Recent OH Zeeman Observations: Do they Really Contradict the Ambipolar-Diffusion Theory of Star Formation?

Until recently, many of the dozens of quantitative predictions of the ambipolar-diffusion theory of gravitational fragmentation (or core formation) of molecular clouds have been confirmed by observations and, just as importantly, no prediction has been contradicted by any observation. A recent paper, however, claims that measurements of the variation of the mass-to-flux ratio from envelopes to cores in four clouds {\it de}creases, in direct contrast to a prediction of the theory but in agreement with turbulent fragmentation (in the absence of gravity) and, therefore, the ambipolar-diffusion theory is invalid (Crutcher et al 2008). The paper treats magnetic-field nondetections as if they were detections. We show that the analysis of the data is fundamentally flawed and, moreover, the comparison with the theoretical prediction ignores major geometrical effects, suggested by the data themselves if taken at face value. The magnetic fluxes of the envelopes are also miscalculated. We carry out a proper error analysis and treatment of the nondetections and we show that the claimed measurement of the variation of the mass-to-flux ratio from envelopes to cores is not valid, no contradiction with the ambipolar-diffusion theory can be concluded, and no theory can be tested on the basis of these data.