  To avoid known difficulties in planetesimal formation such as the drift or
fragmentation barriers, many scenarios have been proposed. However, in these
scenarios, planetesimals form in general only at some specific locations in
protoplanetary discs. On the other hand, it is generally assumed in planet
formation models and population synthesis models, that planetesimals are
broadly distributed in the protoplanetary disc. Here we propose a new scenario
in which planetesimals can form in broad areas of the discs. Planetesimals form
at the gas pressure bump formed by a first-generation planet (e.g. formed by
pebble accretion) and the formation region spreads inward in the disc as the
planet migrates. We use a simple 1D Lagrangian particle model to calculate the
radial distribution of pebbles in the gas disc perturbed by a migrating
embedded planet. We consider that planetesimals form by streaming instability
at the points where the pebble-to-gas density ratio on the mid-plane becomes
larger than unity. We also study the effect of some key parameters like the
ones of the gas disc model, the pebble mass flux, the migration speed of the
planet, and the strength of turbulence. We find that planetesimals form in wide
areas of the discs provided the flux of pebbles is typical and the turbulence
is not too strong. The planetesimal surface density depends on the pebble mass
flux and the migration speed of the planet. The total mass of the planetesimals
and the orbital position of the formation area depend strongly on the pebble
mass flux. We also find that the profile of the planetesimal surface density
and its slope can be estimated by very simple equations. We show that our new
scenario can explain the formation of planetesimals in broad areas. The simple
estimates we provide for the planetesimal surface density profile can be used
as initial conditions for population synthesis models.
