A Homogeneous Catalog of Rossiter-McLaughlin Systems: Distinct $e$-$\lambda$ Trends in Three Gas-Giant Mass Regimes

Problem
Stellar obliquity ($\lambda$) and orbital eccentricity ($e$) are critical observables for tracing the dynamical histories of close-in giant planets. Historically, distinct formation and migration pathways (e.g., disk migration vs. high-eccentricity migration) were expected to produce specific correlations between these parameters. However, the current observational picture is obscured by heterogeneous analyses. Previous studies often suffer from inconsistent modeling strategies, including the Lucy-Sweeney bias in eccentricity fitting, the assumption of circular orbits where data is insufficient, and varying forward models for the Rossiter-McLaughlin (RM) effect. These inconsistencies introduce systematic biases in $\lambda$ and $v \sin i_*$, particularly when $v \sin i_*$ is poorly constrained or when RM signals are modeled in isolation rather than jointly with other data. Consequently, the true population-level trends in the $e-\lambda$ plane remain debated, with some studies suggesting a correlation between high eccentricity and alignment while others find no such relation.

Methodology
To address these issues, the authors perform a homogeneous global analysis of 255 exoplanetary systems with RM measurements. The study utilizes a custom code, allesfast (built upon allesfitter and incorporating features from EXOFASTv2), to simultaneously fit:

1. Spectral Energy Distributions (SEDs) using MIST evolutionary tracks to constrain stellar parameters ($T_{\text{eff}}$, [Fe/H], $\log g$, $M_*$, $R_*$).
2. Transit light curves (from ground-based surveys and space missions like CoRoT, Kepler, K2, TESS, and Spitzer) and mid-transit times.
3. Out-of-transit radial velocities (RVs) to constrain orbital parameters.
4. In-transit RM signals to constrain the projected spin-orbit angle ($\lambda$) and stellar rotation ($v \sin i_*$).

The fitting process employs a Differential Evolution Markov chain Monte Carlo (PT-DE-MCMC) algorithm to derive self-consistent posterior distributions. To mitigate the Lucy-Sweeney bias, the authors fit $\sqrt{e} \cos \omega_*$ and $\sqrt{e} \sin \omega_*$ rather than $e$ and $\omega$ directly. The sample is refined to 145 single-star systems with reliable planet-mass measurements, excluding systems with significant transit timing variations, young/active stars requiring complex activity modeling, and those with poorly constrained masses. The final sample is stratified into three mass regimes: Sub-Saturns ($M_p \lesssim 0.3 M_J$), Jupiters ($0.3 M_J < M_p \lesssim 3 M_J$), and Super Jupiters/Brown Dwarfs ($M_p \gtrsim 3 M_J$).

Key Contributions

• Homogeneous Catalog: The paper presents a uniformly re-analyzed catalog of 255 systems, providing self-consistent posteriors for physical and orbital parameters, available at www.stellarobliquity.com.
• Unified Modeling Framework: By jointly modeling SEDs, transits, RVs, and RM signals, the study eliminates systematic biases arising from inconsistent treatment of uncertainties and degeneracies (e.g., between $v \sin i_*$ and $\lambda$).
• Mass-Stratified Analysis: The work explicitly investigates the dependence of spin-orbit architecture on planet mass, moving beyond previous analyses that often treated giant planets as a monolithic population.

Results
The analysis reveals pronounced, distinct structures in the $e-\lambda$ plane that depend critically on planet mass:

1. Sub-Saturns ($M_p \lesssim 0.3 M_J$): These planets can be both eccentric and misaligned. Misalignments are observed across the full range of eccentricities.
2. Jupiters ($0.3 M_J < M_p \lesssim 3 M_J$): A distinct trend emerges where misalignment is confined to circular orbits. Eccentric Jupiters in this mass regime are predominantly aligned.
3. Super Jupiters and Brown Dwarfs ($M_p \gtrsim 3 M_J$): These massive companions are aligned across the full eccentricity range, regardless of whether their orbits are circular or eccentric.

A two-dimensional Kolmogorov-Smirnov test confirms that the joint $(e, \lambda)$ distributions differ significantly among these three mass regimes (p-values < 0.05 in all pairwise comparisons).

Significance
The paper argues that stellar obliquity ($\lambda$) alone is not a unique tracer of evolutionary history. The observed trends demonstrate that $\lambda$ depends jointly on eccentricity and planet mass. This finding challenges existing theoretical frameworks that rely solely on $\lambda$ to distinguish between migration channels (e.g., disk migration vs. high-eccentricity migration). Specifically, the result that eccentric Jupiters are aligned contradicts the expectation that high-eccentricity migration naturally produces misaligned orbits, while the alignment of massive companions across all eccentricities suggests different dynamical origins or tidal evolution timescales compared to lower-mass giants. The authors conclude that a unified theoretical framework for the origins of spin-orbit misalignment is currently lacking and that strong inferences about migratory histories drawn solely from obliquity measurements are premature without considering the joint dependence on mass and eccentricity.