Probing the large-scale magnetic field inside the Sun from three decades of observed surface magnetograms

TL;DR

The paper addresses reconstructing the Sun's interior magnetic field by assimilating three decades of surface magnetograms into a 3D Babcock-Leighton dynamo (STABLE) driven by helioseismic rotation data. It builds a data-driven poloidal source term from extrapolated radial surface fields (S_C) and evolves the interior field without explicit sunspot buoyancy parameterization. The results reproduce the observed surface butterfly diagram, polar field, and axial dipole, and reveal equatorward migration of a predominantly toroidal interior field with a modest non-axisymmetric component near the surface. The approach demonstrates 3-4 year lead-time predictive capability for cycle amplitudes, offering a path toward self-consistent solar-cycle forecasting and interior-field inference from surface observations.

Abstract

Space-weather and disturbances in the heliosphere are manifestations of the solar magnetic field, which is solely driven by the interior dynamo, and constraining the solar interior magnetic field and its oscillatory behavior is one of the major challenges in solar physics. Observationally, none of the techniques, including helioseismology, are able to provide an estimation of the interior magnetic field. We reconstruct, for the first time, the dynamics of the interior large-scale magnetic fields by assimilating observed line-of-sight photospheric magnetogram data from MDI/SOHO & HMI/SDO along with helioseismic differential rotation data over three decades (1996-2025) into a 3D Babcock-Leighton dynamo model. The assimilation of observational magnetogram data allows us in realistic modelling of Babcock-Leighton mechanism as observed on the Sun without any simplified parameterization. As a result, our data-driven model successfully reproduces key observational features such as the surface butterfly diagram, accurate polar field evolution, and axial dipole moment. The reconstructed interior field dominated by toroidal component exhibits an equatorward migration and reproduces the realistic amplitude and modulation of cycles 23-25. We observe that the non-axisymmetric behaviour of the interior toroidal field becomes less prominent as we move deep towards the tachocline according to our model. A strong correlation between the simulated toroidal field and sunspot number establishes our 3D magnetogram-driven model as a robust predictive model of the solar cycle.

Figures (10)

• Figure 1: (a) Assimilated $B_{r,reduced}$ in the STABLE model corresponding to the MDI magnetogram observed on December 30, 2010, after processing with the MagMAP package and applying the weight factor shown in (b). (c) Assimilated $B_{r,reduced}$ corresponding to the HMI magnetogram observed on January 1, 2011, processed similarly using MagMAP with the weight factor shown in the panel (d).
• Figure 2: Subsurface extrapolation of active regions inside the convection zone. Red and blue colors show the positive and negative polarities of active regions. Active regions are extrapolated deeper in the convection zone up to $0.98R_\odot$ based on their sizes. The bigger active regions go up to a maximum $0.98R_\odot$, but other active regions get extrapolated in between the surface and $0.98R_\odot$ based on their area. The solar surface is shown using the filled contour and extrapolation below the convection zone is shown vertically upward using streamlines till $0.98 R_\odot$.
• Figure 3: Schematic representation of the data assimilation procedure implemented in our model.
• Figure 4: Time evolution of the unsigned radial magnetic flux from daily magnetic maps observed by MDI and HMI (gray), compared with simulations using assimilation cadences of 1 day (red), 2 days (green), 5 days (blue), and 10 days (brown).
• Figure 5: Evolution of the longitude-averaged radial magnetic field at the Solar surface - commonly known as the butterfly diagram from (a) Observational data from 1996 to 2025, derived from MDI and HMI magnetograms, and (b) Simulated data from 1996 to 2025, obtained from our simulation. (c) Time evolution of the polar magnetic fields from our simulation (red) compared with observations from the Wilcox Solar Observatory (gray). Solid lines represent the northern polar field; dashed lines represent the southern polar field. (d) Same as (c) but for the axial dipole moment.