Systematic description of wind-driven protoplanetary discs^★

Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
e-mail: geoffroy.lesur@univ-grenoble-alpes.fr

Received: 10 December 2020
Accepted: 24 January 2021

Abstract

Aims. Planet-forming discs are believed to be very weakly turbulent in the regions outside of 1 AU. For this reason, it is now believed that magnetised winds could be the dominant mechanism driving accretion in these systems. However, currently, no self-consistent approach can describe discs that are subject to a magnetised wind in a way similar to the α disc model. In this article, I explore the parameter space of wind-driven protoplanetary discs in a systematic manner and present scaling laws that can be used in reduced models in a similar way to α disc models.

Methods. I computed a series of self-similar wind solutions, assuming that the disc is dominated by ambipolar and Ohmic diffusion. These solution were obtained by searching for stationary solutions in the finite-volume code PLUTO using a relaxation method and continuation.

Results. Self-similar solutions are obtained for values of plasma β ranging from 10² to 10⁸ for several Ohmic and ambipolar diffusion strengths. Mass accretion rates of about 10⁻⁸ M_⊙ yr⁻¹ are obtained for the poloidal field strength β = O(10⁴) or equivalently, 1 mG at 10 AU. In addition, the ejection efficiency is always close to 1, implying that wind mass-loss rate can be higher than the inner mass accretion rate when the wind-emitting region is large. The resulting magnetic lever arms are typically lower than 2, possibly reaching 1.5 in the weakest field cases. Remarkably, the mean transport properties (accretion rate and mass-loss rate) mostly depend on the field strength and much less on the disc diffusivities or surface density. The disc internal structure is nevertheless strongly affected by Ohmic resistivity, strongly resistive discs being subject to accretion at the surface while ambipolar only models lead to mid-plane accretion. Finally, I provide a complete set of scaling laws and semi-analytical wind solutions, which can be used to fit and interpret observations.

Conclusions. Magnetised winds are unavoidable in protoplanetary discs as soon as they are embedded in an ambient poloidal magnetic field. Very detailed disc microphysics are not always needed to describe them, and simplified models such as self-similar solutions can capture most of the physics seen in full 3D simulations. The remaining difficulty to set up a complete theory of wind-driven accretion lies in the transport of the large-scale field, which remains poorly constrained and is not well understood.