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Abstract Magnetic fields play a crucial role in various astrophysical processes within the intracluster medium, including heat conduction, cosmic-ray acceleration, and the generation of synchrotron radiation. However, measuring magnetic field strength is typically challenging due to the limited availability of Faraday rotation measure sources. To address the challenge, we propose a novel method that employs Convolutional Neural Networks (CNNs) alongside synchrotron emission observations to estimate magnetic field strengths in galaxy clusters. Our CNN model is trained on either magnetohydrodynamic (MHD) turbulence simulations or MHD galaxy cluster simulations, which incorporate complex dynamics such as cluster mergers and sloshing motions. The results demonstrate that CNNs can effectively estimate magnetic field strengths with mean-squared error of approximately 0.135µG², 0.044µG², and 0.02µG²forβ = 100, 200, and 500 conditions, respectively. Additionally, we have confirmed that our CNN model remains robust against noise and variations in viewing angles with sufficient training, ensuring reliable performance under a wide range of observational conditions. We compare the CNN approach with the traditional magnetic field strength estimate method that assumes equipartition between cosmic-ray electron energy and magnetic field energy. In contrast to the equipartition method, this CNN approach relies on the morphological feature of synchrotron images, offering a new perspective for complementing traditional estimates and enhancing our understanding of cosmic-ray acceleration mechanisms. 

Abstract Cosmic rays (CRs) interact with turbulent magnetic fields in the interstellar medium (ISM), generating nonthermal emission. After many decades of studies, the theoretical understanding of their diffusion in the ISM continues to pose a challenge. This study numerically explores a recent prediction termed “mirror diffusion” and its synergy with the traditional diffusion mechanism based on gyroresonant scattering. Our study combines 3D MHD simulations of star-forming regions with test particle simulations to analyze CR diffusion. We demonstrate the significance of mirror diffusion in CR diffusion parallel to the magnetic field when the mirroring condition is satisfied. Our results support the theoretical expectation that the resulting particle propagation arising from mirror diffusion in combination with much faster diffusion induced by gyroresonant scattering resembles a Levy-flight-like propagation. Our study highlights the necessity to reevaluate the diffusion coefficients traditionally adopted in the ISM based on gyroresonant scattering alone. For instance, our simulations imply a diffusion coefficient ∼10²⁷cm²s^–1for particles with a few hundred TeV within regions spanning a few parsecs around the source. This estimate is in agreement with gamma-ray observations, which show the relevance of our results for the understanding of gamma-ray emission in star-forming regions. 

Abstract We present a detailed study of the magnetic field structure in the G111 molecular cloud, a ring-like filamentary cloud within the NGC 7538 region. Our analysis combines multiwavelength polarization data and molecular-line observations to investigate the magnetic field’s role in the cloud’s formation and evolution. We utilized interstellar dust polarization from the Planck telescope to trace large-scale field orientations, starlight extinction polarization from the Kanata telescope to probe the cloud’s magnetic field after foreground subtraction, and velocity gradients derived from CO isotopologues observed with the IRAM 30 m telescope to examine dense regions. Our results reveal a coherent yet spatially varying magnetic field within G111. The alignment between Planck-derived orientations and starlight extinction polarization highlights significant foreground dust contamination, which we correct through careful subtraction. The global alignment of the magnetic field with density structures suggests that the field is dynamically important in shaping the cloud. Variations in CO-derived orientations further suggest that local dynamical effects, such as gravitational interactions and turbulence, influence the cloud’s structure. The curved magnetic field along the dense ridges, coinciding with mid-infrared emission in WISE data, indicates shock compression, likely driven by stellar feedback or supernova remnants. Our findings support a scenario where G111’s morphology results from turbulent shock-driven compression, rather than simple gravitational contraction. The interplay between magnetic fields and external forces is crucial in shaping molecular clouds and regulating star formation. Future high-resolution observations will be essential to further constrain the magnetic field’s role in cloud evolution. 

Abstract We investigate the impact of turbulence on magnetic reconnection through high-resolution 3D magnetohydrodynamic (MHD) simulations, spanning Lundquist numbers fromS= 10³to 10⁶. Building on the A. Lazarian & E. T. Vishniac theory, which asserts reconnection rate independence from ohmic resistivity, we introduce small-scale perturbations untilt= 0.1t_A. Even after the perturbations cease, turbulence persists, resulting in sustained high reconnection rates ofV_rec/V_A∼ 0.03–0.08. These rates exceed those generated by resistive tearing modes (plasmoid chain) in 2D and 3D MHD simulations by factors of 5–6. Our findings match observations in solar phenomena and previous 3D MHD global simulations of solar flares, accretion flows, and relativistic jets. The simulations show a steady-state fast reconnection rate compatible with the full development of turbulence in the system, demonstrating the robustness of the process in turbulent environments. We confirm reconnection rate independence from the Lundquist number, supporting Lazarian and Vishniac’s theory of fast turbulent reconnection. Additionally, we find a mild dependence ofV_recon the plasma–βparameter, decreasing from 0.036 to 0.028 (in Alfvén units) asβincreases from 2.0 to 64.0 for simulations with a Lundquist number of 10⁵. Lastly, we explore the magnetic Prandtl number’s (Pr_m=ν/η) influence on the reconnection rate and find it negligible during the turbulent regime across the range tested, from Pr_m= 1 to 60. 

Abstract 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 thanr^1/2between 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 withr^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. 

Abstract Understanding the role of turbulence in shaping the interstellar medium (ISM) is crucial for studying star formation, molecular cloud evolution, and cosmic-ray propagation. Central to this is the measurement of the sonic Mach number (M_s), which quantifies the ratio of turbulent velocity to the sound speed. In this work, we introduce a convolutional-neural-network-(CNN)-based approach for estimatingM_sdirectly from spectroscopic observations. The approach leverages the physical correlation between increasingM_sand the shock-induced small-scale fluctuations that alter the morphological features in intensity, velocity centroid, and velocity channel maps. These maps, derived from 3D magnetohydrodynamic turbulence simulations, serve as inputs for the CNN training. By learning the relationship between these structural features and the underlying turbulence properties, CNNs can predictM_sunder various conditions, including different magnetic fields and levels of observational noise. The median uncertainty of the CNN-predictedM_sranges from 0.5 to 1.5 depending on the noise level. While intensity maps offer lower uncertainty, channel maps have the advantage of predicting the 3DM_sdistribution, which is crucial in estimating 3D magnetic field strength. Our results demonstrate that machine-learning-based tools can effectively characterize complex turbulence properties in the ISM. 

Abstract In this study, we apply the velocity gradient technique to the merging Centaurus galaxy. We compare gradient maps derived from the PHANGS-Atacama Large Millimeter/submillimeter Array survey using CO emission lines with magnetic field tracings from dust polarization data obtained via the HAWC+ instrument. Our analysis reveals a strong correspondence between the directions indicated by these two tracers across most of the galactic image. Specifically, we identify jet regions as areas of antialignment, consistent with previous reports that gradients tend to rotate 90° in outflow regions. Statistically, we find that the alignment of magnetic fields, as revealed by polarization, is most accurate in regions with the highest signal-to-noise ratios. Our findings underscore the utility of velocity gradients as a valuable complementary tool for probing magnetic fields and dynamical processes in merging galaxies. This proves the general utility of velocity gradients for mapping magnetic fields in astrophysical objects with complex dynamics. 

Abstract Measuring the 3D spatial distribution of magnetic fields in the interstellar medium and the intracluster medium is crucial yet challenging. The probing of the 3D magnetic field’s 3D distribution, including the field plane-of-sky orientation (ψ), the magnetic field’s inclination angle (γ) relative to the line of sight, and the magnetization (∼the inverse Alfvén Mach number $M_{\mathrm{A}}^{-1}$), at different distances from the observer makes the task even more formidable. However, the anisotropy and Faraday decorrelation effect in polarized synchrotron emission offer a unique solution. We show that due to the Faraday decorrelation, only regions up to a certain effective path length along the line of sight contribute to the statistical correlation of the measured polarization. The 3D spatial information can be consequently derived from synchrotron polarization derivatives (SPDs), which are calculated from the difference in synchrotron polarization across two wavelengths. We find that the 3D magnetic field can be estimated from the anisotropy observed in SPDs: the elongation direction of the SPD structures probesψ, and the degree of SPD anisotropy, along with its morphological curvature, provides insights into $M_{\mathrm{A}}^{-1}$andγ. To extract these anisotropic features and their correlation with the 3D magnetic field, we propose utilizing a machine learning approach, specifically the Vision Transformer (ViT) architecture, which was exemplified by the success of ChatGPT. We train the ViT using synthetic synchrotron observations generated from magnetohydrodynamic turbulence simulations in sub-Alfvénic and super-Alfvénic conditions. We show that ViT’s application to multiwavelength SPDs can successfully reconstruct the 3D magnetic fields’ 3D spatial distribution. 

Abstract Magnetic fields and their dynamical interplay with matter in galaxy clusters contribute to the physical properties and evolution of the intracluster medium. However, the current understanding of the origin and properties of cluster magnetic fields is still limited by observational challenges. In this article, we map the magnetic fields at hundreds-kpc scales of five clusters RXC J1314.4-2515, Abell 2345, Abell 3376, MCXC J0352.4-7401, and El Gordo using the synchrotron intensity gradient technique in conjunction with high-resolution radio observations from the Jansky Very Large Array (JVLA) and the Karoo Array Telescope (MeerKAT). We demonstrate that the magnetic field orientation of radio relics derived from synchrotron intensity gradient is in agreement with that obtained with synchrotron polarization. Most importantly, the synchrotron intensity gradient is not limited by Faraday depolarization in the cluster central regions and allows us to map magnetic fields in the radio halos of RXC J1314.4-2515 and El Gordo. We find that magnetic fields in radio halos exhibit a preferential direction along the major merger axis and show turbulent structures at higher angular resolution. The results are consistent with expectations from numerical simulations, which predict turbulent magnetic fields in cluster mergers that are stirred and amplified by matter motions. 

Abstract 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 Alfvén 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 Alfvén Mach numberM_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 the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.