Dust enrichment and growth in the earliest stages of protoplanetary disk formation

Aims. We numerically investigated dust enrichment and growth during the initial stages of protoplanetary disk formation. A particular objective was to determine the effects of various growth barriers, mimicked by imposing a series of upper permissible limits on maximum dust sizes.Methods. We used the Formation and Evolution of Stars and Disks on nested meshes (ngFEOSAD) code to simulate the three-dimensional dynamics of gas and dust under the polytropic approximation, from the gravitational collapse of a slowly rotating Bonnor-Ebert sphere to ≈12 kyr after the first hydrostatic core and disk formation.Results. We found that dust growth begins in the contracting cloud in the evolution stage that precedes disk formation, and that the disk begins to form in an environment already enriched with grown dust. The efficiency of dust growth in the disk is limited by dust growth barriers. For dust grains with maximum sizes <100 μm, electrostatic or bouncing barriers likely dominate, whereas fragmentation and drift barriers are more important for larger grains. The disk midplane quickly becomes enriched with dust, while the vertically integrated dust distribution shows notable local variations around the canonical 1:100 dust-to-gas mass ratio. These positive and negative deviations are likely caused by local hydrodynamic flows, as the globally integrated dust-to-gas ratio deviates negligibly from the initial 1:100 value. We note that care should be taken when using models with fixed dust sizes, as disks exhibit profound negative radial gradients in dust size even during the earliest stages of disk formation. Models with a constant Stokes number may be preferable in this context.Conclusions. Early dust enrichment and growth may facilitate planet formation, as suggested by observations of protoplanetary disk substructures.