Combined Surface Flux Transport and Helioseismic Far-Side Active Region Model (FARM)

Maps of the magnetic field at the Sun’s surface are commonly used as boundary conditions in space-weather modeling. However, continuous observations are only available from the Earth-facing part of the Sun’s surface. One commonly used approach to mitigate the lack of far-side information is to apply a surface flux transport (SFT) model to model the evolution of the magnetic field as the Sun rotates. Helioseismology can image active regions on the far side using acoustic oscillations and hence has the potential to improve the modeled surface magnetic field. In this study, we propose a novel approach for estimating magnetic fields of active regions on the Sun’s far side based on seismic measurements and then include them into an SFT model. To calibrate the conversion from helioseismic signal to magnetic field, we apply our SFT model to line-of-sight magnetograms from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to obtain reference maps of global magnetic fields (including the far side). The resulting magnetic maps are compared with helioseismic phase maps on the Sun’s far side computed using helioseismic holography. The spatial structure of the magnetic field within an active region is reflected in the spatial structure of the helioseismic phase shifts. We assign polarities to the unipolar magnetic-field concentrations based upon Hale’s law and require approximate flux balance between the two polarities. From 2010 to 2024, we modeled 859 active regions, with an average total unsigned flux of 7.84⋅1021\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$7.84 \cdot 10^{21}$\end{document} Mx and an average area of 4.48⋅1010\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$4.48 \cdot 10^{10}$\end{document} km2. Approximately 4.2%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$4.2\%$\end{document} of the active regions were found to have an anti-Hale configuration, which we manually corrected. Including these far-side active regions resulted in an average increase of 1.2%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1.2\%$\end{document} (up to 25.3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$25.3\%$\end{document}) in the total unsigned magnetogram flux. Comparisons between modeled open-field areas and EUV observations reveal a substantial improvement in agreement when far-side active regions are included. This proof of concept study demonstrates the potential of the “combined surface flux transport and helioseismic Far-side Active Region Model” (FARM) to improve space-weather modeling.