The Formation of Rings and Gaps in Magnetized Wind-Launching Disks

Radial substructures in disks around young stellar objects are now routinely detected by state-of-the-art observational facilities. There is also growing evidence that large-scale magnetic fields threading the disks are responsible for launching wide-angle outflows. The magnetic fields that launch disk winds play a crucial role in the dynamics of protoplanetary disks. In this thesis we investigate theoretically the formation of radial structures, i.e., rings and gaps, in magnetized disks through three numerical simulation projects of increasing complexity.

We start with two-dimensional (2D) disk simulations under the assumption of axisymmetry, and we include the simplest of the non-ideal magnetohydrodynamic (MHD) effects, Ohmic dissipation. We find two distinct modes of disk accretion depending on the Ohmic resistivity and magnetic field strength. A small resistivity or high field strength promotes the development of rapidly infalling ``avalanche accretion streams'' in a vertically extended disk envelope that dominates the dynamics of the system, especially the mass accretion. These streams are suppressed in simulations with larger resistivities or lower field strengths, where most of the accretion instead occurs through a laminar disk. In these simulations, the disk accretion is driven mainly by a slow wind that is typically accelerated by the pressure gradient from a predominantly toroidal magnetic field; however, there are lightly mass-loaded regions that are accelerated magnetocentrifugally to speeds exceeding 100 km/s. Both the wind-dominated and stream-dominated modes of accretion create prominent features in the surface density distribution of the disk, with a strong spatial variation of the (poloidal) magnetic flux relative to the mass. Regions with low mass-to-flux ratios accrete quickly and lead to the development of gaps, whereas regions with higher mass-to-flux ratios accrete more slowly, allowing matter to accumulate and form dense rings. In some cases, avalanche accretion streams produce dense rings directly through continuous feeding.

In the second project, we retain the simplifying assumption of axisymmetry but focus on ambipolar diffusion (AD), the dominant non-ideal MHD effect at disk radii of tens of au or larger (scales that are observationally accessible using current facilities). We find that rings and gaps naturally develop in the AD-dominated disks as well. In particular, we find that disks which are moderately well-coupled to the magnetic field remain relatively laminar, with a radial electric current that is steepened by AD into a thin layer near the midplane. The toroidal magnetic field sharply reverses polarity in this layer, generating a large magnetic torque that drives fast accretion. The poloidal magnetic field is dragged inward through this accretion layer into a highly pinched radial configuration. The reconnection of this pinched field creates magnetic loops where the net poloidal magnetic flux (and thus the accretion rate) is reduced, yielding dense rings. Neighboring regions with stronger poloidal magnetic fields accrete faster, forming gaps. In better magnetically coupled simulations, the accretion streams develop continuously near the disk surface as before, rendering the disk-wind system more chaotic. Nevertheless, prominent rings and gaps are still produced by reconnection, which again enables the segregation of the poloidal field and the disk material. However, the reconnection is now driven by the non-linear growth of MRI channel flows.

In the last part of the thesis, we present ongoing work that extends the 2D (axisymmetric) simulations of AD-dominated disks to three dimensions (3D). We find that rings and gaps develop naturally in 3D from the same basic mechanism that was identified in 2D: namely, the redistribution of poloidal magnetic flux (relative to disk material) from the reconnection of sharply pinched poloidal magnetic field lines. There is still a clear anti-correlation between the mass surface density and the vertical magnetic flux through the disk midplane. The formation of rings and gaps proceeds in an axisymmetric fashion at early simulation times; non-axisymmetric variations arise spontaneously at later times, but they do not grow to such an extent as to disrupt the rings and gaps. These radial disk substructures persist through the full duration of the simulations, which run for thousands of orbital periods at the innermost edge of the simulated disks. The longevity of the azimuthally coherent rings make them attractive sites for trapping large grains that would otherwise rapidly migrate inward due to gas drag. We find that rings and gaps are formed over a range of ambipolar diffusivities and magnetic field strengths in 3D. They are more prominent in disks that are better coupled to the magnetic field and disks that are more strongly magnetized.