The Orbital Eccentricity--Radius Distribution for Warm, Single Planets in TESS

Abstract

We characterize the radius-dependent eccentricity distribution of 347 warm (P = 8-200 days) systems with only one transiting planetary candidate identified during Sectors 1-69 of the TESS mission. Using the ``photoeccentric effect'' in a hierarchical Bayesian framework, we first model the population using discrete planetary size bins (sub-Neptunes, sub-Saturns, and Jovians). We then develop a continuous mixture model with weights governed by a logistic sigmoid function of radius. We find that the warm-single population is best described by two components: a dominant low-eccentricity mode ( <e_low> = 0.070-0.068+0.026) and a secondary dynamically excited mode (<e_high> = 0.616-0.075+0.091). The fraction of planets belonging to this high-eccentricity component increases strongly with planet radius, characterized by a transition at a break radius of R_br = 9.8-1.1+1.4 R_e. This trend places warm sub-Saturns predominantly on the same low-eccentricity track as sub-Neptunes. In contrast, warm Jovians (8--16 R_e) are frequently eccentric, with 59+-13% of the population in the high eccentricity mode. We detect this bimodality at >4sigma, providing statistically significant evidence that warm gas giants are sculpted by two distinct pathways, or a single mechanism with subsequent eccentricity excitation. Finally, we identify a non-negligible tail of highly eccentric sub-Neptunes (1--4 R_e), which comprise 14.9-6.5+5.1% of the population, consistent with excitation by non-transiting external companions.

Figures (14)

• Figure 1: Planet radius versus orbital period for the final sample. Points and error bars represent median posterior values and 68% credible intervals. The side panels show the 1-D histograms for radius (right) and period (top).
• Figure 1: Host--planet properties for the $R_p<4\,R_\oplus$ subsample. Planet radius is shown as a function of orbital period (upper left), stellar effective temperature (upper right), stellar surface gravity $\log g$ (lower left), and stellar density $\rho_\star$ (lower right). Blue points denote the full small-planet sample, while red points highlight systems whose individual photoeccentric posteriors have eccentricity modes $e_{\rm mode}>0.5$. Error bars show the 68% credible intervals.
• Figure 2: Orbital eccentricity (in $e^2$) versus semi-major axis for the planet sample with eccentricities constrained to better than 40% for clarity (or if $e<0.1$). Colors denote sub-Neptunes (1--4 $R_\oplus$, blue), sub-Saturns (4--8 $R_\oplus$, purple), and Jovians (8--16 $R_\oplus$, orange). Overlaid curves show theoretical formation channels from Dawson:2018 for a fiducial planet of $\sim$6 $R_\oplus$ and $\sim$80 $M_\oplus$: high-eccentricity migration (red shaded region) and planet-planet scattering (gray dashed line, gray shaded region). The concentration of larger planets at high eccentricities and small semi-major axes is consistent with high-eccentricity migration.
• Figure 2: Corner plot of fiducial 3-stage sigmoid model.
• Figure 3: Joint posterior constraints of $e$--$\omega$ from our photoeccentric-effect analysis. Each mini-corner panel shows the marginalized posteriors of $\omega$ (top) and $e$ (right), along with their joint distribution (lower-left). The top row displays previously known high-eccentricity systems, while the bottom row shows newly identified candidate high-$e$ planets with $R_p \lesssim 4,R_\oplus$. For the known systems, the published radial-velocity solutions toi3362toi3362_newGupta:2023toi5110Bieryla:2025 are overlaid as orange Gaussian approximations in $e$ and $\omega$ for visual comparison.