Time evolution of the dust gap width for different planetary masses. We fixed the Stokes number St = 10^–3 and the Mach number ℳ_hw = 0.03, and set α_diff = 10^–4 in panel a and α_diff = 10^–5 in panel b. The solid lines with the circle symbols and the dashed lines are the numerically calculated and the semi-analytic dust gap widths, respectively (Eq. (26); Sect. 4.4). We note that in panels a and b, the numerically calculated dust gap width for m = 0.03 is not shown because we obtained ${\mathcal{W}}_{\text{gap\hspace{0.17em}}}^{\text{num\hspace{0.17em}}}=0$.