Self-consistent model for dust-gas coupling in protoplanetary disks

¹ Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA
e-mail: kbatygin@gps.caltech.edu
² Laboratoire Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, CS 34229, 06304 Nice, France
e-mail: alessandro.morbidelli@oca.eu

Received: 25 January 2022
Accepted: 28 March 2022

Abstract

Various physical processes that ensue within protoplanetary disks - including vertical settling of icy and rocky grains, radial drift of solids, planetesimal formation, as well as planetary accretion itself - are facilitated by hydrodynamic interactions between H/He gas and high-Z dust. The Stokes number, which quantifies the strength of dust-gas coupling, thus plays a central role in protoplanetary disk evolution and its poor determination constitutes an important source of uncertainty within the theory of planet formation. In this work, we present a simple model for dust-gas coupling and we demonstrate that for a specified combination of the nebular accretion rate, Ṁ, and turbulence parameter a, the radial profile of the Stokes number can be calculated in a unique way. Our model indicates that the Stokes number grows sublinearly with the orbital radius, but increases dramatically across the water-ice line. For fiducial protoplanetary disk parameters of Ṁ = 10⁻⁸ M_⊙ per year and α = 10⁻³, our theory yields characteristic values of the Stokes number on the order of St ~ 10⁻⁴ (corresponding to ~mm-sized silicate dust) in the inner nebula and St ~ 10⁻¹ (corresponding to icy grains of a few cm in size) in the outer regions of the disk. Accordingly, solids are expected to settle into a thin subdisk at large stellocentric distances, while remaining vertically well mixed inside the ice line.