ar X iv : a st ro - p h / 07 01 21 0 v 1 8 J an 2 00 7 Collapse and Fragmentation of Molecular Cloud Cores . IX . Magnetic Braking of Initially

The collapse and fragmentation of initially filamentary, magnetic molecular clouds is calculated in three dimensions with a gravitational, radiative hydrodynamics code. The code includes magnetic field effects in an approximate manner: magnetic pressure, tension, braking, and ambipolar diffusion are all modelled. The parameters varied are the ratio of the ambipolar diffusion time to the free fall time at the center of the filamentary cloud (tad/tff = 10, 20, or 10 6 ∼ ∞), the cloud’s reference magnetic field strength (Boi = 0, 200, or 300 microgauss – the latter two values leading to magnetically subcritical clouds), the ratio of rotational to gravitational energy of the filament (10 or 10), and the efficiency of magnetic braking (represented by a factor fmb = 0, 10 , or 10). Three types of outcomes are observed: direct collapse and fragmentation into a multiple protostar system (models with Boi = 0), periodic contraction and expansion without collapse (models with tad/tff = 10 ), or periodic contraction and expansion leading eventually to collapse on a time scale of ∼ 6 to 12 tff (all other models). Because the computational grid is a finite volume sphere, the expanding clouds bounce off the spherical boundary and re-collapse toward the center of the spherical grid, leading to the periodic formation of shocked regions where the infalling gas collides with itself, forming dense layers susceptible to sustained collapse and eventual fragmentation. While the models begin their evolution at rest except for the assumed solid-body rotation, they develop weakly supersonic velocity fields as a result of the rebounding prior to collapse. The models show that magnetically-supported clouds subject to magnetic braking can undergo dynamic collapse leading to protostellar fragmentation on scales of 10 AU to 100 AU, consistent with typical binary star separations. Subject headings: hydrodynamics — ISM: clouds — ISM: kinematics and dynamics — MHD — stars: formation