  A crucial missing ingredient in previous theoretical studies of fragmentation
is the inclusion of dynamically important levels of magnetic fields. As a
minimal model for a candidate presursor to the formation of binary and multiple
stars, we therefore consider the equilibrium configuration of isopedically
magnetized, scale-free, singular isothermal disks, without the assumption of
axial symmetry. We find that lopsided (M=1) configurations exist at any
dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...)
configurations bifurcate from an underlying axisymmetric sequence at
progressively higher dimensionless rates of rotation, but such nonaxisymmetric
sequences always terminate in shockwaves before they have a chance to fission
into separate bodies. We advance the hypothesis that binary and multiple
star-formation from smooth (i.e., not highly turbulent) starting states that
are supercritical but in unstable mechanical balance requires the rapid (i.e.,
dynamical) loss of magnetic flux at some stage of the ensuing gravitational
collapse.
