  Isolated low-mass stars are formed in dense cores of molecular clouds. In the
standard picture, the cores are envisioned to condense out of strongly
magnetized clouds through ambipolar diffusion. Most previous calculations based
on this scenario are limited to axisymmetric cloud evolution leading to a
single core, which collapses to form an isolated star or stellar system at the
center. These calculations are here extended to the nonaxisymmetric case under
thin-disk approximation, which allows for a detailed investigation into the
process of fragmentation, fundamental to binary, multiple system, and cluster
formation. We have shown previously that initially axisymmetric, magnetically
subcritical clouds with an $m=2$ density perturbation of modest fractional
amplitude ($\sim 5%$) can develop highly elongated bars, which facilitate
binary and multiple system formation. In this paper, we show that in the
presence of higher order ($m\ge 3$) perturbations of similar amplitude such
clouds are capable of breaking up into a set of discrete dense cores. These
multiple cores are magnetically supercritical. They are expected to collapse
into single stars or stellar systems individually and, collectively, to form a
small stellar group. Our calculations demonstrate that the standard scenario
for single star formation involving magnetically subcritical clouds and
ambipolar diffusion can readily produce more than one star, provided that the
cloud mass is well above the Jeans limit and relatively uniformly distributed.
The fragments develop in the central part of the cloud, after the region has
become magnetically supercritical but before rapid collapse sets in. It is
enhanced by the flattening of mass distribution along the field lines and by
the magnetic tension force.

Astrophysics