标题： 统一处理开普勒任务中的行星形成与演化 I：方法学 显示英文标题

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

摘要： 我们展示了开普勒系外行星的出现率，针对位于$0.5-16$R$_\oplus$和$1-400$天之间的行星。 为了测量出现率，我们通过核密度估计器使用非参数方法，并利用自助法随机抽样进行不确定性估计。 我们使用了开普勒 DR25 目录中完整的表现力和可靠性测量特征，包括探测效率、审查完整性、天文学和虚假警报可靠性。 我们还纳入了来自盖亚 DR2 中更准确且一致的恒星半径。 为了观察这些最终的开普勒特性的影响，我们回顾了文献中的基准系外行星出现率测量值。 我们将我们的测量结果与之前的研究进行比较，以验证我们的方法，并观察这些基准值对更新后的恒星和行星属性的依赖性。 对于 FGK 型恒星，在$0.5-16$R$_\oplus$和$1-400$天之间，我们发现每颗恒星的行星出现率为$1.52\pm0.08$颗。 我们研究了作为半径、轨道周期和恒星类型函数的出现率依赖关系，并与之前的研究进行了对比，结果高度一致。 我们测量了半径谷的最小值为 FGK 型恒星的$1.78^{+0.14}_{-0.16}$R$_\oplus$，并发现其对于更冷的恒星会移动到较小的半径。我们还提供了在$3-4$R$_\oplus$处发生峭壁斜率的新测量值，并发现该峭壁在长轨道周期时变得不那么陡峭。我们的方法将使我们能够在未来限制行星形成和演化的理论模型。 显示英文摘要

摘要： 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.