We investigate protostellar collapse of molecular cloud cores by numerical simulations, taking into account turbulence and magnetic fields. By using the adaptive mesh refinement technique, the collapse is followed over a wide dynamic range from the scale of a turbulent cloud core to that of the first core. The cloud core is lumpy in the low density region owing to the turbulence, while it has a smooth density distribution in the dense region produced by the collapse. The shape of the dense region depends mainly on the mass of the cloud core; a massive cloud core tends to be prolate while a less massive cloud core tends to be oblate. In both cases, anisotropy of the dense region increases during the isothermal collapse. The minor axis of the dense region is always oriented parallel to the local magnetic field. All the models eventually yield spherical first cores supported mainly by the thermal pressure. Most of turbulent cloud cores exhibit protostellar outflows around the first cores. These outflows are classified into two types, bipolar and spiral flows, according to the morphology of the associated magnetic field. Bipolar flow often appears in the less massive cloud core. The rotation axis of the first core is oriented parallel to the local magnetic field for bipolar flow, while the orientation of the rotation axis from the global magnetic field depends on the magnetic field strength. In spiral flow, the rotation axis is not aligned with the local magnetic field.
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