A Hierarchical Bayesian Framework for Inferring the Stellar Obliquity Distribution

Stellar obliquity, the angle between a planet's orbital axis and its host star's spin axis, traces the formation and evolution of a planetary system. In transiting exoplanet observations, only the sky-projected stellar obliquity can be measured, but this can be de-projected using an estimate of the stellar obliquity. In this paper, we introduce a flexible, hierarchical Bayesian framework that can be used to infer the stellar obliquity distribution solely from sky-projected stellar obliquities, including stellar inclination measurements when available. We demonstrate that while a constraint on the stellar inclination is crucial for measuring the obliquity of an individual system, it is not required for robust determination of the population-level stellar obliquity distribution. In practice, the constraints on the stellar obliquity distribution are mainly driven by the sky-projected stellar obliquities. When applying the framework to all systems with measured sky-projected stellar obliquity, which are mostly Hot Jupiter systems, we find that the inferred population-level obliquity distribution is unimodal and peaked at zero degrees. The misaligned systems have nearly isotropic stellar obliquities with no strong clustering near 90 degrees. The diverse range of stellar obliquities prefers dynamic mechanisms, such as planet-planet scattering after a convergent disk migration, which could produce both prograde and retrograde orbits of close-in planets with no strong inclination concentrations other than 0 degrees.