Terrestrial Planet Occurrence Rates for the Kepler GK Dwarf Sample (1506.04175v1)

Abstract: We measure planet occurrence rates using the planet candidates discovered by the Q1-Q16 Kepler pipeline search. This study examines planet occurrence rates for the Kepler GK dwarf target sample for planet radii, 0.75<Rp<2.5 Rearth, and orbital periods, 50<Porb<300 days, with an emphasis on a thorough exploration and identification of the most important sources of systematic uncertainties. Integrating over this parameter space, we measure an occurrence rate of F=0.77 planets per star, with an allowed range of 0.3<F<1.9. The allowed range takes into account both statistical and systematic uncertainties, and values of F beyond the allowed range are significantly in disagreement with our analysis. We generally find higher planet occurrence rates and a steeper increase in planet occurrence rates towards small planets than previous studies of the Kepler GK dwarf sample. Through extrapolation, we find that the one year orbital period terrestrial planet occurrence rate, zeta_1=0.1, with an allowed range of 0.01<zeta_1<2, where zeta_1 is defined as the number of planets per star within 20% of the Rp and Porb of Earth. For G dwarf hosts, the zeta_1 parameter space is a subset of the larger eta_earth parameter space, thus zeta_1 places a lower limit on eta_earth for G dwarf hosts. From our analysis, we identify the leading sources of systematics impacting Kepler occurrence rate determinations as: reliability of the planet candidate sample, planet radii, pipeline completeness, and stellar parameters.

• The paper employs a Bayesian framework with Monte Carlo simulations to determine an overall occurrence rate of 0.77 terrestrial planets per GK dwarf star.
• It rigorously assesses systematic uncertainties from stellar parameters, pipeline completeness, and candidate reliability to refine occurrence rate estimates.
• The results suggest an increasing trend for smaller terrestrial planets, emphasizing the need for improved models in future exoplanet surveys.

An Analysis of Terrestrial Planet Occurrence Rates around GK Dwarfs in the Kepler Dataset

The paper "Terrestrial Planet Occurrence Rates for the Kepler GK Dwarf Sample" presents an analysis of data from the Kepler mission focusing on the occurrence rates of terrestrial planets orbiting within certain parameters around GK dwarf stars. The work aims to refine our understanding of how common terrestrial planets are in the Milky Way, especially those in orbits similar to Earth's.

Methodology

The authors adopt a comprehensive approach, employing a parametric model for the planet distribution function (PLDF) analyzed through a Bayesian framework. They assess planet occurrence rates using Kepler's pipeline data from Q1-Q16, focusing on planets with radii between 0.75 and 2.5 Earth radii (R⊕) and orbital periods between 50 and 300 days. This paper emphasizes assessing systematic uncertainties, such as the reliability of the planet candidate sample, completeness of the pipeline, planet radius estimates, and stellar parameters.

Monte Carlo methods are employed to numerically evaluate the posterior distribution of PLDF parameters, allowing the authors to account for both statistical and systematic uncertainties. The analysis relies on the Kepler dataset, which includes substantial detail about the completeness of the data and applies detailed filtering criteria to mitigate potential biases.

Findings

The analysis measures an overall occurrence rate $F_{0}=0.77$ planets per star within the specified parameter space, indicating a higher than previously reported frequency of terrestrial planet candidates among GK dwarfs. The paper identifies that systematic uncertainties are significant and emphasizes that they often outweigh statistical uncertainties. The model indicates an increasing occurrence rate of smaller terrestrial planets, although with considerable uncertainties suggesting caution in making strong conclusions about planets smaller than 1.5R⊕.

The results show considerable variations in occurrence rates as a function of specific assumptions about data completeness, systematic biases, and stellar parameters. Notably, these estimates are sensitive to assumptions about the planetary completeness function and potential false positives in candidate evaluation. The paper reports a power-law dependent PLDF with significant implications for the distribution of terrestrial planets.

Implications and Future Work

This research provides the astrophysical community with a refined lens focused on the prevalence of Earth-like planets within habitable zones of GK dwarfs. The effective application of probabilistic models highlights both the breadth of existing uncertainty and the inherent limitations in current planet detection methodologies.

Subsequent research will need to address the significant systematic sources of uncertainty identified here. The current paper recommends refined models for stellar parameters, heightened scrutiny of candidate validation procedures, and improved data analysis pipelines to reduce systematic errors further. The paper’s identification of key systematic influencers provides a roadmap for reducing uncertainties in subsequent research phases, which should enhance the precision of terrestrial planet occurrence estimates.

Investigating further the implications of these findings, particularly regarding the optimism in finding Earth analogs, could influence the design of future exoplanet missions. Such missions may focus on more robust verification of candidates and extend searches into different regions of parameter space, building on the frameworks and methodologies developed in this paper.