Dust-gas coupling in turbulence- and MHD wind-driven protoplanetary disks: Implications for rocky planet formation

The degree of coupling between dust particles and their surrounding gas in protoplanetary disks is quantified by the Stokes number. The Stokes number governs particle size and spatial distributions, in turn establishing the dominant mode of planetary accretion in different disk regions. In this paper, we model the characteristic Stokes number of dust particles across time in disks evolving under both turbulent viscosity and MHD disk winds. In both turbulence- and wind-dominated disks, we find that collisional fragmentation is the limiting mechanism of particle growth. The water-ice sublimation line constitutes a critical transition point between dust settling, drift, and size regimes. For a fiducial value disk evolution parameter α̃≃10−3, silicate particles interior to the ice-line in our model are characterized by low Stokes numbers (≲ 10−2) and sizes in the sub-mm- to 1cm-scale. Icy particle/boulders beyond the ice-line are characterized by high Stokes numbers (≳10−2) and sizes in the cm to dm size range. Hence, icy particles settle into a thin layer at the outer disk midplane and drift inward at velocities exceeding the gaseous accretionary flow due to substantial headwind. Silicate particles in the inner disk remain relatively well dispersed and are to a large extent advected inward with their surrounding gas.The dichotomy in Stokes number also translates to distinct planet formation pathways between the inner and outer disk. While rocky embryos in the inner disk are largely confined to inefficient pebble accretion in the 3D regime, sufficiently massive volatile-rich embryos in the outer disk can partake in rapid 2D pebble accretion when turbulence therein is sufficiently low. Through simulations of rocky planet growth, we demonstrate that the dominance of pebble accretion can only be realized in disks that are driven by MHD winds, slow-evolving (α̃∼10−4), and devoid of pressure maxima that may concentrate solids and give rise to planetesimal rings. Such disks are extremely quiescent, with Shakura-Sunyaev turbulence parameters on the order of αν∼10−5. We conclude that for most of parameter space reflected in astronomical observations of protoplanetary disks, pairwise planetesimal collisions constitute the dominant pathway of rocky planet accretion. Our results lend support to proposition that rocky planets formed in planetesimal rings and argue against a significant contribution (≳ 10%) of outer disk, carbonaceous, material to the proto-Earth in the form of pebbles.