A Unified Treatment of Kepler Occurrence to Trace Planet Evolution I: Methodology

TL;DR

This paper introduces a non-parametric method to measure Kepler exoplanet occurrence rates, incorporating comprehensive data corrections and stellar properties, to better understand planet distribution and evolution.

Contribution

It presents a novel, robust methodology for calculating exoplanet occurrence rates using kernel density estimation and updated stellar data, improving accuracy over previous studies.

Findings

Occurrence rate of 1.52 planets per star for FGK stars.

Minimum radius valley at 1.78 R_⊕ for FGK stars.

The occurrence cliff slope varies with orbital period.

Abstract

We present Kepler exoplanet occurrence rates for planets between $0.5-16$ R$_\oplus$ and between $1-400$ days. To measure occurrence, we use a non-parametric method via a kernel density estimator and use bootstrap random sampling for uncertainty estimation. We use a full characterization of completeness and reliability measurements from the Kepler DR25 catalog, including detection efficiency, vetting completeness, astrophysical- and false alarm reliability. We also include more accurate and homogeneous stellar radii from Gaia DR2. In order to see the impact of these final Kepler properties, we revisit benchmark exoplanet occurrence rate measurements from the literature. We compare our measurements with previous studies to both validate our method and observe the dependence of these benchmarks on updated stellar and planet properties. For FGK stars, between $0.5-16$ R$_\oplus$ and between $1-400$ days, we find an occurrence of $1.52\pm0.08$ planets per star. We investigate the dependence of occurrence as a function of radius, orbital period, and stellar type and compare with previous studies with excellent agreement. We measure the minimum of the radius valley to be $1.78^{+0.14}_{-0.16}$ R$_\oplus$ for FGK stars and find it to move to smaller radii for cooler stars. We also present new measurements of the slope of the occurrence cliff at $3-4$ R$_\oplus$, and find that the cliff becomes less steep at long orbital period. Our methodology will enable us to constrain theoretical models of planet formation and evolution in the future.