Machine Learning Approach for Estimating Magnetic Field Strength in Galaxy Clusters from Synchrotron Emission

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 \SI{0.135}{\micro G}$^2$, \SI{0.044}{\micro G}$^2$, and \SI{0.02}{\micro G}$^2$ for $\beta = 100$, 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 estimates method that assumes equipartition between cosmic ray electron energy and magnetic field energy. Different from 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.