This paper aims to derive a map of relative planet occurrence rates that can provide constraints on the overall distribution of terrestrial planets around FGK stars. Based on the planet candidates in the Kepler DR25 data release, I first generate a continuous density map of planet distribution using a Gaussian kernel model and correct the geometric factor that the discovery space of a transit event decreases along with the increase of planetary orbital distance. Then, I fit two exponential decay functions of detection efficiency along with the increase of planetary orbital distance and the decrease of planetary radius. Finally, the density map of planet distribution is compensated for the fitted exponential decay functions of detection efficiency to obtain a relative occurrence rate distribution of terrestrial planets. The result shows two regions with planet abundance: one corresponds to planets with radii between 0.5 and 1.5 R⊕ within 0.2 au, and the other corresponds to planets with radii between 1.5 and 3 R⊕ beyond 0.5 au. It also confirms the features that may be caused by atmospheric evaporation: there is a vacancy of planets of sizes between 2.0 and 4.0 R⊕ inside of ∼0.5 au, and a valley with relatively low occurrence rates between 0.2 and 0.5 au for planets with radii between 1.5 and 3.0 R⊕.

中文翻译：

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围绕FGK恒星运行的类地行星的相对发生率

本文旨在推导出一张相对行星出现率的地图，该地图可以限制 FGK 恒星周围类地行星的整体分布。基于开普勒DR25数据发布中的行星候选，我首先使用高斯核模型生成行星分布的连续密度图，并修正了凌日事件的发现空间随着行星轨道距离的增加而减小的几何因素。然后，我拟合了探测效率随着行星轨道距离的增加和行星半径的减小的两个指数衰减函数。最后对行星分布密度图进行探测效率拟合指数衰减函数的补偿，得到类地行星的相对出现率分布。结果显示了两个行星丰度区域：一个对应半径在 0.2 au 内 0.5 到 1.5 R⊕ 之间的行星，另一个对应半径在 1.5 到 3 R⊕ 超过 0.5 au 的行星。这也证实了大气蒸发可能引起的特征：在~0.5 au内有2.0~4.0 R⊕大小的行星空缺，半径在0.2~0.5 au范围内的行星出现率相对较低的山谷介于 1.5 和 3.0 R⊕之间。