Evidence for a Peak at $\sim$0.3 in the Eccentricity Distribution of Typical Super-Jovian Exoplanets

TL;DR

This work introduces a completeness-corrected, hierarchical Bayesian framework to measure the 3D occurrence rate of giant exoplanets as a function of eccentricity $e$, semi-major axis $a$, and mass $M$ using the California Legacy Survey RV sample. By incorporating injection-recovery completeness, inclination marginalization, and posterior samples, the authors uncover a robust peak in the eccentricity distribution for super-Jovian planets at $e\approx0.3$, indicating dynamically hot histories not captured by simple beta or Rayleigh forms. A truncated Gaussian fit further pinpoints the peak at $e\sim0.3$, and robustness tests—including comparisons to Fulton (2021a), assessments of stellar activity, and the 2-for-1 planet-signal test—argue that this feature is statistically significant and not an artifact of data or analysis. The results have important implications for giant planet formation and dynamical evolution, suggesting that high-mass giants at near-peak occurrence often experience moderate eccentricities likely driven by processes such as secular perturbations, giant impacts, or other dynamical interactions; Gaia DR4 and future RV surveys will be crucial to refining these trends and testing formation scenarios.

Abstract

In this study, we compute completeness-corrected occurrence rates of giant exoplanets as a function of mass, semimajor axis, and eccentricity, using the approximately uniform California Legacy Survey sample of RV-discovered planets published in Rosenthal et al. 2021. We recover the previously-detected rise in occurrence with semimajor axis for both lower- and higher-mass subsets of the population out to $\sim$5 au. When restricting to planets with semimajor axes between 0.1 and 4.5 au (roughly speaking, the "peak" of giant planet occurrence), we find evidence for distinct eccentricity distributions for each of two mass sub-populations. Most strikingly, we observe a peak in the eccentricity distribution of super-Jovian planets (3-20~M$_{\rm J}$) at 0.3, which is apparent using two different parameterizations of the eccentricity distribution model. A hierarchical histogram model reveals that $\sim$92% of posterior samples indicate an elevated occurrence rate of super-Jupiters with modest eccentricities (0.2-0.4) compared to lower or higher eccentricities (i.e. evidence for a moderate eccentricity "peak"), and 99% of samples indicate super-Jupiters with modest eccentricities are more common than those with lower eccentricities (i.e. evidence that moderate eccentricities are more common than low eccentricities). We use a truncated Gaussian model fit to pinpoint the location of the super-Jupiter eccentricity peak with more precision, finding a maximum a posterior (MAP) peak location of $e=0.3$. This low but elevated characteristic eccentricity could be the result of dynamically hot histories, perhaps involving a giant impacts phase. All analysis code for this project is publicly available on Zenodo (https://zenodo.org/records/18089157) and GitHub (github.com/sblunt/eccentricities).

Figures (8)

• Figure 1: Completeness model $Q(\boldsymbol{\omega})$ constructed for the CLS survey. Completeness is constructed using injection-recovery tests, and is shown in each survey box in blue. The CLS sample, shown as white points with error bars, is overplotted for reference. Individual planet are plotted either in the left or right panel based on their median M$\sin{i}$, but in the hierarchical model, a posterior sample from a given planet might fall in either the left or right panel (i.e. the mass space is continuous, not disjointed as it appears here). Takeaway: completeness worsens not only with decreasing M$\sin{i}$, but also with increasing eccentricity. This highlights the importance of including completeness in calculations of population-level eccentricity distributions using RVs.
• Figure 2: Completeness-corrected occurrence rate estimates for sub-Jovian planets (left), super-Jovian planets (middle) and brown dwarfs (right), acknowledging the caveat that brown dwarf occurrence rates may be contaminated by face-on stellar binaries; see Section \ref{['sec:binaries']}. Color indicates overall occurrence rate in each "box" in the 3D parameter space, converted to a relative probability within a mass bin following the discussion in the text. Detected planets in the CLS sample are overplotted as white points with error bars. Takeaway: we recover the expected monotonically decreasing eccentricity distribution of sub-Jovian planets. The occurrence of super-Jovian planets, however, shows a peak at moderate eccentricities.
• Figure 3: Marginalized posterior distributions of the hierarchical truncated Gaussian fits to the CLS data described in Section \ref{['sec:results']}, showing the contrast between a preference for a negative (or 0) Gaussian mean eccentricity value among the sub-Jupiter population, and a preferred value of 0.3 for the super-Jupiter population. The dashed line is at the mode value of the high mass population posterior (e=0.275). Takeaway: while we recommend using our hierarchical histogram fit for direct comparison with simulations, the Gaussian fit indicates that the preferred eccentricity "peak" location for typical super-Jupiters is at e=0.3.
• Figure 4: Another view of Figure \ref{['fig:money']}; each panel corresponds to a column of the corresponding panel in Figure \ref{['fig:money']}. Rather than as a relative probability, the y-axis here is shown as an occurrence rate, highlighting that there are more sub-Jovian than super-Jovian planets per star; occurrence rates in the brown dwarf desert are upper limits. Takeaway: the population-level eccentricity distributions of super- and sub-Jovian planets appear distinct.
• Figure 5: Occurrence rate estimates for super-Jovian planets (transparent triangles), sub-Jovian planets (black circles), and brown dwarfs (transparent stars) as a function of semimajor axis. Left: occurrence in log-constant steps of semimajor axis, for two bins in M$\sin{i}$. Right: same as left, but for two bins in mass, marginalizing over inclination following the method in the Appendix. This figure can be directly compared to Figure 5 of Fulton:2021a, with the caveat stated throughout the text that brown dwarf occurrence rates may be overestimated. Takeaway: we recover the previously identified trend that giant planet occurrence rises with semimajor axis out to $\sim$5 au, both when marginalizing over inclination and not.