On the growth of pebble-accreting planetesimals

Context. Pebble accretion is a newly discovered mechanism to quickly grow the cores of planets. In pebble accretion, gravity and gas drag conspire to yield large collisional cross sections for small particles in protoplanetary disks. However, before pebble accretion commences, aerodynamic deflection may act to prevent planetesimals from becoming large, because particles tend to follow gas streamlines. Aims. We derive the planetesimal radius where pebble accretion is initiated and determine the growth timescales of planetesimals by sweep-up of small particles. Methods. The equation of motion for a pebble, including gas drag and gravitational interactions, was integrated in three dimensions at distances of 1, 3, and 10 AU from the star. We obtained the collision efficiency factor as the ratio of the numerically obtained collisional cross section to the planetesimal surface area, from which we obtained the growth timescales. Integrations were conducted in the potential flow limit (steady, inviscid) and in the Stokes flow regime (steady, viscid). Results. Only particles of stopping time ts ≪ tX where tX ≈ 103 s experience aerodynamic deflection. Even in this case, the planetesimal’s gravity always ensures positive collision factors. The planetesimal radius where growth proceeds slowest is ≈ 100 km (less for colder disks) corresponding to interactions shifting from the geometric to the Safronov focusing regime. For particles ts ≫ tX pebble accretion only commences after this phase and is characterized by a steep drop in growth timescales. At 1 AU, growth timescales are shorter than the disk lifetime for pebbles larger than 0.03 cm. The planetesimal radius RPA where pebble accretion commences increases with disk orbital radius. At distances beyond ~ 10 AU, sweep-up growth times are always longer than 10 Myr, while in the inner disk (≲3 AU) the viability of the sweep-up scenario is determined by the outcome of pebble-planetesimal collisions in the geometric regime. We present analytical fits for the collision efficiency factors and the minimum planetesimal radius RPA required for pebble accretion.