  Stars form in dense cores of molecular clouds that are observed to be
significantly magnetized. A dynamically important magnetic field presents a
significant obstacle to the formation of protostellar disks. Recent studies
have shown that magnetic braking is strong enough to suppress the formation of
rotationally supported disks in the ideal MHD limit. Whether non-ideal MHD
effects can enable disk formation remains unsettled. We carry out a first study
on how disk formation in magnetic clouds is modified by the Hall effect, the
least explored of the three non-ideal MHD effects in star formation (the other
two being ambipolar diffusion and Ohmic dissipation). For illustrative
purposes, we consider a simplified problem of a non-self-gravitating,
magnetized envelope collapsing onto a central protostar of fixed mass. We find
that the Hall effect can spin up the inner part of the collapsing flow to
Keplerian speed, producing a rotationally supported disk. The disk is generated
through a Hall-induced magnetic torque. Disk formation occurs even when the
envelope is initially non-rotating, provided that the Hall coefficient is large
enough. When the magnetic field orientation is flipped, the direction of disk
rotation is reversed as well. The implication is that the Hall effect can in
principle produce both regularly rotating and counter-rotating disks around
protostars. We conclude that the Hall effect is an important factor to consider
in studying the angular momentum evolution of magnetized star formation in
general and disk formation in particular.
