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