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The Zeeman effect has been the only method to directly probe the magnetic field strength in molecular clouds. The Bayesian analysis of Zeeman measurements carried out by Crutcher et al. is the only reference for cloud magnetic field strength. Here we extended their model and Bayesian analysis of the relation between field strength (B) and volume density (n) in the following three directions based on the recent observational and theoretical development. First, we take R, the observational uncertainty of n, as a parameter to be estimated from data. Second, the restriction of α, the index of the B–n relationship, is relieved from [0, 0.75] to [0, 1]. Third, we allow f, the minimum-to-maximum B ratio, to vary with n. Our results show that taking R as a parameter provides a better fitting to the B–n relationship and much more reliable estimates on R, f, and the changing point of α. Arguably our most important finding is that α cannot be reliably estimated by any of the models studied here, either from us or Crutcher et al., if R > 2, which is indeed the case from our estimate. This is the so-called errors-in-variables bias, a well known problem for statisticians. [ABSTRACT FROM AUTHOR]

The line width of ions has been observed to be systematically narrower than that of the coexisting neutrals in molecular clouds and been interpreted as the signature of the decoupling of the neutral turbulence from magnetic fields in partially ionized medium. As a sequel of Li & Houde, here we present further observational evidence that supports these earlier proposals with the velocity coordinate spectrum analysis. We recover the turbulent energy spectra of HCN and HCO+ (4 − 3) in a starless molecular cloud in NGC 6334 where magnetic fields play a dynamically important role. Our analysis showed that the neutral spectrum is consistent with Kolmogorov type (, where k is the wavenumber), while that of the ions is the same on the large scale, but steeper (∼k−2), for scales smaller than 0.404 pc. We carefully ruled out the possibilities that the spectrum difference can stem from the differences of ion and neutral optical depth and hyperfine structure. [ABSTRACT FROM AUTHOR]

The complex interplay between turbulence, magnetic fields, and self-gravity leads to the formation of molecular clouds out of the diffuse interstellar medium (ISM). One avenue of studying this interplay is by analyzing statistical features derived from observations, where the interpretation of these features is greatly facilitated by comparisons with numerical simulations. Here we focus on the statistical anisotropy present in synthetic maps of velocity centroid data, which we derive from three-dimensional magnetohydrodynamic simulations of a turbulent, magnetized, self-gravitating patch of ISM. We study how the orientation and magnitude of the velocity anisotropy correlate with the magnetic field and with the structures generated by gravitational collapse. Motivated by recent observational constraints, our simulations focus on the supersonic (sonic Mach number ) but sub- to trans-alfvénic (alfvénic Mach number ) turbulence regime, and we consider clouds that are barely to mildly magnetically supercritical (mass-to-flux ratio equal to once or twice the critical value). Additionally we explore the impact of the turbulence driving mechanism (solenoidal or compressive) on the velocity anisotropy. While we confirm previous findings that the velocity anisotropy generally aligns well with the plane-of-sky magnetic field, our inclusion of the effects of self-gravity reveals that in regions of higher column density, the velocity anisotropy may be destroyed or even reoriented to align with the gravitationally formed structures. We provide evidence that this effect is not necessarily due to the increase of inside the high-density regions. [ABSTRACT FROM AUTHOR]