Fig. 2

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Ratio of the crossing timescale τcross (Eq. (3)) to the libration timescale τlib (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 τtide,a. The solid, dash-dotted, and dotted lines show the cases of the planet-to-star mass ratio Mp ∕Ms= 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 0.03r1∕4, respectively.
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