Statistical studies of exoplanets and the properties of their host stars have been critical to informing models of planet formation. Numerous trends have arisen in particular from the rich \textit{Kepler} dataset, including that exoplanets are more likely to be found around stars with a high metallicity and the presence of a "gap" in the distribution of planetary radii at 1.9\,$R_\oplus$. Here we present a new analysis on the \textit{Kepler} field, using the APOGEE spectroscopic survey to build a metallicity calibration based on \textit{Gaia}, 2MASS and Stromgren photometry. This calibration, along with masses and radii derived from a Bayesian isochrone fitting algorithm, is used to test a number of these trends with unbiased, photometrically derived parameters, albeit with a smaller sample size in comparison to recent studies. We confirm that planets are indeed more frequently found around higher metallicity stars: planetary frequencies are $0.88\pm0.12$~percent for [Fe/H]\,<\,0 and $1.37\pm0.16$~percent for [Fe/H]\,$\geq$\,0. We also recover the planet radius gap, along with a slight positive correlation with stellar mass. We conclude that this method shows promise to derive robust statistic of exoplanets. We also remark that spectrophotometry from \textit{Gaia} DR3 will have an effective resolution similar to narrow band filters and allow to overcome the small sample size inherent in this study.

中文翻译：

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使用光度选择的开普勒样本确认已知的行星趋势

对系外行星及其主星特性的统计研究对于为行星形成模型提供信息至关重要。许多趋势尤其来自丰富的 \textit{Kepler} 数据集，包括系外行星更有可能在金属丰度高的恒星周围被发现，并且行星半径分布存在“间隙”在 1.9\,$ R_\oplus$。在这里，我们提出了对 \textit{Kepler} 场的新分析，使用 APOGEE 光谱调查建立基于 \textit{Gaia}、2MASS 和 Stromgren 光度计的金属度校准。这种校准以及从贝叶斯等时线拟合算法得出的质量和半径，用于通过无偏、光度学派生的参数来测试许多这些趋势，尽管与最近的研究相比，样本量较小。我们确认行星确实更频繁地在金属丰度较高的恒星周围发现：[Fe/H]\,<\,0 的行星频率为 $0.88\pm0.12$~%，[Fe/ H]\,$\geq$\,0。我们还恢复了行星半径间隙，以及与恒星质量的轻微正相关。我们得出的结论是，这种方法有望推导出系外行星的稳健统计数据。我们还注意到 \textit{Gaia} DR3 的分光光度法将具有类似于窄带滤波器的有效分辨率，并允许克服本研究中固有的小样本量。以及与恒星质量的轻微正相关。我们得出的结论是，这种方法有望推导出系外行星的稳健统计数据。我们还注意到 \textit{Gaia} DR3 的分光光度法将具有类似于窄带滤波器的有效分辨率，并允许克服本研究中固有的小样本量。以及与恒星质量的轻微正相关。我们得出的结论是，这种方法有望推导出系外行星的稳健统计数据。我们还注意到 \textit{Gaia} DR3 的分光光度法将具有类似于窄带滤波器的有效分辨率，并允许克服本研究中固有的小样本量。