Ruizhu Chen

Surface flux transport (SFT) models are routinely used to model the Sun’s photospheric magnetic field and provide inner boundary conditions for coronal and heliospheric models, yet they remain fundamentally limited by the lack of direct information about flux emergence on the farside of the Sun. To address this, we develop a framework for incorporating helioseismic images of far-side active regions (HIFAR) into the advective flux transport (AFT) model. Using near-simultaneous magnetic flux maps (HIFARM) inferred from HIFAR, and Solar Terrestrial Relations Observatory (STEREO)/Extreme Ultraviolet Imager (EUVI) 304 Å observations from 2010 May 13 to 2014 August 18, we develop a logistic regression model to estimate the probability that a helioseismic detection corresponds to an active region (AR) based on descriptors of magnetic flux, field strength, and location. The model achieves a precision of 0.93 for AR detections at a probability threshold of 0.73, selected to reject 90% of “ghost” ARs. We also derive an empirical scaling relationship between HIFARM and AFT flux to place HIFARM on the AFT flux scale, and demonstrate that the framework reproduces the flux evolution of ARs consistent with near-side observations over multiple solar rotations. At the global scale, we find that conventional nearside-driven AFT simulations underestimate the total unsigned magnetic flux by ≈10%−20% of the Sun’s total magnetic flux budget. The probabilistic AR detection model and the complete framework developed in this work provide a practical pathway for incorporating helioseismic far-side ARs into SFT models, a step toward realistic modeling of the full-Sun magnetic field.

Large solar active regions (ARs) tend to be long-lived and spatially clustered, with repeated emergence occurring in persistent solar activity nests over extended timescales. By analyzing long-term spatiotemporal magnetic flux maps constructed from near-side magnetic field observations and far-side helioseismic AR maps, we investigate the recurrence and clustering properties of large ARs during solar cycle 24. We find that, in both hemispheres, over 63% of magnetic flux emerges and clusters within or near three distinct bands in the spatiotemporal maps, two of which rotate faster than the Carrington rate and one more slowly. These bands closely correspond to low-order nonaxisymmetric modes, primarily the azimuthal order m = 1 mode. The drift rates of the three spatiotemporal bands are in good agreement with the phase speeds inferred for these modes. The frequencies of the dominant modes are consistent with slow magneto-Rossby waves originating in the solar tachocline, which are associated with odd harmonic degrees ℓ and a toroidal magnetic field strength of approximately 4.0 kG. Our results suggest that magneto-Rossby waves play an important role in modulating both the timing and longitudinal localization of major AR emergence. Rieger-type periodicities may arise from interactions between a dominant mode and weaker modes, while longer quasi-periodic variations on 0.6–4 yr timescales are likely linked to intersections of multiple major modes. These findings point to a potential connection between surface magnetic flux patterns and dynamical processes in the tachocline.

Using time–distance helioseismology applied to 14 yr of Solar Dynamics Observatory/Helioseismic and Magnetic Imager observations spanning solar cycle 24 and the rising phase of cycle 25, we present evidence that meridional flows in the lower half of the near-surface shear layer (NSSL), modulated by active-region magnetic fields, play a central role in the episodic global transport of magnetic flux. In particular, polar-field buildup is tightly linked to plasma outflows diverging from active latitudes within the deeper NSSL. The magnitude and timing of hemispheric polar-field evolution are regulated by depth-dependent meridional flow, including its cross-equatorial component, responding to active-region flux asymmetries. During cycle 24 maximum, stronger southern outflows accelerated flux transport, causing the southern polar field to peak nearly 4 yr before the northern. Global magnetic flux transport patterns in the previous three solar cycles (21, 22, and 23) show broad consistency with the deeper meridional flow modulation inferred in cycles 24 and 25. These results identify activity-dependent flow variations in deeper layers of the NSSL as a dynamically significant component of the Babcock–Leighton process that governs the generation and hemispheric asymmetry of the global dipole field.

The interplanetary magnetic field (IMF) measured near Earth can be up to 2 times greater than that derived from models using remote solar observations. We investigate this discrepancy by modeling the IMF using a potential field source surface (PFSS) model using synoptic maps of the photospheric magnetic field from 2010 May to 2024 April. Five types of radial field synoptic maps are used in this work: the B _r synoptic maps from vector magnetic field data, the M _r synoptic maps from the line-of-sight field data, the rescaled M _r synoptic maps rescaled from the M _r maps by a center-to-limb distance dependent rescaling factor of B _r / M _r , and composite and rescaled composite synoptic maps comprised of a combination of strong-field pixels from the B _r maps and the rest from either the original M _r or rescaled M _r maps. The modeled IMFs from all five types of synoptic maps agree with each other well in the solar maximum phase, when they are about 2 times smaller than in situ measurements. The IMF calculated from the B _r and both composite and rescaled composite synoptic maps match well with in situ observations during solar minimum from 2017 to 2022. The IMF values modeled from both the M _r and rescaled M _r synoptic maps are still significantly smaller in this time interval. This suggests that (1) the B _r maps represent the radial field better than the M _r ; and (2) the PFSS model is appropriate to model the heliospheric magnetic field in solar minimum, but has limitations when used near solar maximum.

Over the past decade, solar equatorial Rossby waves have been unambiguously identified and are considered potential diagnostics of solar interior dynamics. We investigate their inclined structure and temporal evolution in the solar interior across multiple depths using approximately 14.5 yr of ring-diagram and time–distance helioseismology data from Solar Dynamics Observatory/Helioseismic and Magnetic Imager. Normalized phase differences and cross power are computed from filtered spherical harmonic coefficients of radial vorticity to probe the structural tilt and power of Rossby waves. We find a systematic and robust depth-dependent phase behavior that shows no clear significant correlation with the solar cycle, while the depth-dependent cross power exhibits a positive correlation with the solar cycle for both data sets. Our results show that deeper depths lead in phase over shallower ones, with increasing negative phases with depth. We infer that Rossby waves exhibit a retrograde tilt relative to the Sun’s rotation that is stable throughout the solar cycle. Analogous small tilts have been noted in planetary atmospheres and in magnetohydrodynamic simulations of the Sun, indicating that this behavior is not uncommon in rotating, stratified bodies and has implications for angular momentum and energy transport in the solar interior.

Using time–distance helioseismic measurements of meridional flow in the near-surface shear layer over a period of 14 yr starting from 2010 May, we probe the depth structure and evolution of its cross-equatorial part. We confirm that the hemispheric magnetic asymmetry determines the amplitude and direction of such flows. Additionally, we find that these flows turn over and change direction at depths below 0.97 R _⊙ forming circulation cells with lifetimes dictated again by the hemispheric magnetic imbalance, which is dominated by the occurrences of large sunspots. We also examine connections between cross-equatorial magnetic flux plumes and flows and discuss their implications for the equatorial flux cancellation/submergence and the poleward transport of flux.

Using time-distance helioseismic measurements of meridional flow in the near-surface shear layer over a period of 14 years, starting from May 2010, we probe the depth structure and evolution of its cross-equatorial part. We confirm that the hemispheric magnetic asymmetry determines the amplitude and direction of such flows. Additionally, we find that these flows turn over and change direction at depths below 0.97R, forming circulation cells with lifetimes dictated again by the hemispheric magnetic imbalance, which is dominated by the occurrences of large sunspots. We also examine connections between cross-equatorial magnetic flux plumes and the flows, and discuss their implications for the equatorial flux cancellation/submergence and the poleward transport of flux.

Using solar-cycle long helioseismic measurements of meridional and zonal flows in the near-surface shear layer (NSSL) of the Sun, we study their spatio-temporal variations and connections to active regions. We find that near-surface inflows towards active latitudes are part of a local circulation with an outflow away from them at depths around 0.97 R, which is also the location where the deviations in the radial gradient of rotation change sign. These results, together with opposite-signed changes over latitude and depth in the above quantities observed during the solar minimum period, point to the action of the Coriolis force on large-scale flows as the primary cause of changes in the rotation gradient within the NSSL. We also find that such Coriolis force-mediated changes in near-surface flows towards active latitudes only marginally change the amplitude of zonal flow and hence are not likely to be its driving force. Our measurements typically achieve a high signal-to-noise ratio ($>$5$σ$) for near-surface flows but can drop to 3$σ$ near the base (0.95 R) of the NSSL. Close agreements between the depth profiles of changes in rotation gradient and in meridional flows measured from quite different global and local helioseismic techniques, respectively, show that the results are not dependent on the analysis techniques.

Low-m inertial modes have been recently discovered in the Sun’s high-latitude regions. In this study, we characterize the observational properties of the m = 1 mode by analyzing time–distance subsurface flow maps. Synoptic flow maps, constructed from daily subsurface flow maps using a tracking rate corresponding to the rotation at latitude 65°, are filtered in both the spherical harmonic and Fourier domains to retain only the m = 1 mode and its dominant frequencies. Our analysis reveals a power distribution that is significantly stronger in the northern polar region. The mode’s power exhibits an anticorrelation with solar activity, remaining strong and persistent during the solar activity minimum and becoming weaker and more fragmented during the solar maximum. Magnetic flux transported from low to high latitudes influences both the mode’s power and lifetime, enhancing its power and shortening its lifetime upon arrival. The phases of the m = 1 mode in the northern and southern polar regions are near-antisymmetric for most of the time with short deviations. We also compute zonal and meridional phase velocities of the mode and find that it exhibits significantly less differential rotation than its surrounding plasma. The meridional phase velocity, comprising both the local plasma’s meridional flow and the mode’s intrinsic phase motion, is directed poleward below latitude 70° and equatorward above this latitude. These observational findings underscore the need for a deeper understanding of the internal dynamics of the low-m modes, which may offer valuable insights into the structure and dynamics of the solar interior.