  Hydrodynamic supersonic turbulence can only prevent local gravitational
collapse if the turbulence is driven on scales smaller than the local Jeans
lengths in the densest regions, a very severe requirement (Paper I). Magnetic
fields have been suggested to support molecular clouds either magnetostatically
or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form
sheet-like clouds, the second mechanism not only could exert a pressure onto
the gas counteracting the gravitational forces, but could lead to a transfer of
turbulent kinetic energy down to smaller spatial scales via MHD wave
interactions. This turbulent magnetic cascade might provide sufficient energy
at small scales to halt local collapse.
  We test this hypothesis with MHD simulations at resolutions up to 256^3
zones, done with ZEUS-3D. We first derive a resolution criterion for
self-gravitating, magnetized gas: in order to prevent collapse of
magnetostatically supported regions due to numerical diffusion, the minimum
Jeans length must be resolved by four zones. Resolution of MHD waves increases
this requirement to roughly six zones. We then find that magnetic fields cannot
prevent local collapse unless they provide magnetostatic support. Weaker
magnetic fields do somewhat delay collapse and cause it to occur more uniformly
across the supported region in comparison to the hydrodynamical case. However,
they still cannot prevent local collapse for much longer than a global
free-fall time.
