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

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.