Time evolution of a) radius of the pebble formation front, b) pebble accretion rate (Ṁ_peb), and c) ξ_peb = Ṁ_peb/Ṁ_∗ for two values of α, 10^-4 (red) and 10^-3 (blue). The lines labeled “grow” (dotted) and “GI” (dashed) represent the pebble growth and disk GI limits, respectively. The thick solid lines express the actual values obtained by the minima of the two limits. Here we assumed τ_s,peb = 0.1 and Z₀ = 0.01. In panel c), the small squares represent the points with ξ_peb>ξ_crit, see Eq. (18).