The Sun's meridional circulation — a slow poleward flow at the surface with an equatorward return flow at depth — sets the period and memory of the flux-transport solar dynamo. Georgieva and Kirov (2007; published in expanded form 2011) reconstructed multi-decadal variations of its surface and deep branch speeds and of the reversal depth from the varying lag between sunspot maximum and the declining-phase geomagnetic activity peak, and speculated that an over-slow surface flow pushing the return branch into low-diffusivity layers triggers grand minima. That reconstruction averaged the two hemispheres, assumed a single circulation cell and an unconstrained turbulent-diffusivity profile, and left the cause of the secular changes explicitly open. Later work has measured flow variations only since about 1996, remains divided on even the present-day deep structure (single versus double cell), and dynamo models show that flow fluctuations can produce grand minima without identifying the actual solar mechanism. The open problem is a hemisphere-resolved, century-scale reconstruction of the internal flow together with the identification of the mechanism behind its secular variations.

Background

The Sun's magnetic activity varies on an approximately 11-year cycle (the sunspot cycle), driven by a dynamo that cyclically converts a poloidal field (dipole-like, north–south) into a toroidal field (azimuthal, east–west) and back. In the currently favored Babcock–Leighton–type flux-transport dynamo, the poloidal field is regenerated at the surface from the decay of tilted sunspot groups, while the toroidal field is amplified by rotational shear at the tachocline — the thin shear layer at the base of the convection zone separating the differentially rotating envelope from the nearly uniformly rotating radiative interior. A slow axisymmetric meridional circulation — plasma flowing poleward at the surface at a few meters per second and returning equatorward at depth — couples these generation regions: it carries surface poloidal flux to the poles, down to the base of the convection zone, and back toward the equator, thereby setting the cycle period and the 'memory' of the dynamo. The competition between this advective transport and turbulent diffusion of magnetic flux, quantified by the magnetic Reynolds number Rm=VL/ηR_m=VL/\eta (flow speed VV, length LL, turbulent magnetic diffusivity η\eta), defines two dynamo regimes: diffusion-dominated (Rm<1R_m<1), in which a faster deep flow leaves less time for diffusive decay and raises the cycle amplitude, and advection-dominated (Rm>1R_m>1), in which a faster deep flow lowers it. The depth profile of η\eta in the convection zone is poorly known, so which regime the Sun actually operates in is debated.

The empirical handle used by the source work is geomagnetic. Geomagnetic disturbance is quantified by the aa index, a three-hourly global index compiled from two nearly antipodal observatories and available since 1868. Geomagnetic activity has two peaks in each sunspot cycle: one near sunspot maximum, driven by coronal mass ejections — expulsions of magnetized plasma from closed-field regions, associated with the solar toroidal field — and one on the declining phase, driven by high-speed solar-wind streams from polar coronal holes — open-field regions associated with the poloidal field. A method to separate sunspot-related from non-sunspot-related geomagnetic activity was introduced by Feynman (1982) and developed into source-separated compilations by Richardson et al. (2002). Georgieva and Kirov (2007, published in expanded form 2011) used the varying time lag between sunspot maximum and the declining-phase geomagnetic peak to reconstruct, cycle by cycle since 1868, the speeds of the surface and deep meridional branches and the depth at which the flow reverses from poleward to equatorward, assuming one circulation cell per hemisphere, one full flow turnover per cycle, and a circulation penetration radius near 0.70.7 solar radii; using sunspot and cosmogenic-isotope reconstructions they extended the estimates back through the Maunder minimum (1645–1715), the best-known grand minimum of solar activity. They concluded that the dynamo operated in a diffusion-dominated regime in recent cycles but in an advection-dominated regime during the Maunder minimum, and speculated that a grand minimum begins when the surface flow slows so much that the deep return branch lands in layers of diffusivity below a critical threshold. They also noted that hemisphere-resolved dynamo simulations (Dikpati et al., 2007) already showed the two hemispheres' flows evolving differently, while their own reconstruction necessarily averaged the hemispheres.

Direct measurements of the internal flow exist only through helioseismology — the use of the Sun's acoustic oscillations to probe its interior; in the time-distance technique, travel times of sound waves between pairs of surface points are inverted for the subsurface flow — and only since about 1996. These inversions show that the surface flow varies over the solar cycle and is north–south asymmetric (Gizon and Rempel, 2008; Hathaway and Rightmire, 2010), but they disagree even on the time-averaged deep structure: some analyses find a double-cell circulation (Zhao et al., 2013; Chen and Zhao, 2017), while an analysis of GONG and MDI/HMI data spanning 1996–2019 favors a single cell per hemisphere (Gizon et al., 2020), and systematic center-to-limb artifacts still limit deep-flow inference (Chen and Zhao, 2017, 2023). No direct observation constrains the secular, century-scale variation of the internal flow, and the physical cause of the multi-decadal changes reconstructed by Georgieva and Kirov — or the mechanism that would push the Sun into a grand minimum — remains unidentified.

Problem Statement

Determine the multi-decadal to centennial evolution of the Sun's internal meridional circulation and its physical cause. Concretely: (1) reconstruct, separately for the northern and southern hemispheres, the time variation since at least the mid-19th century of the speed of the surface (poleward) branch, the speed of the deep (equatorward) branch, and the depth at which the flow reverses, with quantified uncertainties, validating the reconstruction against direct helioseismic inversions for the era they cover (1996-present); and (2) identify the physical origin of these secular changes — whether they are stochastic fluctuations of the convection or deterministic responses to slow changes in the solar interior (for example in differential rotation, solar radius, or angular-momentum transport), and in particular whether an over-slow surface flow that drives the deep return branch into lower-diffusivity layers is what initiates grand minima such as the Maunder minimum. An answer should also state the consequences for the dynamo regime (diffusion- versus advection-dominated) attributable to each epoch, given the joint constraints on the turbulent-diffusivity depth profile.

References

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