Ponderings on the Possible Preponderance of Perpendicular Planets

Abstract

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.

Damping Obliquities of Hot Jupiter Hosts by Resonance Locking

“…Figure 10 compares our modeled projected obliquities λ with those observed (top panel; observations from Rice et al 2022a). For completeness, we also show our modeled obliquities ψ against the few deprojected obliquities that are available (bottom panel; data from Albrecht et al 2022;Siegel et al 2023). Broadly speaking, our model reproduces the dichotomy between hot oblique stars above the Kraft break and cool aligned stars below.…”

“…Figure 1. Projected stellar obliquities λ (as distinct from deprojected or true 3D obliquities ψ) vs. host star effective temperature T eff of hot Jupiter systems (selecting for planet masses M p 0.3 M J and semimajor axes a 10 R å , where R å is the host star radius; data from Albrecht et al 2022;Rice et al 2022aRice et al , 2022bEspinoza-Retamal et al 2023;Sedaghati et al 2023;Siegel et al 2023;Hu et al 2024). Obliquities are larger for hot high-mass stars (stellar effective temperature T eff > 6100 K; red points) than for cool low-mass stars (blue points).…”

“…Host stellar masses M å are sampled uniformly from the set {0.6, 0.8, 1.0, 1.2, 1.4, 1.6} M e . Around each star, we consider a planet of mass M p = 1 M J , initial semimajor axis a 0 = 8 R å0 , eccentricity e 0 = 0, and obliquity ψ 0 drawn randomly from a uniform distribution in y cos 0 between −1 and 1 (for observational support of the latter distribution, see Dong & Foreman-Mackey 2023; Siegel et al 2023). Our 16)) and accumulated frequency change (middle panel, Equation (18)) vs. mainsequence age for stars of different masses as indicated.…”

“…1. Introduction Winn et al (2010) discovered that hot Jupiters orbiting cool stars have orbit normals that better align with stellar spin axes than hot Jupiters orbiting hot stars (see also, e.g., Schlaufman 2010;Albrecht et al 2012Albrecht et al , 2021Winn et al 2017;Muñoz & Perets 2018;Hamer & Schlaufman 2022;Rice et al 2022aRice et al , 2022bSiegel et al 2023). Figure 1 displays this correlation between stellar obliquity λ and stellar effective temperature T eff .…”

Hot Jupiters Have Giant Companions: Evidence for Coplanar High-eccentricity Migration

“…The implications of this result remain unclear, as 28% ± 9% of the obliquities appear to be isotropically distributed. It may be that an existing multimodal distribution is obscured by our limited sample and/or the underlying biases of the sample (Siegel et al 2023). Regardless, the clear prominence of aligned orientations-72% ± 9% with stellar obliquities less than 40°-provides evidence that high initial mutual inclination mechanisms, like Kozai-Lidov oscillations, are a nondominant formation pathway.…”