The Super-Alfv\'enic Model of Molecular Clouds: Predictions for Zeeman Splitting Measurements

We present synthetic OH Zeeman splitting measurements of a super-Alfvenic model of molecular clouds. We select dense cores from synthetic 13CO maps computed from the largest simulation to date of supersonic and super-Alfvenic turbulence. The synthetic Zeeman splitting measurements in the cores yield a relation between the magnetic field strength, B, and the column density, N, in good agreement with the observations. The large scatter in B at a fixed value of N is partly due to intrinsic variations in the magnetic field strength from core to core. We also compute the relative mass-to-flux ratio between the center of the cores and their envelopes, ${\cal R}_{\mu}$, and show that super-Alfvenic turbulence produces a significant scatter also in ${\cal R}_{\mu}$, including negative values (field reversal between core center and envelope). We find ${\cal R}_{\mu}<1$ for 70% of the cores, and ${\cal R}_{\mu}<0$ for 12%. Of the cores with $|B_{\rm LOS}|>10$ \muG, 81% have ${\cal R}_{\mu}<1$. These predictions of the super-Alfvenic model are in stark contrast to the ambipolar drift model of core formation, where only ${\cal R}_{\mu}>1$ is allowed.