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1. Probing Three-dimensional Magnetic Fields. III. Synchrotron Emission and Machine Learning

   https://doi.org/10.3847/1538-4357/ad7950  

   Hu, Yue; Lazarian, A. (October 2024, The Astrophysical Journal)

   Abstract Synchrotron observation serves as a tool for studying magnetic fields in the interstellar medium and intracluster medium, yet its ability to unveil three-dimensional (3D) magnetic fields, meaning probing the field’s plane-of-the-sky (POS) orientation, inclination angle relative to the line of sight, and magnetization from one observational data, remains largely underexplored. Inspired by the latest insights into anisotropic magnetohydrodynamic (MHD) turbulence, we found that synchrotron emission’s intensity structures inherently reflect this anisotropy, providing crucial information to aid in 3D magnetic field studies: (i) the structure’s elongation gives the magnetic field’s POS orientation and (ii) the structure’s anisotropy degree and topology reveal the inclination angle and magnetization. Capitalizing on this foundation, we integrate a machine learning approach—convolutional neural network (CNN)—to extract this latent information, thereby facilitating the exploration of 3D magnetic fields. The model is trained on synthetic synchrotron emission maps, derived from 3D MHD turbulence simulations encompassing a range of sub-Alfvénic to super-Alfvénic conditions. We show that the CNN is physically interpretable and the CNN is capable of obtaining the POS orientation, inclination angle, and magnetization. Additionally, we test the CNN against the noise effect and the missing low-spatial frequency. We show that this CNN-based approach maintains a high degree of robustness even when only high-spatial frequencies are maintained. This renders the method particularly suitable for application to interferometric data lacking single-dish measurements. We applied this trained CNN to the synchrotron observations of a diffuse region. The CNN-predicted POS magnetic field orientation shows a statistical agreement with that derived from synchrotron polarization. 

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2. Probing three-dimensional magnetic fields: II – an interpretable Convolutional Neural Network

   https://doi.org/10.1093/mnras/stad3766  

   Hu, Yue; Lazarian, A.; Wu, Yan; Fu, Chengcheng (January 2024, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT 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. 

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3. Sub-Alfvénic Turbulence: Magnetic-to-kinetic Energy Ratio, Modification of Weak Cascade, and Implications for Magnetic Field Strength Measurements

   https://doi.org/10.3847/1538-4357/ad8d49  

   Lazarian, A; Ho, Ka Wai; Yuen, Ka Ho; Vishniac, Ethan (December 2024, The Astrophysical Journal)

   Abstract We study the properties of sub-Alfvénic magnetohydrodynamic (MHD) turbulence, i.e., turbulence with Alfvén mach numberM_A=V_L/V_A< 1, whereV_Lis the velocity at the injection scale andV_Ais the Alfvén velocity. We demonstrate that MHD turbulence can have different properties, depending on whether it is driven by velocity or magnetic fluctuations. If the turbulence is driven by isotropic bulk forces acting upon the fluid, i.e., is velocity driven, in an incompressible conducting fluid we predict that the kinetic energy is $M_{\mathrm{A}}^{-2}$times larger than the energy of magnetic fluctuations. This effect arises from the long parallel wavelength tail of the forcing, which excites modes withk_∥/k_⊥<M_A. We also predict that as the MHD turbulent cascade reaches the strong regime, the energy of slow modes exceeds the energy of Alfvén modes by a factor $M_{\mathrm{A}}^{-1}$. These effects are absent if the turbulence is driven through magnetic fluctuations at the injection scale. We confirm our predictions with numerical simulations. Since 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-Alfvénic 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 and consider ways of distinguishing the cases of velocity and magnetically driven turbulence using observational data. 

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4. Detection and Classification of Sporadic E Using Convolutional Neural Networks

   https://doi.org/10.1029/2023SW003669  

   Ellis, J. A.; Emmons, D. J.; Cohen, M. B. (January 2024, Space Weather)

   Abstract In this work, convolutional neural networks (CNN) are developed to detect and characterize sporadic E (E_s), demonstrating an improvement over current methods. This includes a binary classification model to determine ifE_sis present, followed by a regression model to estimate theE_sordinary mode critical frequency (foEs), a proxy for the intensity, along with the height at which theE_slayer occurs (hEs). Signal‐to‐noise ratio (SNR) and excess phase profiles from six Global Navigation Satellite System (GNSS) radio occultation (RO) missions during the years 2008–2022 are used as the inputs of the model. Intensity (foEs) and the height (hEs) values are obtained from the global network of ground‐based Digisonde ionosondes and are used as the “ground truth,” or target variables, during training. After corresponding the two data sets, a total of 36,521 samples are available for training and testing the models. The foEs CNN binary classification model achieved an accuracy of 74% and F1‐score of 0.70. Mean absolute errors (MAE) of 0.63 MHz and 5.81 km along with root‐mean squared errors (RMSE) of 0.95 MHz and 7.89 km were attained for estimating foEs and hEs, respectively, when it was known thatE_swas present. When combining the classification and regression models together for use in practical applications where it is unknown ifE_sis present, an foEs MAE and RMSE of 0.97 and 1.65 MHz, respectively, were realized. We implemented three other techniques for sporadic E characterization, and found that the CNN model appears to perform better. 

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5. Planck Dust Polarization Power Spectra Are Consistent with Strongly Supersonic Turbulence

   https://doi.org/10.3847/1538-4357/ad571b  

   Stalpes, Kye_A; Collins, David_C; Huffenberger, Kevin_M (August 2024, The Astrophysical Journal)

   Abstract The polarization of the cosmic microwave background is rich in information but obscured by foreground emission from the Milky Way’s interstellar medium (ISM). To uncover relationships between the underlying turbulent ISM and the foreground power spectra, we simulated a suite of driven, magnetized, turbulent models of the ISM, varying the fluid properties via the sonic Mach number, ${\mathcal{M}}_{\mathcal{S}}$, and magnetic (Alfvén) Mach number, ${\mathcal{M}}_{\mathrm{A}}$. We measure the power spectra of density (ρ), velocity (v), magnetic field (H), total projected intensity (T), parity-even polarization (E), and parity-odd polarization (B). We find that the slopes of all six quantities increase with ${\mathcal{M}}_{\mathcal{S}}$. Most increase with ${\mathcal{M}}_{\mathrm{A}}$, while the magnetic field spectrum steepens with ${\mathcal{M}}_{\mathrm{A}}$. By comparing spectral slopes ofEandBto those measured by Planck, we infer typical values of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$for the ISM. As the fluid velocity increases, ${\mathcal{M}}_{\mathcal{S}}>4$, the ratio of BB power to EE power increases to approach a constant value near the Planck-observed value of ∼0.5, regardless of the magnetic field strength. We also examine correlation coefficients between projected quantities, and find thatr^TE≈ 0.3, in agreement with Planck, for appropriate combinations of ${\mathcal{M}}_{\mathcal{S}}$and ${\mathcal{M}}_{\mathrm{A}}$. Finally, we consider parity-violating correlationsr^TBandr^EB. 

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