Magnetic Fields in Molecular Cloud Cores

Observations of magnetic field strengths imply that molecular cloud fragments are individually close to being in a magnetically critical state, even though both magnetic field and column density measurements range over two orders of magnitude. The turbulent pressure also approximately balances the self-gravitational pressure. These results together mean that the one-dimensional velocity dispersion $\sigv$ is proportional to the mean \Alf speed of a cloud $\va$. Global models of MHD turbulence in a molecular cloud show that this correlation is naturally satisfied for a range of different driving strengths of the turbulence. For example, an increase of turbulent driving causes a cloud expansion which also increases $\va$. Clouds are in a time averaged balance but exhibit large oscillatory motions, particularly in their outer rarefied regions. We also discuss models of gravitational fragmentation in a sheet-like region in which turbulence has already dissipated, including the effects of magnetic fields and ion-neutral friction. Clouds with near-critical mass-to-flux ratios lead to subsonic infall within cores, consistent with some recent observations of motions in starless cores. Conversely, significantly supercritical clouds are expected to produce extended supersonic infall.