HERMES: HiERarchical Modelling for Exoplanet Science

ESA's Ariel Space Mission will characterise the atmospheres of approximately 1000 exoplanets to quantify population-level trends. We present HERMES (HiERarchical Modelling for Exoplanet Science), a multidimensional Bayesian framework that probes population-level correlations across multiple axes of diversity. The specific use case we present is the multidimensional relation between stellar metallicity, planetary mass, and atmospheric metallicity. Starting from the Ariel Mission Candidate Sample (Edwards & Tinetti 2022), we select confirmed planets with available masses and stellar metallicity, inject plausible multidimensional trends and demonstrate successful parameter recovery. Simulated surveys are generated with a variety of leverage and sample size, in the presence of intrinsic astrophysical scatter and measurement noise. By fitting independent Bayesian models to each survey, we confirm that survey leverage remains a reliable predictor of trend precision even in multiple dimensions and in the presence of intrinsic astrophysical scatter. For an Ariel Tier 2 transit survey of at least 400 planets, HERMES robustly recovers the correlation between stellar and planetary metallicity despite intrinsic scatter in planetary abundances as large as 1.2 dex. These results establish HERMES as a practical tool for survey design and science yield forecasting in preparation for Ariel and other surveys probing population-level trends.