Early evidence for isotropic planetary obliquities in young super-Jupiter systems

TL;DR

The paper addresses how exoplanet obliquities encode formation histories by measuring spin-orbit geometry for four young super-Jupiters. It introduces a hierarchical Bayesian framework that uses a Fisher distribution for the obliquity distribution parameterized by $\kappa$, comparing planet-like and brown-dwarf-like formation scenarios. On real data, the posterior for $\kappa$ peaks at 0 and yields a Bayes factor $BF_{0,5}=15$ in favor of isotropic obliquities, consistent with turbulent fragmentation. The approach is robust to priors and scalable to larger samples with upcoming JWST data, offering a path to statistically diagnose planetary vs substellar formation in wide-orbit companions.

Abstract

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. This approach constrains both the spin axis and orbital inclination relative to the line of sight, allowing obliquity measurements for individual systems and offering new insights into their formation. To test whether these super-Jupiters form more like scaled-up planets or scaled-down stars, we develop a hierarchical Bayesian 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.

Figures (8)

• Figure 1: Three illustrations highlighting the relative orientation of a planet spin axis $\mathbf{\hat{n}_p}$ and orbit normal $\mathbf{\hat{n}_o}$: (a) as a cartoon, (b) in an orbit-oriented coordinate system, with the orbit normal along the $Z$-axis, and (c) in an observer-oriented coordinate system, with the observer along the $X'-$axis, and $Y'-Z'$ as the sky plane. Panels (b) and (c) are related by a $90^\circ - i_o$ rotation along the $Y = Y'-$axis. These diagrams were inspired by Dong+DFM2023, and adapted from Poon+2024a.
• Figure 2: Graphical representation of hierarchical model using quantities depicted in \ref{['fig:coordinate_system']}. The arrows represent the direction of data generation from $\kappa$, the population-level obliquity distribution parameter, to $\psi_i$, the obliquity of planet $i$, to the planet's observed variables $\hat{i}_p$ and $\hat{i}_o$.
• Figure 3: We test whether our hierarchical model can distinguish between planet-like and brown dwarf-like formation using simulated obliquity measurements. Top: Planet-like formation assumes a Fisher distribution with $\kappa=5$ (top-left), while brown dwarf-like formation is modelled as an isotropic distribution with $\kappa=0$ (top-right). Vertical lines mark the obliquities of Earth, Mars, Saturn, and Neptune, which distinctly cluster together. Bottom: For 100 draws of 4 obliquities from the above distribution, we simulate noisy observations for the spin axis and orbital inclinations and infer posteriors on $\kappa$. The median posteriors show qualitatively distinct structure, demonstrating that even 4 measurements can inform formation pathways.
• Figure 4: We test whether a Bayes factor can correctly identify the underlying formation scenario. For each of 100,000 draws, we simulate observations for 4 or 10 systems. For each draw, we compute the Bayes factor $BF_{5,0}$ if the correct scenario is $\kappa=5$, or $BF_{0,5}$ if the correct scenario is $\kappa=0$. A ratio greater than one favors the correct scenario. Top: With 4 systems and $15^\circ$ uncertainties, the correct scenario is recovered for $93\%$ of the draws for $\kappa=5$ and $77\%$ of the draws for $\kappa=0$. Bottom: Using 10 systems and $10^\circ$ uncertainties improves the accuracy to $97\%$ and $93\%$, respectively.
• Figure 5: Planet spin axis inclinations ($i_p$, orange) compared with orbital inclinations ($i_o$, gold). These line-of-sight inclinations are relative to an observer along the $X'-$axis (left side), while the vertical axis represents the sky plane ($Y'-Z'$), following \ref{['fig:coordinate_system']}. $i_p$ is mirrored about the sky plane due to an observational degeneracy. These diagrams were inspired by Bowler+2023.