Gravitational Collapse of Filamentary Magnetized Molecular Clouds

We develop models for the self-similar collapse of magnetized isothermalcylinders. We find solutions for the case of a fluid with a constant toroidalflux-to-mass ratio (Gamma_phi=constant) and the case of a fluid with a constantgas to magnetic pressure ratio (beta=constant). In both cases, we find that alow magnetization results in density profiles that behave as rho ~ r^{-4} atlarge radii, and at high magnetization we find density profiles that behave asrho ~ r^{-2}. This density behaviour is the same as for hydrostatic filamentarystructures, suggesting that density measurements alone cannot distinguishbetween hydrostatic and collapsing filaments--velocity measurements arerequired. Our solutions show that the self-similar radial velocity behaves asv_r ~ r during the collapse phase, and that unlike collapsing self-similarspheres, there is no subsequent accretion (i.e. expansion-wave) phase. We alsoexamine the fragmentation properties of these cylinders, and find that in bothcases, the presence of a toroidal field acts to strengthen the cylinder againstfragmentation. Finally, the collapse time scales in our models are shorter thanthe fragmentation time scales. Thus, we anticipate that highly collapsedfilaments can form before they are broken into pieces by gravitationalfragmentation.Comment: 20 pages, 4 figures, accepted to Ap