Mean particle eccentricity as a function of the steady-state velocity dispersion, physical radius, and bulk density of Q1R ring particles. In panel (a), the particle radius is varied over realistic values for a fixed bulk density of 1000 kg × m⁻³, while in panel (b) the bulk density is varied and the particle radius is fixed at 1 m. The color scale represents the mean eccentricity, with the dotted lines indicating constant values of ﹩\bar{e}﹩ and the solid black lines indicating constant values of the Toomre stability parameter Q. Colored symbols in panel (b) correspond to different collisional steady-state models from B. E. Morgado et al. (2023).