Universal protoplanetary disk size under complete non-ideal magnetohydrodynamics: The interplay between ion-neutral friction, Hall effect, and the Ohmic dissipation

TL;DR

This paper presents a simple model predicting protoplanetary disk sizes considering non-ideal MHD effects, explaining observed phenomena and disk behaviors under various magnetic alignments.

Contribution

The model integrates ambipolar diffusion, Hall effect, and Ohmic dissipation to predict disk sizes, explaining bimodal behaviors seen in simulations under different magnetic alignments.

Findings

Predicted disk size around 20 AU for various initial conditions.

Explained bimodal disk behavior in parallel and anti-parallel magnetic configurations.

Showed the dominance of toroidal magnetic fields over vertical fields during disk evolution.

Abstract

The role of non-ideal magnetohydrodynamics has been proven critical during the formation of the protoplanetary disk, particularly in regulating its size. We provide a simple model to predict the disk size under the interplay among the ambipolar diffusion, the Hall effect, and the Ohmic dissipation. The model predicts a small disk size of around 20 AU, that depends only sub-linearly on disk parameters, for a wide range of initial conditions of sub-Solar mass and moderate magnetization. It is able to explain phenomena manifested in existing numerical simulations, including the bimodal disk behavior under parallel and anti-parallel alignment between the rotation and magnetic field. In the parallel configuration, the disk size decreases and eventually disappears. In the anti-parallel configuration, and the disk has an outer partition (or pseudo-disk) that is flat, shrinking , and short-lived, as well as a inner partition that 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.