Magnetic fields in interstellar clouds from zeeman observations: Inference of total field strengths by bayesian analysis

The only direct measurements of interstellar magnetic field strengths depend on the Zeeman effect, which samples the line-of-sight component B _z of the magnetic vector. In this paper, we use a Bayesian approach to analyze the observed probability density function (PDF) of Bz from Zeeman surveys of Hi, OH, and CN spectral lines in order to infer a density-dependent stochastic model of the total field strength B in diffuse and molecular clouds. We find that at n > 300 cm^-3 (in the diffuse interstellar medium sampled by Hi lines), B does not scale with density. This suggests that diffuse clouds are assembled by flows along magnetic field lines, which would increase the density but not the magnetic field strength. We further find strong evidence for B in molecular clouds being randomly distributed between very small values and a maximum that scales with volume density n as B ∝ n^0.65 for n ≥ 300 cm^-3, with an uncertainty at the 50% level in the power-law exponent of about ±0.05. This break-point density could be interpreted as the average density at which parsec-scale clouds become self-gravitating. Both the uniform PDF of total field strengths and the scaling with density suggest that magnetic fields in molecular clouds are often too weak to dominate the star formation process. The stochasticity of the total field strength B implies that many fields are so weak that the mass/flux ratio in many clouds must be significantly supercritical. A two-thirds power law comes from isotropic contraction of gas too weakly magnetized for the magnetic field to affect the morphology of the collapse. On the other hand, our study does not rule out some clouds having strong magnetic fields with critical mass/flux ratios.