Parallel and perpendicular alignments of velocity gradient and magnetic field observed in the molecular clouds L1478 and L1482

Understanding how star formation is regulated requires studying the energy balance between turbulence, magnetic fields, stellar feedback, and gravity within molecular clouds. However, identifying the transition region where the gravity takes over remains elusive. Recent studies of the Velocity Gradient Technique (VGT), which is an advanced tool for magnetic field studies, reveal that the gradients of spectroscopic observables change their directions by 90° with respect to the magnetic fields in the regions of gravitational collapse. In this study, we perform 3D MHD numerical simulations. We observe that star formation successfully proceeds in strongly magnetized and fully ionized media. We confirm that the self-gravity induces the change of gradients’ orientation and gradients’ high amplitude. We explore two ways of identifying collapsing self-gravitating regions through the double-peak feature in the histogram of gradients’ orientation and the curvature of gradients. We show that velocity gradients’ morphology and amplitude can be synthetically used to trace the convergent inflows. By comparing with the column density Probability Density Functions method, we show that VGT is a powerful new tool for studying the gas dynamics and tracing magnetic field in star-forming regions. By analogy with VGT, we extend the Intensity Gradient Technique (IGT) to locate the gravitational collapsing region and shocks. We demonstrate that the synergy of VGT and IGT can determine the collapsing stages in a star-forming region.

Magnetic fields and turbulence are fundamental to the evolutions of galaxies, yet their precise measurement and analysis present significant challenges. The recently developed Velocity Gradient Technique (VGT), which capitalizes on the anisotropy inherent in magnetohydrodynamic (MHD) turbulence, represents a new method for mapping magnetic fields in galaxies using spectroscopic observations. Most validations of VGT thus far have relied upon idealized MHD turbulence simulations, however, which lack the more complex dynamics found in galaxies and galaxy mergers. In this study, we scrutinize VGT using an AREPO-based cosmological galaxy merger simulation, testing its effectiveness across pre-merger, merging, and post-merger stages. We examine the underlying assumptions of VGT and probe the statistics of gas density, velocity, and magnetic fields over time. We find that the velocity fluctuations are indeed anisotropic at each stage, being larger in the direction perpendicular to the local magnetic field, as required by VGT. We find additionally that galaxy mergers substantially intensify the velocity and density fluctuations and amplify the magnetic fields at all scales. The observed scaling of the velocity fluctuations shows a steeper trend than r 1/2 between 0.6 and 3 kpc and a shallower trend at larger scales. The scaling of the magnetic field and density fluctuations at scales ≲1.0 kpc also predominantly aligns with r 1/2. Finally, we compare results from VGT to those derived from polarization-like mock magnetic field measurements, finding consistent and statistically significant global agreement in all cases.

The recent development of the velocity gradient technique allows observers to map magnetic field orientations and magnetization using the direction of velocity gradients. Aside from the directions, amplitudes of velocity gradients also contain valuable information about the underlying properties of magnetohydrodynamic (MHD) turbulence. In this paper, we explore what physical information is contained in the amplitudes of velocity gradients and discuss how this information can be used to diagnose properties of turbulence in both diffuse and self-gravitating interstellar media. We identify the relations between amplitudes of both intensity and velocity centroid gradients and the sonic Mach number M s , and they are consistent with the theory’s predictions. We test the robustness of the method and discuss how to utilize the amplitudes of gradients into self-gravitating media. To extend the velocity gradient technique, we also discuss the usage of amplitude method to position–position–velocity space as a possible way to retrieve the velocity channel maps before the contamination of thermal broadening. We discuss that the velocity gradient technique with these advancements could potentially give a significantly more accurate statistical insight into the properties of magnetized turbulence.

As a novel approach for tracing interstellar magnetic fields, the velocity gradient technique (VGT) has been proven to be effective for probing magnetic fields in the diffuse interstellar medium (ISM). In this work, we verify the VGT in a broader context by applying the technique to a molecular cloud interacting with the supernova remnant (SNR) W44. We probe the magnetic fields with the VGT using CO, $\rm HCO^+$ and H i emission lines and make a comparison with the Planck 353-GHZ dust polarization. We show that the VGT gives an accurate measurement that coheres with the Planck polarization especially in intense molecular gas emission regions. We further study the foreground’s contribution on the polarization that results in misalignment between the VGT and the Planck measurements in low-intensity molecular gas areas. We advance the VGT to achieve magnetic field tomography by decomposing the SNR W44 into various velocity components. We show that W44’s velocity component at v ∼ 45 km s−1 exhibits the largest coverage and gives best agreement with Planck polarization in terms of magnetic field orientation.

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.

Probing magnetic fields in Giant Molecular Clouds is often challenging. Fortunately, recently simulations show that analysis of velocity gradients (the Velocity Gradient Technique) can be used to map out the magnetic field morphology of different physical layers within molecular clouds when applied CO isotopologues with different optical depths. Here, we test the effectiveness of the Velocity Gradient Technique in reconstructing the magnetic field structure of the molecular cloud Vela C, employing seven chemical tracers that have different optical depths, i.e. 12CO, 13CO, C18O, CS, HNC, HCO+, and HCN. Our results show good correspondence between the magnetic field morphology inferred from velocity gradients using these different molecular tracers and the magnetic field morphology inferred from BLASTPol polarization observations. We also explore the possibility of using a combination of velocity gradients for multiple chemical tracers to explain the structure of the magnetic field in molecular clouds. We search for signatures of gravitational collapse in the alignment of the velocity gradients and magnetic field and conclude that collapsing regions constitute a small fraction of the cloud.

Based on high-resolution 3D data cubes from a magnetohydrodynamic (MHD) turbulence simulation, we study how to reveal the direction of the magnetic field within the optically thick interstellar medium by using the velocity gradient technique (VGT), correlation function anisotropy (CFA), and principal component analysis of anisotropies (PCAA). Considering the CO molecular tracers as a tracing method for radiative transfer processes, we find that the VGT and CFA can successfully trace the orientation of mean magnetic fields, which is in good agreement with the low-resolution numerical results obtained in the case of an optically thin medium. Similar to the simulation of an optically thin ISM, our simulations show that PCCA is still unusable in optically thick media. The synergetic application of the VGT and CFA to high-resolution spectroscopic observations is expected to yield valuable information on the interstellar magnetic field.

Probing magnetic fields in self-gravitating molecular clouds is generally difficult, even with the use of polarimetry. Based on the properties of magnetohydrodynamic turbulence and turbulent reconnection, the velocity gradient technique (VGT) provides a new way of tracing magnetic field orientation and strength based on spectroscopic data. Our study tests the applicability of VGT in various molecular tracers, e.g., 12CO, 13CO, and C18O. By inspecting synthetic molecular-line maps of CO isotopologs generated through radiative transfer calculations, we show that the VGT can be successfully applied in probing the magnetic field direction in the diffuse interstellar medium, as well as in self-gravitating molecular clouds.

Magnetic fields (B-fields) are ubiquitous in the interstellar medium (ISM), and they play an essential role in the formation of molecular clouds and subsequent star formation. However, B-fields in interstellar environments remain challenging to measure, and their properties typically need to be inferred from dust polarization observations over multiple physical scales. In this work, we seek to use a recently proposed approach called the velocity gradient technique (VGT) to study B-fields in star-forming regions and compare the results with dust polarization observations in different wavelengths. The VGT is based on the anisotropic properties of eddies in magnetized turbulence to derive B-field properties in the ISM. We investigate that this technique is synergistic with dust polarimetry when applied to a turbulent diffused medium for the purpose of measuring its magnetization. Specifically, we use the VGT on molecular line data toward the NGC 1333 star-forming region (12CO, 13CO, C18O, and N2H+), and we compare the derived B-field properties with those inferred from 214 and 850 μm dust polarization observations of the region using Stratospheric Observatory for Infrared Astronomy/High-Resolution Airborne Wide-band Camera Plus and James Clerk Maxwell Telescope/POL-2, respectively. We estimate both the inclination angle and the 3D Alfvénic Mach number M A from the molecular line gradients. Crucially, testing this technique on gravitationally bound, dynamic, and turbulent regions, and comparing the results with those obtained from polarization observations at different wavelengths, such as the plane-of-sky field orientation, is an important test on the applicability of the VGT in various density regimes of the ISM. We in general do not find a close correlation between the velocity gradient inferred orientations and the dust inferred magnetic field orientations.

Magnetic fields play an important role in the evolution of molecular clouds and star formation. Using the velocity gradient technique (VGT) model, we measured the magnetic field in Orion A using the 12CO, 13CO, and C18O(1-0) emission lines at a scale of ∼0.07 pc. The measured B field shows an east–west orientation that is perpendicular to the integral shaped filament of Orion A at large scale. The VGT magnetic fields obtained from 13CO and C18O are in agreement with the B field that is measured from the Planck 353 GHz dust polarization at a scale of ∼0.55 pc. Removal of density effects by using a velocity decomposition algorithm can significantly improve the accuracy of the VGT in tracing magnetic fields with the 12CO(1-0) line. The magnetic field strengths of seven subclouds, OMC-1, OMC-2, OMC-3, OMC-4, OMC-5, L 1641-N, and NGC 1999, have also been estimated with the Davis–Chandrasekhar–Fermi and the Two Mach Numbers technique, and these are found to be in agreement with previous results obtained from dust polarization at far-infrared and submillimeter wavelengths. At smaller scales, the VGT prove a good method to measure magnetic fields.

The detection of primordial B-mode polarization is still challenging due to the relatively low amplitude compared to the galactic foregrounds. To remove the contribution from the foreground, a comprehensive picture of the galactic magnetic field is indispensable. The Velocity Gradient Technique (VGT) is promising in tracing magnetic fields based on the modern understanding of the magneto-hydrodynamic turbulence. In this work, we apply VGT to an H i region containing an intermediate velocity cloud and a local velocity cloud, which are distinguishable in position–position–velocity space. We show that VGT gives an excellent agreement with the Planck polarization and stellar polarization. We confirm the advantages of VGT in constructing the 3D galactic magnetic field.

We explore how the velocity gradient technique (VGT) can be applied to absorbing media in the case of$^{13}$CO 2-1 emission. The VGT is a new way to trace magnetic fields in the plane of the sky using only spectroscopic observations. We apply the VGT to magnetohydrodynamic turbulence simulations that have been post-processed to include $^{13}$CO 2-1 emission and we calculate the velocity centroid gradients. We find that the velocity centroid gradients trace the projected magnetic field in media with different $^{13}$CO abundances, densities and optical depths. Our study opens up the possibility of using velocity centroid gradients to trace magnetic fields in molecular clouds using 13CO emission.

Interaction of three-dimensional magnetic fields, turbulence, and self-gravity in the molecular cloud is crucial in understanding star formation but has not been addressed so far. In this work, we target the low-mass star-forming region L1688 and use the spectral emissions of 12CO, 13CO, C18O, and H i, as well as polarized dust emissions. To obtain the 3D direction of the magnetic field, we employ the novel polarization fraction analysis. In combining with the plane-of-the-sky (POS) magnetic field strength derived from the Davis–Chandrasekhar–Fermi (DCF) method and the new differential measure analysis (DMA) technique, we present the first measurement of L1688’s three-dimensional magnetic field, including its orientation and strength. We find that L1688’s magnetic field has two statistically different inclination angles. The low-intensity tail has an inclination angle ≈55° on average, while that of the central dense clump is ≈30°. We find the global mean value of total magnetic field strength is Btot ≈ $135 \,\mathrm{\mu }{\rm G}$ from DCF and Btot ≈ $75 \,\mathrm{\mu }{\rm G}$ from DMA. We use the velocity gradient technique (VGT) to separate the magnetic fields’ POS orientation associated with L1688 and its foreground/background. The magnetic fields’ orientations are statistically coherent. The probability density function of H2 column density and VGT reveal that L1688 is potentially undergoing gravitational contraction at large scale ≈1.0 pc and gravitational collapse at small scale ≈0.2 pc. The gravitational contraction mainly along the magnetic field resulting in an approximate power-law relation $B_{\rm tot}\propto n_{\rm H}^{1/2}$ when volume density nH is less than approximately 6.0 × 103 cm−3.

We use the Velocity Gradient Technique (VGT) in the form of velocity channel gradients (VChGs) and reduced velocity centroid gradients (RVCGs) in early stages of protostellar disk formation to trace the magnetic field surrounding young stellar objects. We applied the VChGs and the RVCGs on a MHD simulation postprocessed to include 13CO 2–1 emission to mimic observational type data. These two different gradients give the plane-of-the-sky (POS) magnetic field as a function of the line-of-sight velocity, producing three-dimensional information about the magnetic field (in position–position–velocity). We find that, using the VGT, we are able to understand the structure of the POS magnetic field, providing a second tool in addition to dust polarization to understand their environment. With that, it is possible to better constrain the role of magnetic fields in early star formation.

Tracing of the magnetic field with Velocity Gradient Technique (VGT) allows observers to probe magnetic field directions with spectroscopic data. In this paper, we employ the method of Principal Component Analysis (PCA) to extract the spectroscopic information most valuable for VGT. By using synthetic observation data from numerical simulations, we show that PCA acts in a way similar to spatial filtering along the velocity axis. We study both subsonic and supersonic simulations and show that with the PCA filtering the tracing of magnetic fields by the VGT is significantly improved. Using 21 cm GALFA data, we demonstrate that the PCA filtering improves the alignment of the velocity gradients and the Planck dust polarization.