A Hierarchical Bayesian Framework for Inferring the Stellar Obliquity Distribution

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