| Summary: | Misalignments between planetary orbits and the equatorial planes of their host stars are clues about the formation and evolution of planetary systems. Earlier work found evidence for a peak near 90° in the distribution of stellar obliquities, based on frequentist tests. We performed hierarchical Bayesian inference on a sample of 174 planets for which either the full three-dimensional stellar obliquity has been measured (72 planets) or for which only the sky-projected stellar obliquity has been measured (102 planets). We investigated whether the obliquities are best described by a Rayleigh distribution or by a mixture of a Rayleigh distribution representing well-aligned systems and a different distribution representing misaligned systems. The mixture models are strongly favored over the single-component distribution. For the misaligned component, we tried an isotropic distribution and a distribution peaked at 90° and found the evidence to be essentially the same for both models. Thus, our Bayesian inference engine did not find strong evidence favoring a “perpendicular peak,” unlike the frequentist tests. We also investigated selection biases that affect the inferred obliquity distribution, such as the bias of the gravity-darkening method against obliquities near 0° or 180°. Further progress in characterizing the obliquity distribution will probably require the construction of a more homogeneous and complete sample of measurements.
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