### Abstract

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.

Original language | English (US) |
---|---|

Article number | 64 |

Journal | Astrophysical Journal |

Volume | 795 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2014 |

### Fingerprint

### Keywords

- catalogs
- methods: data analysis
- methods: statistical
- planetary systems
- stars: statistics Online-only material: color figures, supplemental data

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*795*(1), [64]. https://doi.org/10.1088/0004-637X/795/1/64

**Exoplanet population inference and the abundance of earth analogs from noisy, incomplete catalogs.** / Foreman-Mackey, Daniel; Hogg, David W.; Morton, Timothy D.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 795, no. 1, 64. https://doi.org/10.1088/0004-637X/795/1/64

}

TY - JOUR

T1 - Exoplanet population inference and the abundance of earth analogs from noisy, incomplete catalogs

AU - Foreman-Mackey, Daniel

AU - Hogg, David W.

AU - Morton, Timothy D.

PY - 2014/11/1

Y1 - 2014/11/1

N2 - 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.

AB - 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.

KW - catalogs

KW - methods: data analysis

KW - methods: statistical

KW - planetary systems

KW - stars: statistics Online-only material: color figures, supplemental data

UR - http://www.scopus.com/inward/record.url?scp=84908032434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908032434&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/795/1/64

DO - 10.1088/0004-637X/795/1/64

M3 - Article

AN - SCOPUS:84908032434

VL - 795

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 64

ER -