Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs

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 (Petigura et al. 2013). 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.

• The paper introduces a hierarchical probabilistic framework that addresses selection biases and noise in exoplanet catalogs.
• It employs non-parametric Gaussian processes to model occurrence rates without relying on rigid power-law assumptions.
• Application to G dwarf star data revises Earth analog occurrence rates to ~0.02 per star per natural logarithmic bin, challenging earlier estimates.

Exoplanet Population Inference and the Abundance of Earth Analogs

The study titled "Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs" addresses the complexities involved in deriving the prevalence of extrasolar Earth analogs using exoplanet catalogs. Given that exoplanet catalogs are constrained by substantial selection biases and noise in the measurement of characteristics such as orbital period and planetary radius, the authors propose a hierarchical probabilistic framework to make more robust population inferences. This approach considers both survey completion and observational uncertainties, which have often been overlooked in previous analyses.

A key component of this research is the relaxation of assumptions concerning the distribution of occurrence rates. Rather than imposing rigid parametric forms, such as power laws, the study utilizes a non-parametric method employing Gaussian processes to model the occurrence rate density as a smooth function of period and radius. This flexibility allows the framework to potentially capture complexities in the planet population that may be obscured or mischaracterized by more rigid modeling approaches.

By applying this method to both synthetic and real datasets, the authors demonstrate improved accuracy over conventional methods which often rely on inverse detection efficiency for weighting catalog entries. The synthetic tests confirm that the hierarchical probabilistic approach achieves more accurate population estimates, especially in scenarios hampered by low detection efficiency.

Most notably, when the framework is applied to the real-world dataset of small planets orbiting G dwarf stars (Petigura et al. 2013), the results challenge previously published estimates of the occurrence rate of Earth analogs. The authors find that Earth's analog occurrence rate is approximately 0.02 per star per natural logarithmic bin in period and radius, significantly lower than previous estimates from the same dataset, which employed stronger assumptions on occurrence rate uniformity. This rate is derived under the premise that the occurrence rate density is a smooth function, capturing a more conservative uncertainty range than prior studies.

The implications of this work are significant. The methodological advancement in statistical inference for exoplanet populations offers a pathway to more reliably estimate the prevalence of Earth-like planets, influencing fields such as astrobiology and planetary formation theories. Furthermore, the study's conservative extrapolation methods and considerations for observational uncertainties present a more realistic expectation concerning the detection of Earth analogs in existing and future surveys.

Looking forward, the hierarchical probabilistic framework outlined in this paper can be further expanded to incorporate additional complexities, such as systematic biases in stellar parameter estimation or the incorporation of multi-planetary systems. The methodologies support adaptability for future developments in detection techniques and larger, more comprehensive exoplanet catalogs.

In conclusion, this research sets a rigorous standard for the analysis of exoplanet populations under uncertainty, and the results provide important constraints on the population distribution of Earth-like exoplanets. Such advancements are crucial for delineating the planetary abundance and understanding our place within the galaxy.