The Orbital Eccentricity--Radius Distribution for Warm, Single Planets in TESS
We characterize the radius-dependent eccentricity distribution of 219 warm (P = 8--50 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 ( = 0.039-0.038+0.018) and a secondary dynamically excited mode ( = 0.466-0.068+0.067). 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 = 9.2-1.1+1.9 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 65-12+13% of the population in the high eccentricity mode. Under the assumption of a two-component model, we see tentative evidence for a bimodal Jovian distribution at ~2.7 sigma. Finally, we identify a non-negligible tail of highly eccentric sub-Neptunes (1--4 R_e), which comprise 16.2-6.4+5.2% of the population, consistent with excitation by non-transiting external companions.