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Fig. 3.

image

Midplane pebble-to-gas ratio Z ≡ ρp/ρg in the αmid/αacc − Fp/g space. Included are the cases where r = 5 au, Cη = 11/8 for T ∝ r−1/2, τs = 0.1, and Ri = 0.5. Left and right panels: cases where αacc = 10−2 and αacc = 10−3, respectively. The color contours are obtained by directly solving Eq. (11). The red regions indicate the no-drift runaway pile-up. The diagonal dashed black line (Eq. (16)) and the horizontal dashed black line (Eq. (20)) are the analytically derived critical Fp/g, crit above which the ND runaway pile-up takes place. The critical Z above which the ND runaway pile-up occurs (i.e., Zcrit = 1) is shown by the white lines. The parameter map is very weakly dependent on the radial distance to the star (see Eqs. (16) and (20)), and the ND mode can occur irrespective of the shape and position of a dead zone.

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