Universal Protoplanetary Disk Size under Complete Nonideal Magnetohydrodynamics: The Interplay between Ion-neutral Friction, Hall Effect, and Ohmic Dissipation

The role of nonideal magnetohydrodynamics has been proven critical during the formation of protoplanetary disks, particularly in regulating their sizes. We provide a simple model to predict the disk size under the interplay among ambipolar diffusion, the Hall effect, and ohmic dissipation. The model predicts a small disk size of around 20 au that depends only sublinearly on disk parameters, for a wide range of initial conditions of subsolar mass and moderate magnetization. It is able to explain phenomena manifested in existing numerical simulations, including the bimodal disk behavior under parallel and antiparallel alignment between the rotation and magnetic field. In the parallel configuration, the disk size decreases and eventually disappears. In the antiparallel configuration, the disk has an outer partition (or pseudodisk), which is flat, shrinking, and short-lived, as well as an inner partition, which grows slowly with mass and is long-lived. Even with significant initial magnetization, the vertical field in the disk can only dominate at the early stage when the mass is low, and the toroidal field eventually dominates in all disks.