We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implemented via free parameters. This enables us to study the influence of the disk properties on the formation of planetesimals, predicting their time dependent formation rates and location of primary pebble accretion. We show that large $alpha$-values of $0.01$ (strong turbulence) prevent the formation of planetesimals in the inner part of the disk, arguing for lower values of around $0.001$ (moderate turbulence), at which planetesimals form quickly at all places where they are needed for proto-planets. Planetesimals form as soon as dust has grown to pebbles ($simmathrm{mm}$ to $mathrm{dm}$) and the pebble flux reaches a critical value, which is after a few thousand years at $2-3,$AU and after a few hundred thousand years at $20-30,$AU. Planetesimal formation lasts until the pebble supply has decreased below a critical value. The final spatial planetesimal distribution is steeper compared to the initial dust and gas distribution which helps to explain the discrepancy between the minimum mass solar nebula and viscous accretion disks.
Download