Probing Three-dimensional Magnetic Fields. IV. Synchrotron Polarization Derivative and Vision Transformer

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> ), 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 probes ψ , and the degree of SPD anisotropy, along with its morphological curvature, provides insights into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and γ . 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.