Dust trapping, collisional velocity and velocity dispersion in gravito-turbulent discs

Abstract: High-resolution ALMA observations indicate that planet formation is already well underway in the earliest stages of disc evolution, when discs are typically massive enough to be regulated by gravitational instability (GI). In this regime, the interplay between dust dynamics and GI may enable rapid core formation, but the conditions under which this process operates remain poorly constrained. In this work, we use three-dimensional global SPH simulations to investigate the dynamics of dust particles in gravitationally unstable discs over a wide range of Stokes numbers. We focus on three key quantities that regulate early planet formation: dust trapping in spiral arms, collisional velocities between dust grains, and the dust velocity dispersion. We find that particles with Stokes numbers in the range St ~ 0.1-1 undergo the strongest concentration within spiral arms while simultaneously exhibiting low velocity dispersion. This combination makes this aerodynamic regime the most favourable for the onset of dust-driven gravitational instability and direct dust collapse. Where direct comparisons of collision velocities are possible, our three-dimensional results are in excellent agreement with previous two-dimensional studies and are consistent with a picture in which grains are partially coupled to a Kolmogorov-like turbulent velocity field in the gas. Our results indicate that, in young self-gravitating discs, dust particles in this intermediate coupling regime provide a natural pathway to the formation of planetary cores.