Space–time plots of an m = 7 density wavewith scaled torque passing through a region (r–r_L ~ 60–100 km) of increased (τ₀ = 3, left panel) and decreased (τ₀ = 0.5, right panel) equilibrium surface mass density. As in Figs. 1–3 the blue solid curve indicates the expected curve of the density wavefront in a homogeneous ring (Eq. (42)). These plots only show the density perturbation on top of the background density.