  Dense, star-forming, cores of molecular clouds are observed to be
significantly magnetized. A realistic magnetic field of moderate strength has
been shown to suppress, through catastrophic magnetic braking, the formation of
a rotationally supported disk during the protostellar accretion phase of
low-mass star formation in the ideal MHD limit. We address, through 2D
(axisymmetric) simulations, the question of whether realistic levels of
nonideal effects, computed with a simplified chemical network including dust
grains, can weaken the magnetic braking enough to enable a rotationally
supported disk to form. We find that ambipolar diffusion, the dominant nonideal
MHD effect over most of the density range relevant to disk formation, does not
enable disk formation, at least in 2D. The reason is that ambipolar diffusion
allows the magnetic flux that would be dragged into the central stellar object
in the ideal MHD limit to pile up instead in a small circumstellar region,
where the magnetic field strength (and thus the braking efficiency) is greatly
enhanced. We also find that, on the scale of tens of AU or more, a realistic
level of Ohmic dissipation does not weaken the magnetic braking enough for a
rotationally supported disk to form, either by itself or in combination with
ambipolar diffusion. The Hall effect, the least explored of these three
nonideal MHD effects, can spin up the material close to the central object to a
significant, supersonic rotation speed, even when the core is initially
non-rotating, although the spun-up material remains too sub-Keplerian to form a
rotationally supported disk. The problem of catastrophic magnetic braking that
prevents disk formation in dense cores magnetized to realistic levels remains
unresolved. Possible resolutions of this problem are discussed.
