Most molecular clouds are filamentary or elongated. For those forming low-mass stars (<8 solar masses), the competition between self-gravity and turbulent pressure along the dynamically dominant intercloud magnetic field (10 to 100 parsecs) shapes the clouds to be elongated either perpendicularly or parallel to the fields. A recent study also suggested that on the scales of 0.1 to 0.01 parsecs, such fields are dynamically important within cloud cores forming massive stars (>8 solar masses). But whether the core field morphologies are inherited from the intercloud medium or governed by cloud turbulence is unknown, as is the effect of magnetic fields on cloud fragmentation at scales of 10 to 0.1 parsecs. Here we report magnetic-field maps inferred from polarimetric observations of NGC 6334, a region forming massive stars, on the 100 to 0.01 parsec scale. NGC 6334 hosts young star-forming sites where fields are not severely affected by stellar feedback, and their directions do not change much over the entire scale range. This means that the fields are dynamically important. The ordered fields lead to a self-similar gas fragmentation: at all scales, there exist elongated gas structures nearly perpendicular to the fields. Many gas elongations have density peaks near the ends, which symmetrically pinch the fields. The field strength is proportional to the 0.4th power of the density, which is an indication of anisotropic gas contractions along the field. We conclude that magnetic fields have a crucial role in the fragmentation of NGC 6334.

We identify velocity channel map intensities as a new way to trace magnetic fields in turbulent media. This work makes use of both of the modern theory of MHD turbulence predicting that the magnetic eddies are aligned with the local direction of magnetic field, and also the theory of the spectral line Position-Position-Velocity (PPV) statistics describing how the velocity and density fluctuations are mapped into the PPV space. In particular, we use the fact that, the fluctuations of intensity of thin channel maps are mostly affected by the turbulent velocity, while the thick maps are dominated by density variations. We study how contributions of the fundamental MHD modes affect the Velocity Channel Gradients (VChGs) and demonstrate that the VChGs arising from Alfven and slow modes are aligned perpendicular to the local direction of magnetic field, while the VChGs produced by the fast mode are aligned parallel to the magnetic field. The dominance of the Alfven and slow modes in the interstellar media will therefore allow a reliable magnetic field tracing using the VChGs. We explore ways of identifying self-gravitating regions that do not require polarimetric information. In addition, we also introduce a new measure termed "Reduced Velocity Centroids" (RVCGs) and compare its abilities with the VChGs. We employed both measures to the GALFA 21cm data and successfully compared thus magnetic field directions with the PLANCK polarization. The applications of the suggested techniques include both tracing magnetic field in diffuse interstellar media and star forming regions, as well as removing the galactic foreground in the framework of cosmological polarization studies. 1 The idea behind the studies, which is employing the PCA is the same and, in fact, our study in Correia et al. (2016) shows that there is no practical advantage of using the PCA compared to the velocity centroids. On the contrary, the anisotropies of centroids, unlike the PCA eigen-images, are analytically related to the properties of the underlying turbulence, i.e. to the properties of the Alfven, slow and fast modes that constitute the MHD cascade (see Kandel et al. 2017a). This opens prospects of separating the contribution of the compressible (slow and fast) and the in-compressible (Alfven) modes using velocity centroids.2 By itself, the IGs were shown to be inferior to the VCGs in the ability of tracing magnetic field (GL17, YL17a,b), but synergistic in terms of studying shocks and regions dominated by self-gravity.

Magnetic fields, while ubiquitous in many astrophysical environments, are challenging to measure observationally. Based on the properties of anisotropy of eddies in magnetized turbulence, the Velocity Gradient Technique is a method synergistic to dust polarimetry that is capable of tracing plane-of-the-sky magnetic field, measuring the magnetization of interstellar media and estimating the fraction of gravitational collapsing gas in molecular clouds using spectral line observations. In this paper, we apply this technique to five low-mass star-forming molecular clouds in the Gould Belt and compare the results to the magnetic-field orientation obtained from polarized dust emission. We find the estimates of magnetic field orientations and magnetization for both methods are statistically similar. We estimate the fraction of collapsing gas in the selected clouds. By means of the Velocity Gradient Technique, we also present the plane-of-the-sky magnetic field orientation and magnetization of the Smith cloud, for which dust polarimetry data are unavailable.

On the basis of the modern understanding of MHD turbulence, we propose a new way of using synchrotron radiation, namely using synchrotron intensity gradients for tracing astrophysical magnetic fields. We successfully test the new technique using synthetic data obtained with the 3D MHD simulations and provide the demonstration of the practical utility of the technique by comparing the directions of magnetic field that are obtained with PLANCK synchrotron intensity datas to the directions obtained with PLANCK synchrotron polarization data. We demonstrate that the synchrotron intensity gradients (SIGs) can reliably trace magnetic field in the presence of noise and can provide detailed maps of magnetic-field directions. We also show that the SIGs are relatively robust for tracing magnetic fields while the low spacial frequencies of the synchrotron image are removed. This makes the SIGs applicable to tracing of magnetic fields using interferometric data with single dish measurement absent. We discuss the synergy of using the SIGs together with synchrotron polarization in order to find the actual direction of the magnetic field and quantify the effects of Faraday rotation as well as with other ways of studying astrophysical magnetic fields. We test our method in the presence of noise and the resolution effects. We stress the complementary nature of the studies using the SIG technique and those employing the recently-introduced velocity gradient techniques that traces the magnetic fields using spectroscopic data.