Growth rate in units of the reciprocal orbital time (1 /torbit = ΩK/ 2π) of the dust-driven viscous instability, as a function of dust particle size (expressed as Stokes number St), according to the simplified analysis of Sect. 3. Dashed lines: case 1 (i.e. φg = 0), solid lines: case 2 (i.e. φg = −φd). The different lines show modes of different dimensionless wavelength λ in the dimensionless coordinate x, where λ = 2π/k. A dimensionless wavelength λ = 1 means a wavelength as large as r0. The parameters of the model shown here are φd = −1.0, α1 = 10-4, M∗ = 1 M⊙, L∗ = 10 L⊙, r0 = 60 au, T = 43,K, Sc = 1 (i.e. cs = 0.39 km s-1 and torbit = 465 yr).
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