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Observing 3D magnetic fields, including orientation and strength, within the interstellar medium is vital but notoriously difficult. However, recent advances in our understanding of anisotropic magnetohydrodynamic (MHD) turbulence demonstrate that MHD turbulence and 3D magnetic fields leave their imprints on the intensity features of spectroscopic observations. Leveraging these theoretical frameworks, we propose a novel Convolutional Neural Network (CNN) model to extract this embedded information, enabling the probe of 3D magnetic fields. This model examines the plane-of-the-sky magnetic field orientation (ϕ), the magnetic field’s inclination angle (γ) relative to the line-of-sight, and the total magnetization level (M$_{\rm A}^{-1}$) of the cloud. We train the model using synthetic emission lines of 13CO (J  = 1–0) and C18O (J  = 1–0), generated from 3D MHD simulations that span conditions from sub-Alfvénic to super-Alfvénic molecular clouds. Our tests confirm that the CNN model effectively reconstructs the 3D magnetic field topology and magnetization. The median uncertainties are under 5° for both ϕ and γ, and less than 0.2 for MA in sub-Alfvénic conditions (MA ≈ 0.5). In super-Alfvénic scenarios (MA ≈ 2.0), they are under 15° for ϕ and γ, and 1.5 for MA. We applied this trained CNN model to the L1478 molecular cloud. Results show a strong agreement between the CNN-predicted magnetic field orientation and that derived from Planck 353 GHz polarization. The CNN approach enabled us to construct the 3D magnetic field map for L1478, revealing a global inclination angle of ≈76° and a global MA of ≈1.07.

The coupling state between ions and neutrals in the interstellar medium plays a key role in the dynamics of magnetohydrodynamic (MHD) turbulence, but is challenging to study numerically. In this work, we investigate the damping of MHD turbulence in a partially ionized medium using 3D two-fluid (ions + neutrals) simulations generated with the athenak code. Specifically, we examine the velocity, density, and magnetic field statistics of the two-fluid MHD turbulence in different regimes of neutral-ion coupling. Our results demonstrate that when ions and neutrals are strongly coupled, the velocity statistics resemble those of single-fluid MHD turbulence. Both the velocity structures and kinetic energy spectra of ions and neutrals are similar, while their density structures can be significantly different. With an excess of small-scale sharp density fluctuations in ions, the density spectrum in ions is shallower than that of neutrals. When ions and neutrals are weakly coupled, the turbulence in ions is more severely damped due to the ion-neutral collisional friction than that in neutrals, resulting in a steep kinetic energy spectrum and density spectrum in ions compared to the Kolmogorov spectrum. We also find that the magnetic energy spectrum basically follows the shape of the kinetic energy spectrum of ions, irrespective of the coupling regime. In addition, we find large density fluctuations in ions and neutrals and thus spatially inhomogeneous ionization fractions. As a result, the neutral-ion decoupling and damping of MHD turbulence take place over a range of length-scales.

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.

The alignment of striated intensity structures in thin neutral hydrogen (H i) spectroscopic channels with Galactic magnetic fields has been observed. However, the origin and nature of these striations are still debatable. Some studies suggest that the striations result solely from real cold-density filaments without considering the role of turbulent velocity fields in shaping the channel’s intensity distribution. To determine the relative contribution of density and velocity in forming the striations in channel maps, we analyse synthetic observations of channel maps obtained from realistic magnetized multiphase H i simulations with thermal broadening included. We vary the thickness of the channel maps and apply the Velocity Decomposition Algorithm to separate the velocity and density contributions. In parallel, we analyse GALFA-H i observations and compare the results. Our analysis shows that the thin channels are dominated by velocity contribution, and velocity caustics mainly generate the H i striations. We show that velocity caustics can cause a correlation between unsharp-masked H i structures and far-infrared emission. We demonstrate that the linear H i fibers revealed by the Rolling Hough Transform (RHT) in thin velocity channels originate from velocity caustics. As the thickness of channel maps increases, the relative contribution of density fluctuations in channel maps increases and more RHT-detected fibers tend to be perpendicular to the magnetic field. Conversely, the alignment with the magnetic field is the most prominent in thin channels. We conclude that similar to the velocity channel gradients (VChGs) approach, RHT traces magnetic fields through the analysis of velocity caustics in thin channel maps.

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 technique 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 technique, 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 astrophysical conditions for which our technique can be applied, we consider turbulence in both media with magnetic pressure higher than the gas pressure, corresponding, e.g., to molecular clouds, and media with gas pressure higher than the magnetic pressure, corresponding to the warm neutral medium. We provide general expressions for arbitrary admixtures of Alfvén, slow, and fast modes in these media and consider in detail 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, unlike the DCF technique, 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 induced large-scale variations of nonturbulent nature. Furthermore, our study uncovers the deficiencies of earlier DCF research.

Polarization of interstellar dust emission is a powerful probe of dust properties and magnetic field structure. Yet studies of external galaxies are hampered by foreground dust contribution. The study aims at separating the polarized signal from the Large Magellanic Cloud (LMC) from that of the Milky Way (MW) to construct a wide-field, spatially complete map of dust polarization using the Planck 353 GHz data. To estimate the foreground polarization direction, we used velocity gradients in H i spectral line data and assessed the performance of the output by comparing to starlight extinction polarization. We estimate the foreground intensity using the dust-to-gas correlation and the average intensity around the LMC and we assume the foreground polarization to be uniform and equal to the average of the MW around the galaxy to derive foreground I, Q, and U parameters. After foreground removal, the geometry of the plane-of-the-sky magnetic field tends to follow the structure of the atomic gas. This is notably the case along the molecular ridges extending south and south-east of the 30 Doradus star-forming complex and along the more diffuse southern arm extending towards the Small Magellanic Cloud. There is also an alignment between the magnetic field and the outer arm in the western part. The median polarization fraction in the LMC is slightly lower than that observed for the MW as well as the anticorrelation between the polarization angle dispersion function and the polarization fraction. Overall, polarization fraction distribution is similar to that observed in the MW.

Measuring magnetic fields in the interstellar medium and obtaining their distribution along line-of-sight (LOS) is very challenging with the traditional techniques. The Velocity Gradient Technique (VGT), which utilizes anisotropy of magnetohydrodynamic turbulence, provides an attractive solution. Targeting the central molecular zone (CMZ), we test this approach by applying the VGT to $\rm ^{12}CO$ and $\rm ^{13}CO$ (J = 1–0) data cubes. We first used the scousepy algorithm to decompose the CO line emissions into separate velocity components, and then we constructed pseudo-Stokes parameters via the VGT to map the plane-of-the-sky magnetic fields in three-dimension. We present the decomposed magnetic field maps and investigate their significance. While the LOS integrated magnetic field orientation is shown to be consistent with the polarized dust emission from the Planck survey at 353 GHz, individual velocity components may exhibit different magnetic fields. We present a scheme of magnetic field configuration in the CMZ based on the decomposed magnetic fields. In particular, we observe a nearly vertical magnetic field orientation in the dense clump near the Sgr B2 and a change in the outflow regions around the Sgr A*. Two high-velocity structures associated with an expanding ring in the CMZ show distinct swirling magnetic field structures. These results demonstrate the potential power of the VGT to decompose velocity or density-dependent magnetic structures.

Owing to the complexity of turbulent magnetic fields, modelling the diffusion of cosmic rays is challenging. Based on the current understanding of anisotropic magnetohydrodynamic (MHD) turbulence, we use test particles to examine the cosmic rays’ superdiffusion in the direction perpendicular to the mean magnetic field. By changing Alfvén Mach number MA and sonic Mach number MS of compressible MHD simulations, our study covers a wide range of astrophysical conditions including subsonic warm gas phase and supersonic cold molecular gas. We show that freely streaming cosmic rays’ perpendicular displacement increases as 3/2 to the power of the time travelled along local magnetic field lines. This power-law index changes to 3/4 if the parallel propagation is diffusive. We find that the cosmic rays’ parallel mean free path decreases in a power-law relation of $M_\mathrm{ A}^{-2}$ in supersonic turbulence. We investigate the energy fraction of slow, fast, and Alfvénic modes and confirm the dominance of Alfvénic modes in the perpendicular superdiffusion. In particular, the energy fraction of fast mode, which is the main agent for pitch-angle scattering, increases with MA, but is insensitive to MS ≥ 2. Accordingly, our results suggest that the suppressed diffusion in supersonic molecular clouds arises primarily due to the variations of MA instead of MS.

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.

The central molecular zone (CMZ) plays an essential role in regulating the nuclear ecosystem of our Galaxy. To get an insight into magnetic fields of the CMZ, we employ the gradient technique (GT), which is rooted in the anisotropy of magnetohydrodynamic turbulence. Our analysis is based on the data of multiple wavelengths, including molecular emission lines, radio 1.4 GHz continuum image, and Herschel $70\, {\mu }{\rm m}$ image, as well as ionized [Ne ii] and Paschen-alpha emissions. The results are compared with the observations of Planck 353 GHz and High-resolution Airborne Wideband Camera Plus (HWAC+) $53\, {\mu }{\rm m}$ polarized dust emissions. We map the magnetic fields orientation at multiple wavelength across the central molecular zone, including close-ups of the Radio Arc and Sagittarius A West regions, on multiscales from ∼0.1 pc to 10 pc. The magnetic fields towards the central molecular zone traced by the GT are globally compatible with the polarization measurements, accounting for the contribution from the galactic foreground and background. This correspondence suggests that the magnetic field and turbulence are dynamically crucial in the galactic center. We find that the magnetic fields associated with the Arched filaments and the thermal components of the Radio Arc are in good agree with the HAWC+ polarization. Our measurement towards the non-thermal Radio Arc reveals the poloidal magnetic field components in the galactic center. For Sagittarius A West region, we find a great agreement between the GT measurement using [Ne ii] emission and HWAC+ $53\, {\mu }{\rm m}$ observation. We use the GT to predict the magnetic fields associated with ionized Paschen-alpha gas down to scales of 0.1 pc.