Dust settling and rings in the outer regions of protoplanetary discs subject to ambipolar diffusion

Abstract

Context. Magnetohydrodynamic (MHD) turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes in discs, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into large scale structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. Moreover, the low velocity dispersion observed in CO and strong sedimentation of millimetre dust measured in T-Tauri discs are in contradiction with predictions based on ideal MRI turbulence. Aims. In this paper, we study the effects of non-ideal MHD and magnetised winds on the dynamics and sedimentation of dust grains. We consider a weakly ionized plasma subject to ambipolar diffusion characterizing the disc outer regions ( 1 AU). Methods. To compute the dust and gas motions, we perform numerical MHD simulations in the stratified shearing box, using a modifed version of the PLUTO code. We explore different grain sizes from micrometer to few centimetres and different disc vertical magnetizations with plasma beta ranging from 10 3 to 10 5 . Results. Our simulations show that the mm-cm dust is contained vertically in a very thin layer, with typical heightscale 0.4 AU at R = 30 AU, compatible with recent ALMA observations. Horizontally, the grains are trapped within the pressure maxima (or zonal flows) induced by ambipolar diffusion, leading to the formation of dust rings. For micrometer grains and strong magnetization, we find that the dust layer has a size comparable to the disc heightscale H. In this regime, dust settling cannot be explained by a simple 1D diffusion theory but results from a large scale 2D circulation induced by both MHD winds and zonal flows. Conclusions. Our results suggest that non-ideal MHD effects and MHD winds associated with zonal flows play a major role in shaping the radial and vertical distribution of dust in protoplanetary discs. Leading to effective accretion efficiency α 10 −3 − 10 −1 , non-ideal MHD models are also a promising avenue to reconcile the low turbulent activity measured in discs with their relatively high accretion rates.

Dust dynamics and vertical settling in gravitoturbulent protoplanetary discs

“…This is to be expected, because small dust particles are less sensitive to gravitational settling and will tend to follow the turbulent gas motion. At larger St, the ratio H d /Hg depends on St −1/2 , a result that has been obtained in other simulations coupling dust and turbulent gas (Fromang & Papaloizou 2006;Okuzumi & Hirose 2011;Zhu et al 2015;Yang et al 2018;Riols & Lesur 2018). This dependence can be understood, in a rather crude way, within the framework of a simple diffusion theory (Morfill 1985;Dubrulle et al 1995, see Section 3.3.2), where the vertical equilibrium is set by the balance between the gravitational settling and turbulent diffusion.…”

“…For the dynamics of the dust, we use the method described and tested in Appendix A of Riols & Lesur (2018). In brief, we employ a HLL Riemann solver to compute the density and momentum flux at cell interfaces.…”

“…The third term accounts for the mean vertical drift of dust due to gravitational settling (including the self-gravity of the disc). Using classical assumptions, detailed in Section 5.1.2 and Appendix B of Riols & Lesur (2018), in particular the terminal velocity approximation, it is possible to recast Eq. (A2) in the useful form of an advection-diffusion equation:…”

“…HH30 and many others, see Louvet et al 2018;Duchene et al 2019). A direct comparison of this size with that measured in simulations could provide precious information on the origin and nature of disk turbulence (Riols & Lesur 2018). Because GI can develop strong supersonic motions, it is expected that the settling process differs significantly from other type of turbulence (driven by the magneto-rotational instability or the vertical shear instability for example, see Fromang & Papaloizou 2006;Picogna et al 2018) and could leave a detectable imprint on the vertical dust distribution.…”

Morphological signatures induced by dust back reaction in discs with an embedded planet

“…On the other hand, there exists some general confusion between viscosity discussed above and turbulent diffusion of dust particles. Turbulence near the mid-plane of a disc driven by non-ideal MHD can be highly anisotropic and the magnitude of viscous stress can significantly differ from that of turbulent diffusion of dust particles (Zhu, Stone & Bai 2015a;Riols & Lesur 2018;Yang et al 2018). The dimensionless diffusion coefficients for mm/cm-sized dust particles inferred by recent ALMA observations are on the order of α t ∼ 10 −4 (Pinte et al 2016;Dullemond et al 2018).…”