Ratio of the crossing timescale τ_cross (Eq. (3)) to the libration timescale τ_lib (Eq. (9)) as a function of the planetesimal’s semi-major axis. Here, the type II regime obtained in Kanagawa et al. (2018) is considered for the migration timescale τ_tide,a. The solid, dash-dotted, and dotted lines show the cases of the planet-to-star mass ratio M_p ∕M_s= 10⁻², 10⁻³, and 10⁻⁴, respectively. Shown are the inner first-order mean motion resonances (or j:j − 1 resonances): thick lines are for j = 2 and thin lines are for j = 3. To calculate the migration timescale, the same disk model was used as in Ida et al. (2018). The disk accretion rate, disk viscosity parameter, and disk aspect ratio is set to 10⁻⁸ M_⊙ yr⁻¹, 10⁻³, and 0.03r^1∕4, respectively.