. 2014; Dressing & Charbonneau 2013, 2015; Burke et al. 2015; Mulders et al. 2015a,b).”
TERRESTRIAL PLANET OCCURRENCE RATES FOR THE KEPLER GK DWARF SAMPLE (2015, methodology): “…in Section 5.3.2 of Loredo (1992), and the Poisson likelihood is commonly used in order to interpret astronomical detections with a varying survey sensitivity (Tabachnik & Tremaine 2002; Allen 2007; Cumming et al. 2008; Kraus & Hillenbrand 2012; Foreman-Mackey et al. 2014; Nielsen et al. 2014).”
The Exoplanet Population Observation Simulator. I. The Inner Edges of Planetary Systems (2018, background): “…rates of Earth-sized planets in the habitable zone, η⊕, can be estimated by considering smaller M and K dwarf stars (Dressing & Charbonneau 2013, 2015) or by extrapolating from shorter orbital periods and/or larger planet radii (Petigura et al. 2013a; Foreman-Mackey et al. 2014; Burke et al. 2015).”