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

Abstract

The degree of coupling between dust particles and their surrounding gas in protoplanetary disks is quantified by the dimensionless Stokes number. The Stokes number (St) 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 St of particles across time in disks evolving under both turbulent viscosity and magnetohydrodynamic (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 in dust settling, drift, and size regimes. For a fiducial disk evolution parameter α̃≃10−3, silicate particles inteior to the ice-line are characterized by low St (≲10−2) and sizes in the sub-mm- to 1cm-scale. Icy particles/boulders beyond the ice-line are characterized by high St (≳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 drag. Silicate particles in the inner disk remain relatively well dispersed and are to a large extent advected inward with their surrounding gas.The St dichotomy across the ice-line translates to distinct planet formation pathways between the inner and outer disk. While pebble accretion proceeds slowly for rocky embryos within the ice-line (across most of parameter space), it does so rapidly for volatile-rich embryos beyond it, allowing for the growth of giant planet cores before disk dissipation. Through simulations of rocky planet growth, we evaluate the competition between pebble accretion and classical pairwise collisions between planetesimals. We conclude that the dominance of pebble accretion can only be realized in disks that are driven by MHD winds, slow-evolving (α̃≲10−3.5), and devoid of pressure maxima that may concentrate solids and give rise of planetesimal rings in which classical growth is enhanced. Such disks are extremely quiescent, with Shakura-Sunyaev turbulence parameters αν≲10−4. We conclude that for most of parameter space corresponding to values of αν reflected in observations of protoplanetary disks (≳10−4), pairwise planetesimal collisions constitute the dominant pathway of rocky planet accretion. Our results are discussed in the context of super-Earth origins, and lend support to the emerging view that they formed in planetesimal rings. Moreover, these results argue against a significant contribution (≳ 10%) of outer disk, carbonaceous material to the proto-Earth in the form of pebbles, in agreement with chemical and isotopic investigations of Earth’s accretion history.