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Planetesimal formation is still mysterious. One of the ways to formplanetesimals is to invoke a gas pressure bump in a protoplanetary disc. In ourprevious paper, we propose a new scenario in which the piled-up dust at a gaspressure bump created by a migrating planet form planetesimals by streaminginstability in a wide region of the disc as the planet migrates inward. In thiswork, we consider the global time evolution of dust and investigate thedetailed conditions and results of the planetesimal formation in our scenario.We use a 1D grid single-sized dust evolution model, which can follow the growthof the particles by their mutual collision and their radial drift anddiffusion. We calculate the time-evolution of the radial distribution of thepeak mass and surface density of the dust in a gas disc perturbed by anembedded migrating planet and investigate if the dust satisfies the conditionfor planetesimal formation. We find that planetesimals form in a belt-likeregion between the snowline and the position where the planet reaches itspebble-isolation mass when the strength of turbulence is$10^{-4}\leq\alpha\leq10^{-3}$, which is broadly consistent with observedvalue. The mechanism of the formation, streaming instability or mutualcollision, depends on the timescale of the streaming instability. The totalmass of planetesimals also depends on $\alpha$ and is about $30-100~M_{\rm E}$if the planetary core has already existed at the beginning and grows by gasaccretion, but it decreases as the timing of the formation of the planetarycore is later. We also provide simple approximate expressions of the surfacedensity and total mass of the planetesimals and find that the total massstrongly depends on the dust mass. We show that planetesimals form in abelt-like region by the combination of the dust pile-up at the gas pressurebump formed by a planet and its inward migration.

Planetesimal formation at the gas pressure bump following a migrating planet II. Effects of dust growth