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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 ($\rm ^{12}CO$, $\rm ^{13}CO$, $\rm C^{18}O$, and $\rm N_{2}H^{+}$), and we compare the derived B-field properties with those inferred from 214 and 850~$\mu$m dust polarization observations of the region using SOFIA/HAWC+ and JCMT/POL-2, respectively. We estimate both the inclination angle and the 3D Alfv\'enic 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 wavelength, such as the plane-of-the-sky field orientation, is an important test on the applicability of the VGT in various density regimes of the ISM., Comment: 16 pages, 6 figures, Accepted for publication in ApJ

We present results from a high-resolution interstellar turbulence simulation and show that it closely reproduces recent $Planck$ measurements. Our model captures the scaling of $EE$ and $BB$ spectra, and the $EE/BB$ ratio in the inertial range. The PDF of the dust polarization fraction is also consistent with observations. The $TE$ cross-correlation is in broad agreement with observations. This simulation provides new insights into the physical origins of the observed $E/B$ asymmetry and positive $TE$ signal, facilitating the development of advanced Galactic dust emission models for current and future CMB experiments., Comment: 6 pages, 3 figures, 1 table

The term "unstable neutral media" (UNM) has traditionally been used to describe the transient phase formed between the warm and cold neutral hydrogen (HI) phases and has not been the focus of HI studies. However, recent observations suggest that the UNM phase not only has a significantly longer-than-expected lifetime but also occupies at least 20\% to 40\% of both the volume and mass fraction of HI. In this paper, we argue that the existence and dominance of the UNM can be explained by the presence of strong turbulence using an energy balance argument. The mass fraction of UNM is directly proportional to the turbulent velocity dispersion $\sigma_v$: mass fraction of UNM $\propto \sigma_v^{\frac{2n}{1+n}}$, where $n$ is the absolute value of the adiabatic index in the unstable phase. We discuss the implications of long-lived unstable thermal phases on ISM physics, including cold dense filament formation, cosmic ray acceleration, and measurement of galactic foreground statistics., Comment: 8 pages, 5 figures

The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfven Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfven Mach number $M_A$. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to Davis-Chandrasekhar-Fermi way of obtaining the magnetic field strength., Comment: 31 pages, 11 figures, submitted to ApJ

One of the biggest challenges in understanding Magnetohydrodynamic (MHD) turbulence is identifying the plasma mode components from observational data. Previous studies on synchrotron polarization from the interstellar medium (ISM) suggest that the dominant MHD modes can be identified via statistics of Stokes parameters, which would be crucial for studying various ISM processes such as the scattering and acceleration of cosmic rays, star formation, dynamo. In this paper, we present a numerical study of the Synchrotron Polarization Analysis (SPA) method through systematic investigation of the statistical properties of the Stokes parameters. We derive the theoretical basis for our method from the fundamental statistics of MHD turbulence, recognizing that the projection of the MHD modes allows us to identify the modes dominating the energy fraction from synchrotron observations. Based on the discovery, we revise the SPA method using synthetic synchrotron polarization observations obtained from 3D ideal MHD simulations with a wide range of plasma parameters and driving mechanisms, and present a modified recipe for mode identification. We propose a classification criterion based on a new SPA+ fitting procedure, which allows us to distinguish between Alfv\'en mode and compressible/slow mode dominated turbulence. We further propose a new method to identify fast modes by analyzing the asymmetry of the SPA+ signature and establish a new asymmetry parameter to detect the presence of fast mode turbulence. Additionally, we confirm through numerical tests that the identification of the compressible and fast modes is not affected by Faraday rotation in both the emitting plasma and the foreground., Comment: 18 pages, 10 figures, 1 table, accepted for publication in ApJ

The trending term "filament" is extensively used in the interstellar medium (ISM) and the star formation community, and is believed to be one of the most important objects that gauge molecular cloud and star formation. However, the physical definition of these ubiquitous, elongated, high contrast features is poorly defined and still actively debated. Despite the absence of a unified consensus, filaments are believed to be involved in many important physical processes from galaxy structure formation to the emergence of protostellar objects. Therefore, understanding how filaments form, what constrains their growth, and their general physical properties, are extremely important for theorists and observers who study the dynamics of the ISM and consequent star formations. This review serves as a collection of the community's views and develops the concept of "filaments" in the context of the ISM and star-forming clouds. Observationally, filaments are seen across the entire sky and often carry an aspect ratio of the order of hundreds. In the context of the ISM, filaments are believed to form by stretching and tearing from magnetized ISM turbulence. ISM filaments are subjected to heating and cooling phases, and are likely to be magnetically aligned. Cold clouds are formed inside ISM due to turbulence instability. This review updates the understanding of ISM filaments in the community.

While cosmic rays $(E\gtrsim 1\,\mathrm{GeV})$ are well coupled to a galaxy's interstellar medium (ISM) at scales of $L>100\,\mathrm{pc}$, adjusting stratification and driving outflows, their impact on small scales is less clear. Based on calculations of the cosmic ray diffusion coefficient from observations of the grammage in the Milky Way, cosmic rays have little time to dynamically impact the ISM on those small scales. Using numerical simulations, we explore how more complex cosmic ray transport could allow cosmic rays to couple to the ISM on small scales. We create a two-zone model of cosmic ray transport, with the cosmic ray diffusion coefficient set at the estimated Milky Way value in cold gas but smaller in warm gas. We compare this model to simulations with a constant diffusion coefficient. Quicker diffusion through cold gas allows more cold gas to form compared to a simulation with a constant, small diffusion coefficient. However, slower diffusion in warm gas allows cosmic rays to take energy from the turbulent cascade anisotropically. This cosmic ray energization comes at the expense of turbulent energy which would otherwise be lost during radiative cooling. Finally, we show our two-zone model is capable of matching observational estimates of the grammage for some transport paths through the simulation., Comment: Published in ApJ

We study the properties of sub-Alfvenic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfven Mach number $M_A=V_L/V_A<1$, where $V_L$ is the velocity at the injection scale and $V_A$ is the Alfven velocity. We demonstrate that weak turbulence can have different regimes depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces, i.e. velocity-driven, in an incompressible conducting fluid, we predict that the kinetic energy is $M_A^{-2}$ times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes with $k_\|/k_\perp < M_A$. We also predict that as the turbulent cascade reaches the strong regime the energy of slow modes exceeds the energy of Alfven modes by a factor $M_A^{-1}$. These effects are absent if the turbulence is magnetically driven at the injection scale. We confirm these predictions with numerical simulations. As the assumption of magnetic and kinetic energy equipartition is at the core of the Davis-Chandrasekhar-Fermi (DCF) approach to measuring magnetic field strength in sub-Alfvenic turbulence, we conclude that the DCF technique is not universally applicable. In particular, we suggest that the dynamical excitation of long azimuthal wavelength modes in the galactic disk may compromise the use of the DCF technique. We discuss alternative expressions that can be used to obtain magnetic field strength from observations., Comment: 28 pages, 10 figures, Accepted by ApJ

The temporal property of the compressible magneto-hydrodynamic (MHD) turbulence remains a fundamental unsolved question. Recent studies based on the spatial-temporal analysis in the global frame of reference suggest that the majority of fluctuation power in turbulence does not follow any of the MHD wave dispersion relations but has very low temporal frequency with finite wavenumbers. Here, we demonstrate that the Lorentzian broadening of the dispersion relations of the three MHD modes where the nonlinear effects act like the damping of a harmonic oscillator can explain many salient features of frequency spectra for all MHD modes. The low frequency fluctuations are dominated by modes with the low parallel wavenumbers that have been broadened by the nonlinear processes. The Lorentzian broadening widths of the three MHD modes exhibit scaling relations to the global frame wavenumbers and are intrinsically related to energy cascade of each mode. Our results provide a new window to investigate the temporal properties of turbulence which offers insights for building a comprehensive understanding of the compressible MHD turbulence., Comment: 15 pages, 4 figures, submitted

Magnetic fields are ubiquitous in the interstellar medium, including extended objects such as supernova remnants and diffuse halos around Pulsars. Its turbulent characteristics govern the diffusion of cosmic rays and the multi-wavelength emission from PWNe. However, the geometry and turbulence nature of the magnetic fields in the ambient region of PWN is still unknown. Recent gamma-ray observations from HAWC and synchrotron observations suggest a highly suppressed diffusion coefficient compared to the mean interstellar value. In this study, we present the first direct observational evidence of the orientation of the mean magnetic field and turbulent characteristics by employing a recently developed statistical parameter `Y$_{turb}$' in the extended halo around the Monogem pulsar. Our study points two possible scenarios: nearly aligned toward the line of sight (LoS) with compressible modes dominance or high inclination angle toward LoS and characterized by Alfv\'enic turbulence. The first scenario appears consistent with other observational signatures. Furthermore, we report that the magnetic field has an observed correlation length of approximately $3 \pm 0.6 {\rm pc}$ in the Monogem halo. Our study highlights the pivotal role of magnetic field and turbulence in unraveling the physical processes in TeV halos and cosmic ray transport., Comment: 6 pages, 3 figures, 2 tables, Accepted for publication in ApJ

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on small-amplitude compressible MHD turbulence cascade in Earth's magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfv\'en modes, and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field ($\mathbf{B_0}$) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to $\mathbf{B_0}$) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences to anisotropies in the space environment., Comment: Main text: 5 pages, 6 figures. Accepted by ApJ on Dec. 5, 2023. Published on Feb. 08, 2024

Magnetic fields are crucial in numerous astrophysical processes within the interstellar medium. However, the detailed determination of magnetic field geometry is notoriously challenging. Based on the modern magnetohydrodynamic (MHD) turbulence theory, we introduce a novel statistical technique, the "Y-parameter", to decipher the magnetic field inclination in the ISM and identify dominant turbulence modes. The Y-parameter, calculated as the ratio of anisotropies of different Stokes parameter combinations, displays contrasting trends with the mean-field inclination angle in Alfv\'enic and compressible turbulence modes. A Y-parameter value around $1.5\pm0.5$ provide a statistical boundary to determine the dominant MHD turbulence modes. We have discovered specific correlations between the Y-parameter value and the inclination angle that unveil the dominant turbulence mode. This methodology, when applied to future radio polarisation surveys such as LOFAR and SKA, promises to significantly enhance our knowledge of 3D magnetic field in the ISM and improve our understanding of interstellar turbulence., Comment: 13 pages, 10 figures, 1 table, Accepted for publication in MNRAS

Alfven wave is the single most important physical phenomenon of magneto-hydrodynamic turbulence and has far-reaching impact to almost all studies related to astrophysical magnetic field. Yet the restoration of the Alfven wave fluctuations from a given magnetic field, aka the local Alfven wave problem, is never properly addressed in literature albeit its importance. Previous works model the Alfven wave fluctuation as the perturbation along a straight-line, constant magnetic field. However, Lazarian & Pogosyan (2012) suggested that the decomposition of Alfven wave along a straight line, aka. the global frame decomposition, has a factor of discrepancy to the true local Alfven wave fluctuation. Here we provide a geometric interpretation on how the local Alfven wave is related to the global frame through the use of vector frame formulation. We prove both analytically and numerically that the local frame Alfven wave is an orthogonal transformation of that of the global frame and related by the local Alfvenic Mach number. In other words, when we observe Alfven wave in the global frame of reference, some of the Alfven wave will be mistaken as compressible waves. The importance of frame choices have a far-reaching impact to the analytical studies of MHD turbulence. Combining the frame formalism and the new techniques we can have accurate measurement to some of the fundamental turbulence properties like the inclination angle of mean magnetic field relative to the line of sight., Comment: 18 pages, 12 figures, accepted by MNRAS for publication

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described phenomena in nature, its core prediction of an Alfvenic transition from weak to strong MHD turbulence when energy cascades from large to small scales has not been observationally confirmed. Here we report the first observational evidence for the Alfvenic weak-to-strong transition in MHD turbulence in the terrestrial magnetosheath using the four Cluster spacecraft. The observed transition indicates the universal existence of strong turbulence regardless of the initial level of MHD fluctuations. Moreover, the observations demonstrate that the nonlinear interactions of MHD turbulence play a crucial role in the energy cascade, widening the directions of the energy cascade and broadening the fluctuating frequencies. Our work takes a critical step toward understanding the complete picture of turbulence cascade, connecting the weak and strong MHD turbulence systems. It will have broad implications in star formation, energetic particle transport, turbulent dynamo, and solar corona or solar wind heating., Comment: submitted; 24 pages; 4 figures

We report the evidence for the existence of the universal, continuous turbulent cascade of velocity fluctuations with Kolmogorov -5/3 slope spanning 6 orders of length scales, from $10^4$ pc down to $10^{-2}$ pc. This was achieved by applying our innovative technique of separating density and velocity fluctuations to a set of spectroscopic surveys featuring various galactic spectral lines. This unified velocity cascade involves different interstellar phases from diffuse galactic media to dense self-gravitating clouds and persists despite interstellar phase transitions. However, the turbulent density fluctuations do not show this universality as the value of the spectral slope changes in different interstellar phases. This agrees with the expectation of compressible turbulence theory and demonstrates that the density is only an indirect tracer of interstellar turbulence. We report that the density fluctuations for clouds and filaments that are preferentially parallel to magnetic fields exhibit the spectral slope of -2. The universal grand turbulent velocity cascade that is established in our paper has significant implications for key galactic physical processes, including star formation, cosmic ray transport etc. We anticipate our result to be a starting point for in vitro models of multiphase interstellar turbulence studies with a significant impact for modeling of spiral galaxies.

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis-Chandrasekhar-Fermi (DCF) technique. However, we identify the major problem of the DCF to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF, the new technique uses not the dispersion of the polarization angle and line of sight velocities, but increments of these quantities given by the structure functions. To address the variety of the astrophysical conditions for which our technique can be applied, we consider the turbulence in both media with magnetic pressure larger than the gas pressure corresponding e.g. to molecular and the gas pressure larger than the magnetic pressure corresponding to the warm neutral medium. We provide general expressions for arbitrary admixture of Alfv\'en, slow and fast modes in these media and consider in detail the particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our Differential Measure Approach (DMA), unlike the DCF, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data and is much more stable in the presence of large scale variations induces of non-turbulent nature. In parallel, our study uncover the deficiencies of the earlier DCF research., Comment: 53 pages, 32 figures, Accepted by ApJ for publications. Code: https://github.com/kyuen2/MHD_Mode

The existence of magnetized turbulence in the interstellar HI is well accepted. A number of techniques to obtain turbulence spectrum and magnetic field direction and strength have been developed and successfully applied to HI spectroscopic data. To better separate the imprints of density and velocity fluctuations to the channel maps, a new theory-based technique, the Velocity Decomposition Algorithm (VDA,Yuen et.al 2021), has been created. The technique demonstrates that the intensity fluctuations are separated into a component pv that mostly arises from velocity fluctuations and pd that mostly arise from density fluctuations. The VDA helps to clarify the nature of the filamentary structure observed in channel maps. A recent publication (Kalberla et.al 2022,K22) claims that the application of VDA to HI4PI data provides negative correlation of pv and pd,which according to the authors invalidates the technique since it requires that pv and pd have zero correlation. However, the quantities pv and pd given by VDA are naturally orthogonal which can be trivially checked analytically or numerically. That means the correct application of the VDA to any data must provide zero correlation. This is the point that we clarify in this paper and search for the cause of the mistake in the application of the VDA in K22 that resulted in the erroneous conclusion. We prove analytically that by construction pv and pd are not correlated. We identify the likely mistake in the VDA expression that K22 used and reproduce their figures with the incorrect expression. We find that 14 out of 15 figures in K22 are invalid, and thus their criticism of the VDA is ill-founded and arises from their use of incorrect expressions. We conclude that the detrimental mistake that K22 made at their analysis completely invalidate their scientific claim that Y21 isnt compatible to observation., Comment: 5 pages,3 figures, Submitted to A&A, Link of GitHub illustration, see https://github.com/kyuen2/kalberla_2022

A recent publication (Li et al. 2021) discovered one of the largest filamentary neutral hydrogen features dubbed Cattail from high resolution FAST observations that might be a new galactic arm of our own Milky Way. However in the analysis, it was suggested that this neutral hydrogen feature is cold despite having 12km/s total linewidth. We evaluate the probability whether the Cattail is actually cold neutral media via the newly developed Velocity Decomposition Algorithm (Yuen et al. 2021a) and Force Balancing Model (Ho et al. 2021a). We discovered that even with the inclusion of the galactic shear term, the feature is still at the unstable neutral media regime. Moreover, we also discover that the Cattail is two disjoint features in caustics space, suggesting that the Cattail might have two different turbulent systems. We check the spectra of the individual system separated via VDA to confirm this argument. We do not exclude the existence of smaller scale cold media being embedded within this structure.

The ubiquity of very thin and lengthy cold neutral media (CNM) has been reported by multiple authors in the HI community. Yet, the reason of how the CNM can be so long and lengthy is still in debate. In this paper, we recognize a new type of instability due to the attractive nature of the pressure force in the unstable phase. We provide a new estimation of the average CNM filament aspect ratio with the consideration of force balances at the phase boundary, which is roughly 5-20 in common CNM environment. We show that most of the cold filaments are less filamentary than what usually predicted via MHD turbulence theory or inferred from observations: The average length of CNM filament is roughly 1/2 of that in isothermal MHD turbulence with similar turbulence conditions. This suggests that the "cold filaments" that is identified in observations might not be in pressure equilibrium or generated via other mechanisms., Comment: 10 pages, 7 figures, accepted by MNRAS

Based on the theoretical description of Position-Position-Velocity(PPV) statistics in Lazarian & Pogosyan(2000), we introduce a new technique called the Velocity Decomposition Algorithm(VDA) in separating the PPV fluctuations arising from velocity and density fluctuations. Using MHD turbulence simulations, we demonstrate its promise in retrieving the velocity fluctuations from PPV cube in various physical conditions and its prospects in accurately tracing the magnetic field. We find that for localized clouds, the velocity fluctuations are most prominent at the wing part of the spectral line, and they dominate the density fluctuations. The same velocity dominance applies to extended HI regions undergoing galactic rotation. Our numerical experiment demonstrates that velocity channels arising from the cold phase of atomic hydrogen (HI) are still affected by velocity fluctuations at small scales. We apply the VDA to HI GALFA-DR2 data corresponding to the high-velocity cloud HVC186+19-114 and high latitude galactic diffuse HI data. Our study confirms the crucial role of velocity fluctuations in explaining why linear structures are observed within PPV cubes. We discuss the implications of VDA for both magnetic field studies and predicting polarized galactic emission that acts as the foreground for the Cosmic Microwave Background studies. Additionally, we address the controversy related to the filamentary nature of the HI channel maps and explain the importance of velocity fluctuations in the formation of structures in PPV data cubes. VDA will allow astronomers to obtain velocity fluctuations from almost every piece of spectroscopic PPV data and allow direct investigations of the turbulent velocity field in observations., Comment: 48 pages, 11 sections, 6 appendices, 26 figures in the main text, 7 figures in the appendices. Accepted by ApJ for publication

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., Comment: 14 pages, 8 figures

We introduce two new ways of obtaining the strength of plane-of-sky (POS) magnetic field by simultaneous use of spectroscopic Doppler-shifted lines and the information on magnetic field direction. The latter can be obtained either through polarization measurements or using the velocity gradient technique. We show the advantages that our techniques have compared to the traditional Davis-Chandrasekhar-Fermi (DCF) technique of estimating magnetic field strength from observations. The first technique that we describe in detail employs structure functions of velocity centroids and structure functions of Stokes parameters. We provide analytical expressions for obtaining magnetic field strength from observational data. We successfully test our results using synthetic observations obtained with results of MHD turbulence simulations. We measure velocity and magnetic field fluctuations at small scales using two, three and four point structure functions and compare the performance of these tools. We show that, unlike the DCF, our technique is capable of providing the detailed distribution of POS magnetic field and it can measure magnetic field strength in the presence of both velocity and magnetic field distortions arising from external shear and self-gravity. The second technique applies the velocity gradient technique to velocity channel maps in order to obtain the Alfven Mach number and uses the amplitudes of the gradients to obtain the sonic Mach number. The ratio of these two Mach numbers provides the intensity of magnetic field in the region contributing to the emission in the channel map. We test the technique and discuss obtaining the 3D distribution of POS galactic Magnetic field with it. We discuss the application of the second technique to synchrotron data., Comment: 30 pages, 10 figures, submitted to ApJ

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 degrees 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 high gradients' 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 (N-PDFs) 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 the synergy of VGT and IGT can determine the collapsing stages in a star-forming region., Comment: 36 pages, 24 figures, accepted for publication in ApJ

Magnetic field lines in interstellar media have a rich morphology, which could be characterized by geometrical parameters such as curvature and torsion. In this paper, we explore the statistical properties of magnetic field line curvature $\kappa$ in compressible magnetized turbulence. We see that both the mean and standard deviation of magnetic field line curvature obey power-law relations to the magnetization. Moreover, the power-law tail of the curvature probability distribution function is also proportional to the Alfvenic Mach number. We also explore whether the curvature method could be used in the field-tracing Velocity Gradient Technique. In particular, we observe that there is a relation between the mean and standard deviation of the curvature probed by velocity gradients to $M_A$. Finally we discuss how curvature is contributed by different MHD modes in interstellar turbulence, and suggests that the eigenvectors of MHD modes could be possibly represented by the natural Fernet-Serrat frame of the magnetic field lines. We discuss possible theoretical and observational applications of the curvature technique, including the extended understanding on a special length scale that characterize the importance of magnetic field curvature in driving MHD turbulence, and how it could be potentially used to study self-gravitating system., Comment: 18 pages, 7 figures, 1 extra figure in the appendix, accepted by ApJ for publication

The observations of fluctuations in the cosmic microwave background provide information about primordial inhomogeneities in the universe. However, the B-mode polarization of the inflationary gravitational wave is contaminated by the Galactic foreground polarized radiation arising from dust aligned by interstellar magnetic fields. To trace magnetic fields we use the Velocity Gradient Technique, which employs a modern understanding of the nature of magneto-hydrodynamics turbulent motions. In this paper, we combine the VGT with the Principal Component Analysis (PCA) to improve the accuracy of magnetic field tracing. We apply the VGT-PCA to the high-resolution neutral hydrogen data from the GALFA-HI survey to predict the polarization of dust. We report that the predicted directions of dust polarization provide good correspondence with those reported by Planck 353GHz, the alignment measure between the two AM=0.79. We show that our results statistically agree with the Planck polarization in terms of magnetic field tracing. We find that the variation of dust emission efficiency across the sky is small. Using our maps of predicted polarization we calculate the ratio of the E and B modes and show that BB/EE=0.53, which is similar to the result from Plank polarization., Comment: 22 pages, 17 figures, accepted for publication in ApJ

Magnetic fields are ubiquitous in the interstellar medium but are notoriously difficult to study through observation. Making use of the advances in our understanding of MHD turbulence and turbulent reconnection, the Velocity Gradient Technique (VGT) was suggested and successfully applied to study magnetic fields utilizing spectroscopic data. Applying the tools developed for VGT to intensity statistics, we introduce the Intensity Gradients Technique (IGT) as a complementary tool that can be used synergistically with VGT. In this paper, we apply IGT to a diffuse HI region selected from the GALFA-HI survey and compare the intensity gradient maps with those obtained using velocity gradients as well as Planck polarization measurements. We demonstrate the possibility of using IGT and VGT for both studying the magnetic field and identifying shocks in the diffuse interstellar medium. We also explore the ability of IGT in locating self-gravitating regions and calculating Alfvenic Mach number, both alone and in combination with VGT and polarimetry. We compare IGT with the Histogram of Relative Orientation (HRO), which utilizes intensity gradients to characterize the relative orientation of column density structures and local magnetic fields., Comment: 16 pages, 11 figures, accepted for publication in ApJ

We employ synthetic observations obtained with MHD simulations to study how to trace the distribution of turbulent magnetic fields using the synchrotron polarization gradient techniques suggested by Lazarian \& Yuen (2018). Both synchrotron polarization gradients and its derivative gradients with regard to the squared wavelength $\lambda^2$ are used to explore the probing ability of the technique in magnetic fields from sub- to super-Alfv{\'e}nic turbulence. We focus on studies that involve multi-frequency measurements in the presence of strong Faraday rotation and show the ways of how to recover the projected mean magnetic fields in the plane of the sky and the local magnetic fields within a tomographic slice. We conclude that the new techniques can successfully reconstruct the 3D magnetic field within our Milky Way and other galaxies. This paper opens an avenue for applying our new techniques to a large number of data cubes such as those from the Low Frequency Array for Radio astronomy and the Square Kilometer Array., Comment: 10 pages, 8 figures and 1 table. Accepted by MNRAS

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., Comment: 13 pages, 11 figures, accepted for publication in ApJ

A recent publication by Clark et.al (2019, CX19) uses both GALFA-HI observational data and numerical simulations to address the nature of intensity fluctuations in Position-Position-Velocity (PPV) space. The study questions the validity and applicability of the statistical theory of PPV space fluctuations formulated in Lazarian & Pogosyan (2000, LP00) to HI gas and concludes that $"${\it a significant reassessment of many observational and theoretical studies of turbulence in HI}$"$. This implies that dozens of papers that used LP00 theory to explore interstellar turbulence as well as the ongoing research based on LP00 theory are in error. This situation motivates the urgency of our public response. In our Comment we explain why we believe the criticism in CX19 is based on the incorrect understanding of the LP00 theory. In particular, we illustrate that the correlation between PPV slices and dust emissions in CX19 does not properly reveal the relative importance of velocity and density fluctuations in velocity channel maps. While CX19 provides an explanation of the change of the spectral index with respect to the thickness of PPV slice based on the two-phase nature of H1 gas, we failed to see any observational support for this idea. On the contrary, we show that the observations both in two-phase HI and one phase CO show similar results. Moreover, the observed change is in good agreement with LP00 predictions and spectral indexes of velocity and density spectra that are obtained following LP00 procedures are in good agreement with the numerically confirmed expectations of compressible MHD turbulence theory. In short, we could not find any justification of the criticism of LP00 theory that is provided in CX19. On the contrary, our analysis testifies that both available observational and numerical data agree well with the predictions of LP00 theory., Comment: 10 pages, 4 figures

Observations of synchrotron polarization at multiple frequencies in the presence of Faraday rotation can provide a way to reconstruct the 3D magnetic field distribution. In this paper we compare the well known Faraday Tomography (FT, Burn 1966) technique to the new approach named Synchrotron Polarization Gradients (SPG, Lazarian & Yuen 2018b). We compare the strengths and limitations of the two techniques, and describe their synergy. In particular, we show that in the situations when FT technique fails, e.g. due to insufficient frequency coverage, the SPG can still trace the 3D structure of magnetic field., Comment: 10 pages, 5 figures, submitted to ApJ

Probing magnetic fields in self-gravitating molecular clouds are generally difficult even with the use of the polarimetry. Based on the properties of magneto-hydrodynamic (MHD) turbulence and turbulent reconnection, Velocity Gradient Technique (VGT) provides a new way in tracing magnetic field orientation and strength based on the 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 isotopologue generated through radiative transfer calculations, we show that the VGT method can be successfully applied in probing the magnetic field direction in the diffuse interstellar medium as well as in self-gravitating molecular clouds., Comment: 17 pages, 10 figures, ApJ accepted 2019.1.29

Magnetohydrodynamic(MHD) turbulence displays velocity anisotropies which reflect the direction of the magnetic field. This anisotropy has led to the development of a number of statistical techniques for studying magnetic fields in the interstellar medium. In this paper, we review and compare three techniques that use radio position-position-velocity data for determining magnetic field strength and morphology : the correlation function anisotropy (CFA), Principal Component Analysis of Anisotropies (PCAA), and the more recent Velocity Gradient Technique (VGT). We compare these three techniques and suggest improvements to the CFA and PCAA techniques to increase their accuracy and versatility. In particular, we suggest and successfully implement a much faster way of calculating non-periodic correlation functions for the CFA. We discuss possible improvements to the current implementation of the PCAA. We show the advantages of the VGT in terms of magnetic field tracing and stress the complementary nature with the other two techniques., Comment: 18 pages, 18 figures, 3 appendices, accepted by ApJ for publication

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., Comment: 7 pages, 5 figures, accepted for publication in MNRAS

Recent developments of the Velocity Gradient Technique (VGT) show that the velocity gradients provide a reliable tracing of magnetic field direction in turbulent plasmas. In this paper, we explore the ability of velocity gradients to measure the magnetization of interstellar medium. We demonstrate that the distribution of velocity gradient orientations provides a reliable estimation of the magnetization of the media. In particular, we determine the relation between Alfvenic Mach number $M_A$ in the range of $M_A \in [0.2,1.7]$ and properties of the velocity gradient distribution, namely, with the dispersion of velocity gradient orientation as well as with the peak to base ratio of the amplitudes. We apply our technique for a selected GALFA-HI region and find the results consistent with the expected behavior of $M_A$. Using 3D MHD simulations we successfully compare the results with our new measure of magnetization that is based on the dispersion of starlight polarization. We demonstrate that, combined with the velocity dispersion along the line of sight direction, our technique is capable to delivering the magnetic field strength. The new technique opens a way to measure magnetization using other gradient measures such as synchrotron intensity gradients (SIGs) and synchrotron polarization gradients (SPGs)., Comment: 20 pages, 9 figures, 3 appendices, accepted for publication in ApJ

We describe a new technique for probing galactic and extragalactic 2D and 3D magnetic field distribution using gradients of polarized synchrotron emission. The fluctuations of magnetic field are elongated along the ambient magnetic field. Therefore, the field variations are maximal perpendicular to the B-field. This allows tracing B-field with synchrotron polarization gradients (SPGs). We demonstrate that the Faraday depolarization allows to map 3D B-field structure by. The depolarization ensures that the polarization gradients sample the regions close to the observer with the sampling depth controlled by the frequency of radiation. We also analyze the B-field properties along the line-of-sight by applying the gradient technique to the wavelength derivative of synchrotron polarization. This Synchrotron Derivative Polarization Gradients (SDPGs) technique can recover the 3D vectors of the underlying B-fields. The new techniques are different from the Faraday tomography as they provide a way to map the 3D distribution of B-fields components perpendicular to the line of sight. In addition, we find that the alignment of gradients of polarization with the synchrotron polarization can be used to separate the contribution of the foreground from the polarization of cosmological origin. We notice that the same alignment is also present for the dust polarization., Comment: 24 pages, 19 figures, accepted for publication in ApJ

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 magneto-hydrodynamic (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 (PPV) 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 magnetized turbulence., Comment: 18 pages, 8 figures, 1 extra figure in the appendix, accepted by ApJ for publication

This study proceeds with the development of the technique employing velocity gradients that were identified in (\cite{GL17}, henceforth GL17) as a means of probing magnetic field in interstellar media. We demonstrate a number of practical ways on improving the accuracy of tracing magnetic fields in diffuse interstellar media using velocity centroid gradients (VCGs). Addressing the magnetic field tracing in super-Alfvenic turbulence we introduce the procedure of filtering low spatial frequencies, that enables magnetic field tracing in the situations when the kinetic energy of turbulent plasmas dominate its magnetic energy. We propose the synergic way of of using VCGs together with intensity gradients (IGs), synchrotron intensity gradients (SIGs) as well as dust polarimetry. We show that while the IGs trace magnetic field worse than the VCGs, the deviations of the angle between the IGs and VCGs trace the shocks in diffuse media. Similarly the perpendicular orientation of the VCGs and the SIGs or to the dust polarimetry data trace the regions of gravitational collapse. We demonstrate the utility of combining the VCGs, IGs and polarimetry using GALFA HI and Planck polarimetry data. We also provide an example of synergy of the VCGs and the SIGs using the HI4PI full-sky HI survey together with the Planck synchrotron intensity data., Comment: 15 pages, 15 figures, submitted to ApJ

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 {\it 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., Comment: 25 pages, 29 figures, Submitted to ApJ

The advancement of our understanding of MHD turbulence opens ways to develop new techniques to probe magnetic fields. In MHD turbulence, the velocity gradients are expected to be perpendicular to magnetic fields and this fact was used by Gonsalvez-Casanova & Lazarian to introduce a new technique to trace magnetic fields using velocity centroid gradients. The latter can be obtained from spectroscopic observations. We apply the technique to GALFA HI survey data and compare the directions of magnetic fields obtained with our technique with the direction of magnetic fields obtained using PLANCK polarization. We find excellent correspondence between the two ways of magnetic field tracing, which is obvious via visual comparison and through measuring of the statistics of magnetic field fluctuations obtained with the polarization data and our technique. This suggests that the velocity centroid gradients can provide a reliable way of measuring of the foreground magnetic field fluctuations and thus provide a new way of separating foreground and CMB polarization signals., Comment: 7 pages, 5 figures, submitted to ApJL

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 dats 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., Comment: 15 pages, 10 figures

Most molecular clouds are filamentary or elongated. Among those forming low-mass stars, their long axes tend to be either parallel or perpendicular to the large-scale (10-100 pc) magnetic field (B-field) in the surrounding inter cloud medium. This arises because, along the dynamically dominant B-fields, the competition between self-gravity and turbulent pressure will shape the cloud to be elongated either perpendicular or parallel to the fields. Recent study also suggested that, on the scales of 0.1-0.01 pc, fields are dynamically important within cloud cores forming massive stars. But whether the core field morphologies are inherited from the inter cloud medium or governed by cloud turbulence is under vigorous debate, so is the role played by B-fields in cloud fragmentation at 10 - 0.1 pc scales. Here we report B-field maps covering 100-0.01 pc scales inferred from polarimetric observations of a massive-star forming region, NGC 6334. First, the main filament also lies perpendicular to the ambient field. NGC 6334 hosts young star-forming sites where fields are not severely affected by stellar feedback, and their directions do not change significantly over the entire scale range. This means that the fields are dynamically important. At various scales, we find that the hourglass-shaped field lines are pinched where the gas column density peaks and the field strength is proportional to the 0.4-power of the density. We conclude that B-fields play a crucial role in the fragmentation of NGC 6334., Comment: 16 pages, 6 figures