Anisha Sen1, S.P. Rajaguru1, Ruizhu Chen2, Junwei Zhao2, and Shukur Kholikov3
1. Indian Institute of Astrophysics, Bangalore-34, India
2. W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford CA, USA
3. National Solar Observatory, Boulder CO, USA
The Sun’s magnetic cycle depends on the continual redistribution of magnetic flux across its surface. In widely-known Babcock–Leighton dynamo models[1], magnetic fields emerging in sunspot regions are transported away from active latitudes, with the Joy’s law tilt of the bipolar fields typically facilitating the trailing polarity fields toward the poles, where they cancel the fields of the previous solar cycle and build that up for the next one. The physical processes that control such transport and redistribution of solar photospheric magnetic field are collectively described as surface flux transport (SFT)[2].
In recent years, there have been intense efforts to develop observational data-driven modeling of the evolution of magnetic fields due to both mean flows and turbulent convection, and of their variability linked to the emergence and formation of magnetic structures themselves, thus forming a self-regulating feedback loop[3,4]. All the previous studies had primarily emphasized meridional flows modulated by shallow inflows toward active regions near the solar surface. In our work published recently[5], we have presented evidence that outflows that enhance meridional flows in the deeper half of the near-surface shear layer (NSSL) are dynamically much more important for the global transport of magnetic flux.
Figure 1. Time–latitude profile of variations in the residual meridional flow at two depths, 0.99R⊙ and 0.95R⊙, respectively, are in panels (A) and (B). Positive values correspond to poleward flow in both hemispheres. Corresponding time–latitude variations in the longitudinally averaged signed (i.e., the magnetic butterfly diagram) and unsigned magnetic field are in the lower panels (C) and (D), respectively. The solid line overplotted in panel (D) marks the mean latitude, θm, of peak magnetic flux in each hemisphere, and the dotted–dashed lines in panels (A), (B), and (D) enclose the region 10 – 25 deg away from θm. The two vertical dotted lines mark epochs of solar cycle 24 maximum (2014) and minimum (2020). Sunspot locations are overplotted as black dots.
To study the above processes, we applied time–distance helioseismology to 14 yr of SDO/HMI observations. We analyzed flow patterns within the Sun’s near-surface shear layer over solar cycle 24 and the rising phase of cycle 25, and combined these measurements with synoptic magnetic-field observations extending back across four solar cycles.
One of our central findings is that episodic surges of magnetic flux moving toward the poles are closely linked to poleward plasma outflows occurring over depths of 21 Mm (0.97 R⊙) to 35 Mm (0.95 R⊙) beneath the visible solar surface. These deeper outflows appear to regulate both the timing and strength of polar-field buildup (see Figures 1 and 2). In contrast, the shallow near-surface inflows, which are often included in surface-flux-transport models, do not appear to significantly suppress flux transport. A particularly striking example occurred during solar cycle 24. We found that stronger subsurface outflows in the southern hemisphere during 2013–2015 accelerated the poleward transport of magnetic flux, causing the southern polar field to reach its maximum nearly four years earlier than the northern polar field.
Figure 2. Left: panels (A) and (B) show the residual meridional flows averaged over 10–25 deg away from θm (marked by dotted–dashed lines in Figure 1) in the northern (solid) and southern (dashed) hemispheres at depths 0.99R⊙ and 0.95R⊙, respectively. Panel (C) shows the similarly averaged unsigned line of sight (LOS) HMI magnetic field (|B|), while panel (D) shows the unsigned polar field from WSO measurements. Right: scatterplots illustrating the correlation between variation of unsigned magnetic field and the flow residuals covering the period of cycle 24 (2010 October–2018 June), along with the estimated Spearman rank correlation coefficients; the top four panels correspond to both quantities averaged over the same latitudinal range (10–25 deg away from θm), at depths of 0.95R⊙ (left column) and 0.99R⊙ (right column), for the northern (top row) and southern (bottom row) hemispheres, while the bottom four panels show the correlation between same flow signals against the unsigned magnetic field averaged over the whole active latitude range of 5-40 deg.
We also investigated the transport of magnetic flux across the solar equator. During periods when one hemisphere is magnetically more active than the other, deeper subsurface flows can carry magnetic flux across the equator toward the less active hemisphere. These cross-equatorial flux plumes appear to influence the long-term imbalance between the northern and southern polar fields and may help explain several puzzling asymmetries observed in earlier solar cycles (see Ref [5] for more details).
More broadly, our results suggest that the Sun’s near-surface shear layer acts as a dynamically important interface where magnetic activity and plasma flow strongly interact. In this picture, active regions modify subsurface flows, and those flows in turn regulate the redistribution of magnetic flux, hemispheric coupling, and polar-field formation. This provides a physical framework that helps reconcile earlier discrepancies between helioseismic measurements and surface-flux-transport models.
An important implication of this work is for solar-cycle prediction and space-weather forecasting. Since the Sun’s polar magnetic fields are among the best predictors of future cycle strength, understanding the subsurface flow systems that regulate those fields is crucial for improving predictive models. Our study therefore highlights the need for future dynamo and flux-transport models to incorporate depth-dependent, activity-driven meridional flows rather than relying solely on simplified surface descriptions.
Overall, this work provides observational evidence that the Sun’s magnetic cycle is governed not only by magnetic patterns visible at the surface, but also by evolving flow structures hidden beneath it. For more details, please refer to Ref. [5].
References
[1] Charbonneau, P. 2014, ARA&A, 52, 251
[2] Yeates, A. R., Cheung, M. C. M., Jiang, J., Petrovay, K., & Wang, Y.-M. 2023, SSRv, 219, 31
[3] Jiang, J., Işik, E., Cameron, R. H., Schmitt, D., & Schüssler, M. 2010, ApJ, 717, 597
[4] Cameron, R. H., Schunker, H., Brun, A. S., et al. 2025, A&A, 701, A277
[5] Sen, A., Rajaguru, S.P., Chen, R., Zhao, J. & Kholikov, S. 2026, ApJL, 1002, L2