A Bayesian Hierarchical Framework for Inferring the Planetary Obliquity Distribution

This decade has seen the first measurements of extrasolar planetary obliquities, characterizing how an exoplanet's spin axis is oriented relative to its orbital axis. These measurements are enabled by combining projected rotational velocities, planetary rotation periods, and astrometric orbits for directly-imaged super-Jupiters. To test whether these super-Jupiters form more like scaled-up planets or scaled-down stars, we develop a Bayesian hierarchical framework to infer their population-level obliquity distribution. Using a single-parameter Fisher distribution, we compare two models: a planet-like formation scenario (κ = 5) predicting moderate alignment, versus a brown dwarf-like formation scenario (κ = 0) predicting isotropic obliquities. Based on a sample of four young super-Jupiter systems, we find early evidence favoring the isotropic case with a Bayes factor of 15, consistent with turbulent fragmentation.