Relaxation time (Eq. (19)) of the disk in units of the Kepler time for three small-grain dust-to-gas ratios: Normal (Z_small = 10⁻²). depleted by a factor of 10⁻¹ (Z_small = 10⁻³) and depleted by a factor of 10⁻² (Z_small = 10⁻⁴). Dotted lines: optically thin approximation (Eq. (17)). Solid lines: including optical depth effects. In dashed black: upper limit to the relaxation time (Eq. (7)) for which VSI is operational is shown. The disk and stellar parameters are those of the star Oph 163131 (the fiducial model of Appendix A).