Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference

Abstract: We characterize the occurrence rate of planets, ranging in size from 0.5-16 R$\oplus$, orbiting FGK stars with orbital periods from 0.5-500 days. Our analysis is based on results from the "DR25" catalog of planet candidates produced by NASA's Kepler mission and stellar radii from Gaia "DR2". We incorporate additional Kepler data products to accurately characterize the efficiency of planets being recognized as a "threshold crossing events" (TCE) by Kepler's Transiting Planet Search pipeline and labeled as a planet candidate by the robovetter. Using a hierarchical Bayesian model, we derive planet occurrence rates for a wide range of planet sizes and orbital periods. For planets with sizes $0.75-1.5$ R$\oplus$ and orbital periods of 237-500 days, we find a rate of planets per FGK star of $<0.27$ ($84.13$th percentile). While the true rate of such planets could be lower by a factor of $\sim~2$ (primarily due to potential contamination of planet candidates by false alarms), the upper limits on the occurrence rate of such planets are robust to $\sim~10\%$. We recommend that mission concepts aiming to characterize potentially rocky planets in or near the habitable zone of sun-like stars prepare compelling science programs that would be robust for a true rate in the range $f_{R,P} = $ $0.03-0.40$ for $0.75-1.5$ R$\oplus$ planets with orbital periods in 237-500 days, or a differential rate of $\Gamma\oplus \equiv (d^2 f)/[d(\ln P)~d(\ln R_{p})] = $ $0.06-0.76$.

• The paper introduces a hierarchical Bayesian model with Approximate Bayesian Computation to counter detection biases, yielding more accurate exoplanet occurrence rates.
• The study integrates Gaia DR2's refined stellar properties with Kepler data to improve planet radius estimates and bin assignments.
• The results offer robust occurrence rate estimates for Earth-like planets in habitable zones, informing future exoplanet exploration missions.

Occurrence Rates of Planets Orbiting FGK Stars

The paper by Hsu et al. provides a detailed investigation into the occurrence rates of planets orbiting FGK stars, analyzing data from multiple astronomical databases and implementing advanced statistical techniques. The authors leverage data from NASA's Kepler mission, eschewing prior limitations by incorporating updated stellar radii measurements from the Gaia DR2 release and applying a hierarchical Bayesian model to derive more accurate occurrence rates of exoplanets in diverse orbital and radius ranges. This study represents a significant contribution to understanding the frequency of planets, particularly Earth-like planets, in the habitable zones of stars, a key piece of the puzzle in the search for life beyond our solar system.

Methodology and Model Enhancements

Hsu et al. utilize a hierarchical Bayesian framework with Approximate Bayesian Computation (ABC) to infer occurrence rates, thus avoiding biases inherent in earlier studies that analyzed Kepler's data. The authors note that past studies exhibited biases near the detection threshold, which this approach addresses. They introduce several improvements in their modeling process, such as the consideration of stellar properties derived from Gaia DR2, which allow for more precise planet radii determination. This leads to refined allocations of planet candidates into radius bins, accommodating inherent uncertainties in measurements.

The paper details the significance of incorporating a well-characterized detection and vetting efficiency model, which combines both the probability of detection by the Kepler Transiting Planet Search pipeline and the likelihood that a candidate is labeled as a planet through robovetter analysis. Hsu et al. assert that neglecting such vetting efficiency models could lead to underestimated occurrence rates, especially for small and long-period planets.

Results and Implications

Through extensive simulations and validation tests, the study delivers occurrence rates for planets with radii spanning from 0.5 to 16 Earth radii, and orbital periods ranging from 0.5 to 500 days. The results demonstrate lower occurrence rates than some previous estimates, with substantial uncertainty in regions near the habitable zone. For Earth-sized planets with orbital periods of 237-500 days, Hsu et al. assign rates robust against uncertainties due to false alarms or biases in the detection process, yet the true occurrence rate could still vary.

The authors' findings have profound implications for future exoplanet research and mission planning aimed at characterizing potentially habitable worlds. The uncertainties highlighted within the study underscore the complexities in extrapolating occurrence rates to longer periods, suggesting that missions must be prepared for the full range of possible detection scenarios. They advise mission designers to account for potential variations in occurrence rates when planning Earth-like planet characterization missions.

Future Directions

While the study provides a comprehensive analysis with broad implications, Hsu et al. propose areas for future improvement in occurrence rate modeling. These include refining the detection model further to capture more variables such as transit duration or stellar noise characteristics that affect planet detection probabilities. They also suggest that future studies must tackle unrecognized contamination effects and account for potential false alarms rigorously to improve the reliability of occurrence rate estimates, especially for long-period small exoplanets.

In conclusion, the study by Hsu et al. delivers robust statistical modeling techniques and significant advancements in deriving occurrence rates of planets around FGK stars. These methodologies and findings support the ongoing efforts in the astronomical community to refine our understanding of planet populations in our galaxy and lay the groundwork for future explorations in the search for extraterrestrial life.