From streaming instability to the onset of pebble accretion: I. Investigating the growth modes in planetesimal rings

Context. The localised formation of planetesimals can be triggered with the help of streaming instability when the local pebble density is high. This can happen at various locations in the disc, and it leads to the formation of local planetesimal rings. The planetesimals in these rings subsequently grow from mutual collisions and by pebble accretion. Aims. We investigate the early growth of protoplanetary embryos from a ring of planetesimals created from streaming instability to see if they reach sizes where they accrete pebbles efficiently. Methods. We simulated the early stages of planet formation for rings of planetesimals, which we assumed were created by streaming instability at various separations from the star and for various stellar masses using a semi-analytic model. Results. The rings in the inner disc are able to produce protoplanetary embryos in a short time, whereas at large separations there is little to no growth. The growth of the largest bodies is significantly slower around lower-mass stars. Conclusions. The formation of planetary embryos from filaments during the disc lifetime is possible but strongly dependent on the separation from the star and the mass of the host star. Forming the seeds of pebble accretion early in the outer disc, ∼50AU, remains difficult, especially for low-mass stars.