Flux ratio between the disk and the star at 2.1 μm (K band), as function of parent belt radius r₀. Solid lines indicate the flux ratio due to the maximum amount of material moved in by P–R drag, truncated at r = r_pile. Ratios including the small effect due to pile-up are shown with dashed lines. Different colors are used for different stellar types. The light shaded area marks the region in parameter space where no significant pile-up is expected to occur because the orbits of small dust grains cannot circularize sufficiently (see Eq. (22)). The dark shaded area marks where the parent belt r₀ is closer than the pile-up radius r_pile. The observed K-band excess fluxes of main-sequence stars from Table 1 are shown at their respective estimated parent belt distances with a different symbol for each star and coloring according to the star’s spectral type: Vega (the CHARA/FLUOR measurement): circles; β Leo: hexagon; Fomalhaut: squares; β Pic: diamond; η Lep: upward pointing triangles; 110 Her: left-pointing triangle; 10 Tau: right-pointing triangle; τ Cet: pentagon.