2018A&A...616A.116P

The growth process of protoplanets can be sped up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent discs. We investigate the accretion of pebbles in turbulent discs that are driven by the purely hydrodynamical vertical shear instability (VSI). For this purpose, we performed global 3D simulations of locally isothermal, VSI turbulent discs that have embedded protoplanetary cores from 5 to 100M_⊕, which are placed at 5.2 au distance from the star. In addition, we followed the evolution of a swarm of embedded pebbles of different sizes under the action of drag forces between gas and particles in this turbulent flow. Simultaneously, we performed a set of comparison simulations for laminar viscous discs where the particles experience stochastic kicks. For both cases, we measured the accretion rate onto the cores as a function of core mass and Stokes number (τ_s) of the particles and compared these values to recent magneto-rotational instability (MRI) turbulence simulations. Overall the dynamic is very similar for the particles in the VSI turbulent disc and the laminar case with stochastic kicks. For small mass planets (i.e. 5-10M_⊕), well-coupled particles with τ_s=1, which have a size of about 1m at this location, we find an accretion efficiency (rate of particles accreted over drifting inwards) of about 1.6-3%. For smaller and larger particles, this efficiency is higher. However, the fast inwards drift for τ_s=1 particles makes them the most effective for rapid growth, leading to mass doubling times of about 20000yr. For masses between 10 and 30M_⊕ the core reaches the pebble isolation mass and the particles are trapped at the pressure maximum just outside of the planet, shutting off further particle accretion.