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Hydrodynamic supersonic turbulence can only prevent local gravitationalcollapse if the turbulence is driven on scales smaller than the local Jeanslengths in the densest regions, a very severe requirement (Paper I). Magneticfields have been suggested to support molecular clouds either magnetostaticallyor via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would formsheet-like clouds, the second mechanism not only could exert a pressure ontothe gas counteracting the gravitational forces, but could lead to a transfer ofturbulent kinetic energy down to smaller spatial scales via MHD waveinteractions. This turbulent magnetic cascade might provide sufficient energyat small scales to halt local collapse.  We test this hypothesis with MHD simulations at resolutions up to 256^3zones, done with ZEUS-3D. We first derive a resolution criterion forself-gravitating, magnetized gas: in order to prevent collapse ofmagnetostatically supported regions due to numerical diffusion, the minimumJeans length must be resolved by four zones. Resolution of MHD waves increasesthis requirement to roughly six zones. We then find that magnetic fields cannotprevent local collapse unless they provide magnetostatic support. Weakermagnetic fields do somewhat delay collapse and cause it to occur more uniformlyacross the supported region in comparison to the hydrodynamical case. However,they still cannot prevent local collapse for much longer than a globalfree-fall time.Comment: 32 pages, 14 figures, accepted by Ap

Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence