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Transit-Depth Metallicity Correlation: A Bayesian Approach

A negative correlation was previously reported between the transit depth of Kepler's Q1-Q12 gas giant candidates and the stellar metallicity. In this present work, we revisit this correlation to better understand the role of the stellar metallicity in the formation of giant planets, in particular, to investigate the effect of the metallicity on the transit depth. We selected the 82 confirmed giant planets from the cumulative catalog. This is the first large and homogeneous sample of confirmed giant planets used to study this correlation. Such samples are suitable to perform robust statistical analysis. We present the first hierarchical Bayesian linear regression model to revise this correlation. The advantages of using a Bayesian framework are to incorporate measurement errors in the model and to quantify both the intrinsic scatter and the uncertainties on the parameters of the model. Our statistical analysis reveals no correlation between the transit depth of confirmed giant planets and the stellar metallicity.