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Disks are essential to the formation of both stars and planets, but how theyform in magnetized molecular cloud cores remains debated. This work focuses onhow the disk formation is affected by turbulence and ambipolar diffusion (AD),both separately and in combination, with an emphasis on the protostellar massaccretion phase of star formation. We find that a relatively strong, sonicturbulence on the core scale strongly warps but does not completely disrupt thewell-known magnetically-induced flattened pseudodisk that dominates the innerprotostellar accretion flow in the laminar case, in agreement with previouswork. The turbulence enables the formation of a relatively large disk at earlytimes with or without ambipolar diffusion, but such a disk remains stronglymagnetized and does not persist to the end of our simulation unless arelatively strong ambipolar diffusion is also present. The AD-enabled disks inlaminar simulations tend to fragment gravitationally. The disk fragmentation issuppressed by initial turbulence. The ambipolar diffusion facilitates the diskformation and survival by reducing the field strength in the circumstellarregion through magnetic flux redistribution and by making the field lines thereless pinched azimuthally, especially at late times. We conclude that turbulenceand ambipolar diffusion complement each other in promoting disk formation. Thedisks formed in our simulations inherit a rather strong magnetic field from itsparental core, with a typical plasma-$\beta$ of order a few tens or smaller,which is 2-3 orders of magnitude lower than the values commonly adopted in MHDsimulations of protoplanetary disks. To resolve this potential tension,longer-term simulations of disk formation and evolution with increasingly morerealistic physics are needed.

Disk Formation in Magnetized Dense Cores with Turbulence and Ambipolar Diffusion