The Exoplanet Census: A General Method, Applied to Kepler (1105.1782v1)

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 \alpha = -1.2 \pm 0.2 steepens to \alpha = -2.0 \pm 0.2 for the larger planet sample. For shorter periods, the opposite is seen: smaller planets follow a steep powerlaw, \alpha = -1.9 \pm 0.2 that is much shallower, \alpha = -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.

• The paper presents a general maximum likelihood statistical method for analyzing exoplanet survey data, particularly focusing on integrating multi-planet systems.
• Applying the method to Kepler data reveals a high exoplanet occurrence rate and identifies distribution trends, including a deficit of intermediate-sized planets at short orbital periods.
• The findings have significant implications for understanding planet formation and evolution theories like core accretion and migration, and inform future exoplanet missions.

Overview of "The Exoplanet Census: A General Method, Applied to Kepler" by Andrew N. Youdin

The paper by Andrew N. Youdin presents a sophisticated statistical framework for analyzing exoplanetary data, primarily applied to data from the Kepler Space Telescope. Given the increased interest in the composition of planetary systems and their distribution, Youdin's work provides a methodology for characterizing the distribution function of planets observed through transit surveys.

Methodology

Youdin introduces a maximum likelihood method that involves the simultaneous fitting of planetary distribution functions (PLDF) to survey data. The approach can accommodate complex planetary systems with multiple planets per star and integrates several planetary and stellar parameters, making it flexible and comprehensive. The methodology is particularly notable for its ability to include multi-planet systems rather than treating them merely as single detections, which has been a limitation in past statistical analyses. This method fits into the ongoing advancement of understanding planetary distributions, following techniques like those of Tabachnik and Tremaine (2002).

Application to Kepler Data

The paper applies this methodology to Kepler's expansive dataset, focusing on a population of planets revolving around solar-type stars, as characterized by their host star properties and adjusted for survey detection efficiencies. Specifically, Youdin examines planets with radii down to 0.5 Earth radii and orbital periods up to 50 days. The paper uses detection efficiency models derived from Howard et al. (2011), highlighting the continuity between observational and theoretical models for these efficiencies.

Key Results and Trends

• Planet Occurrence: Youdin's analysis suggests a high occurrence rate, estimating between 0.7 and 1.4 planets per star with radii larger than 0.5 Earth radii and periods below 50 days. This finding implies that planetary systems often contain multiple planets, influencing theories on planet formation and migration.
• Distribution Trends: The paper identifies significant differences in the distribution of planets based on their size and orbital periods. Notably, a deficit of intermediate-sized planets at short orbital periods may indicate the evaporation and sublimation of certain planet types, providing evidence that supports theories of core accretion and migration.
• Powerlaw Fit Analysis: A joint powerlaw fit in planetary radius and orbital period across several subdivisions of the data reveals variations in distribution laws, suggesting complex formation histories and environmental influences on exoplanet populations.

Implications

The research has broad implications for the theoretical understanding of planetary formation and evolution. Confirming a deficit of certain planet types at specific periods can refine models of planetary migration and atmospheric retention. Additionally, these findings bolster the core accretion hypothesis, suggesting a need for further investigation into planetary system development scenarios.

Future Directions

Speculation on the future of these findings indicates that continued observations and refinements in survey precision could lead to an even higher number of detected planets per star. These developments could significantly enhance models predicting Earth-like habitats in the galaxy. The approach illustrated by Youdin is poised to be pivotal for ongoing and future missions seeking to expand on Kepler’s remarkable legacy in exoplanet research.

Conclusion

Andrew Youdin's paper provides a comprehensive and statistically robust approach to analyzing exoplanet census data. The insights garnered from the Kepler mission, underpinned by this analysis, continue to transform our understanding of planets beyond the solar system, offering profound implications for the structure and frequency of planetary systems in our galaxy.