Binary and Multiple Star Formation in Magnetic Clouds: Bar Growth and Fragmentation

In the standard scenario of isolated low-mass star formation, strongly magnetized molecular clouds are envisioned to condense gradually into dense cores, driven by ambipolar diffusion. Once the cores become magnetically supercritical, they collapse to form stars. Previous studies based on this scenario are limited to axisymmetric calculations leading to single supercritical core formation. The assumption of axisymmetry has precluded a detailed investigation of cloud fragmentation, generally thought to be a necessary step in the formation of binary and multiple stars. In a series of papers, we studied the non-axisymmetric evolution of initially magnetically subcritical clouds, using a two-dimensional magnetohydrodynamic code based on the physically motivated thin-disk approximation. We found that such clouds become unstable to non-axisymmetric perturbations after the supercritical cores are formed due to ambipolar diffusion. In this paper, we focus on the evolution of clouds perturbed by an m = 2 mode of a modest fractional amplitude of 5%, with an eye on binary and multiple star formation. We show that for a wide range of initial cloud parameters, the m = 2 mode grows nonlinearly into a bar during the isothermal collapse after the supercritical core formation. The instability is driven by the domination of the magnetically-diluted gravity over the combined thermal and magnetic pressure gradient in the supercritical cores. Such gravity-dominated cores can break up into fragments during or after the isothermal phase of cloud evolution. The outcome of fragmentation depends on the initial cloud conditions, such as the magnetic field strength, rotation rate, amount of cloud mass (relative to thermal Jeans mass) and mass distribution. It is classified into three different types: (1) separate core formation, in which the bar (m = 2) mode breaks up into two separate cores during the isothermal collapse, with a core separation of order 10 AU, (2) bar fragmentation, in which the m = 2 mode evolves into a needle-like, opaque “first bar” (at a density n ∼> 10 12 cm), which breaks up into multiple fragments with initial masses of order 10 M⊙ and separations of order 10-10 AU, and (3) disk fragmentation, in which the bar growth remains slow during the isothermal collapse and the central region evolves into a rapidly rotating, opaque “first disk”, which breaks up into several self-gravitating blobs with separations less than the disk size (∼< 10 2 AU). These three types of fragmentation loosely correspond to the empirical classification of embedded binary and multiple systems of Looney, Mundy, & Welch, based on millimeter dust continuum observations. The well-studied starless core, L1544, appears to belong to the bar fragmentation type. We expect it to produce a highly elongated, opaque bar at the center in the future, which should break up into fragments of initial masses in the substellar regime. Subject headings: binaries: formation — ISM: clouds — ISM: magnetic fields — MHD — stars: formation