Disk Formation in Magnetized Dense Cores with Turbulence and Ambipolar
  Diffusion
  Disks are essential to the formation of both stars and planets, but how they
form in magnetized molecular cloud cores remains debated. This work focuses on
how the disk formation is affected by turbulence and ambipolar diffusion (AD),
both separately and in combination, with an emphasis on the protostellar mass
accretion phase of star formation. We find that a relatively strong, sonic
turbulence on the core scale strongly warps but does not completely disrupt the
well-known magnetically-induced flattened pseudodisk that dominates the inner
protostellar accretion flow in the laminar case, in agreement with previous
work. The turbulence enables the formation of a relatively large disk at early
times with or without ambipolar diffusion, but such a disk remains strongly
magnetized and does not persist to the end of our simulation unless a
relatively strong ambipolar diffusion is also present. The AD-enabled disks in
laminar simulations tend to fragment gravitationally. The disk fragmentation is
suppressed by initial turbulence. The ambipolar diffusion facilitates the disk
formation and survival by reducing the field strength in the circumstellar
region through magnetic flux redistribution and by making the field lines there
less pinched azimuthally, especially at late times. We conclude that turbulence
and ambipolar diffusion complement each other in promoting disk formation. The
disks formed in our simulations inherit a rather strong magnetic field from its
parental 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 MHD
simulations of protoplanetary disks. To resolve this potential tension,
longer-term simulations of disk formation and evolution with increasingly more
realistic physics are needed.
