Secular evolution of MHD wind-driven discs: analytical solutions in the expanded α-framework

Abstract

The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds appear as a compelling scenario to account for disc accretion. In this work, we aim to construct the equivalent of the widely used analytical description of viscous evolution for the MHD wind case. The transport of angular momentum and mass induced by the wind is parameterized by an α-like parameter and by the magnetic lever arm parameter λ. Extensions of the paradigmatic Lynden-Bell and Pringle similarity solutions to the wind case are presented. We show that wind-driven accretion leads to a steeper decrease in the disc mass and accretion rate than in viscous models due to the absence of disc spreading. If the decline of the magnetic field strength is slower than that of the gas surface density, the disc is dispersed after a finite time. The evolution of the disc in the $\dot{M}_*-M_{D}$ plane is sensitive to the wind and turbulence parameters. A disc population evolving under the action of winds can exhibit a correlation between $\dot{M}_*$ and MD depending on the initial conditions. The simplified framework proposed in this work opens to a new avenue to test the effectiveness of wind-driven accretion from the observed disc demographics and constitutes an important step to include wind-driven accretion in planet population synthesis models.

Gas Disk Sizes from CO Line Observations: A Test of Angular Momentum Evolution

“…Following the α-framework for viscous evolution, a simple parameterized description of disk evolution for an MHD disk wind was recently provided by Tabone et al (2022a). This introduced a similar dimensionless parameter α DW that describes the wind torque and relates to the local accretion rate driven by the wind.…”

“…This framework therefore controls disk evolution with three key parameters: α DW , initial disk mass M d,0 , and initial characteristic disk radii R c,0 (the accretion timescale t acc,0 is related to α DW and R c,0 , which will be used in the following discussion). Based on the analytical solution from Tabone et al (2022a), Trapman et al (2022 then examined how R CO evolves in the pure disk wind scenario (ignoring the viscous term). When considering a constant α DW , R CO gradually declines with time (between 0.1 and 10 Myr, as shown in the left panel of Figure 9), which is in direct contrast to the case of viscous evolution.…”

“…The time evolution of R CO in this disk wind scenario largely depends on the rate at which the disk surface density decreases. If we consider a time-dependent α DW that scales with Σ c (t) −1 , the decrease of R CO becomes much shallower until a sharp drop occurs when the disk starts to dissipate (at 2t acc,0 ; Tabone et al 2022a). This difference is demonstrated in the two panels of Figure 9.…”

A Self-Consistent Model for Dust-Gas Coupling in Protoplanetary Disks

“…Perhaps most trivially, our "activedisk" treatment of the energy balance can be extended to account for "passive" stellar irradiation as well as more realistic radiative transfer. Additionally, it is possible to consider radially variable accretion rates (Laibe et al 2012) or incorporate non-viscous drivers of gas accretion, such as disk winds (Tabone et al 2021), although this would complicate the relationship between Ṁ and the surface density. As yet another example, the viscosity parameter itself can be endowed with a radial dependence (Penna et al 2013), given that distinct modes of (magneto-)hydrodynamic turbulence are expected to operate in different regions of the disk (Lyra and Umurhan 2019).…”

Lecture notes on accretion disk physics

“…Hartmann et al, 1998). It can be generalized to the case where disk evolution is driven by a combination of viscous transport and MHD winds (Tabone et al, 2021).…”