Dust gap width as a function of the dust gap location. We set St = 10⁻³ and ℳ_hw = 0.03, and varied the turbulent parameter in each panel, α_diff = 10⁻⁴ (panel a) and α_diff = 10⁻⁵ (panel b). The blue and orange solid lines denote H and 5 H, respectively (Eq. (A.3)). Panel a: Blue shaded region given by ${\mathcal{W}}_{\text{gap\hspace{0.17em}}}^{\text{SA}}\left(t\right)$ (Eq. (26)) at t ≤ 10⁴. The lower and upper limits were set by m = 0.05 and 0.5, respectively. Panel b: Dashed lines given by Eq. (26) with a fixed planetary mass, m = 0.1 . The different colors correspond to different times, t ≤ 10⁴, t = 3 × 10⁴, 10⁵, and 3 × 10⁵, respectively. We hatched the region in which the time required for gap formation exceeds 3 Myr for the assumed dimensionless time, t. The observational data indicated with pink and purple markers show the observed gaps that are accompanied by a ring, taken from Zhang et al. (2023) (compiled from Huang et al. (2018); Long et al. (2018), and Zhang et al. (2023)) and Huang et al. (2018) (DSHARP sample), respectively. These samples do not include disks with inner dust cavities.