Relaxation timescale versus perturbation wavelength of midplane modes at different radial separations from the central star: 1au(a); 10au(b); 30au(c); and 100au(d). In each panel: the relaxation timescale (thick solid), the optically thin timescale (short dashed), the optically thick timescale (long dashed), the dust-to-gas collision timescale (dot-dashed), the Rosseland thickness of the mode (dotted, the values on the right ordinate).
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