Transition between accumulation and dispersal, a test of Eq. (10). Left panel: same as the left column of Fig. 5, but exploring a grid of simulations near the 1/3 SOR. The particle radii increase from left to right in the range R = 1.25 × 10⁻⁴ − 4 × 10⁻³, corresponding to R = 25-0800 m in the case of Chariklo’s rings, while the mass anomaly increases upward from 0.003 to 0.1. The number of particles and the initial width of the rings were chosen in order to provide the same initial optical depth τ₀ = 0.015 for all simulations. The vertical axes span values of L_z between 1.35 and 1.55 for µ = 0.1 and 0.03, and between 1.4 and 1.5 for µ = 0.01 and 0.003. The small insets covering the radial range 1.9–2.4 show snapshots of the ring in polar coordinates at the end of the run; the label indicates the duration of the run in Chariklo rotation periods. Increasing the particle size (and thus the viscosity) for a given perturbation strength prevents the resonance accumulation. Right panel: filled and open symbols respectively distinguish between simulations leading to resonance confinement and dispersal. The black line indicates the accumulation threshold for the simulations displayed in the left panel, following Eq. (10); the dashed portion of the line indicates the region where the linear relation fails since the resonance excitation at large µ ≳ 0.03 becomes somewhat weaker than predicted by the analytical formulas (see footnote 1). The shaded region bounded by the red line extrapolates the accumulation region to a denser ring with τ = 1.