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The role of non-ideal magnetohydrodynamics has been proven critical duringthe formation of the protoplanetary disk, particularly in regulating its size.We provide a simple model to predict the disk size under the interplay amongthe ambipolar diffusion, the Hall effect, and the Ohmic dissipation. The modelpredicts a small disk size of around 20 AU, that depends only sub-linearly ondisk parameters, for a wide range of initial conditions of sub-Solar mass andmoderate magnetization. It is able to explain phenomena manifested in existingnumerical simulations, including the bimodal disk behavior under parallel andanti-parallel alignment between the rotation and magnetic field. In theparallel configuration, the disk size decreases and eventually disappears. Inthe anti-parallel configuration, and the disk has an outer partition (orpseudo-disk) that is flat, shrinking , and short-lived, as well as a innerpartition that grows slowly with mass and is long-lived. Even with significantinitial magnetization, the vertical field in the disk can only dominate at theearly stage when the mass is low, and the toroidal field eventually dominatesin all disks.

astrophysical journal/the astrophysical journal

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