The Sun's meridional circulation — the large-scale axisymmetric flow that carries plasma poleward at the surface at roughly 10–20 m/s and must return equatorward somewhere in the interior — is a central conveyor belt of flux-transport dynamo models of the solar cycle, yet its structure below the near-surface layers is not known. Competing helioseismic inversions of comparable data disagree qualitatively: a single circulation cell per hemisphere closing at the base of the convection zone, a double cell with the equatorward return flow near 0.820.82–0.91R⊙0.91R_\odot (where R⊙R_\odot denotes the solar radius), a three-layer structure, and possible cycle-to-cycle changes have all been reported, and later work has shown both that the deep flows (a few m/s) sit at the noise-and-systematics floor of current measurements and that distinct cell configurations fit the same travel-time data equally well. The problem is to determine the detailed depth–latitude profile of the meridional circulation through the convection zone — the number of circulation cells stacked in radius, the depth and latitude of the return flow(s), and the variability of this structure over the activity cycle — with systematic errors controlled well enough that the few-m/s deep-flow signal is reliably resolved.

Background

Helioseismology infers the Sun's internal flows from the oscillations observed at the surface: acoustic waves traveling between two surface points through the interior take slightly different times when the plasma along the ray path moves with or against the wave, so "travel-time" differences measured by time–distance helioseismology encode interior flow velocities. Inverting travel times for flows uses weighting functions called averaging kernels, which describe where in the interior a given measurement is sensitive; imperfect kernels have extended off-target "side lobes" that can mix signals from one depth into another. Beyond the surface flow tracers, the meridional circulation (MC) — a flow that is poleward in each hemisphere near the surface with a compensating equatorward return flow at depth, in planes through the solar rotation axis — is the least securely measured large-scale solar flow. Its amplitude at the surface is approximately 10–20 m/s poleward, but the deep return flow is expected to be only a few m/s, at or below the noise level of travel-time measurements, and the inference is contaminated by known systematic effects, most prominently a center-to-limb effect (a travel-time shift that depends only on the position of the measurement on the solar disk, not on interior flows) and by travel-time perturbations from near-surface magnetic activity. The convection zone extends from the visible surface down to about 0.71R⊙0.71R_\odot (with R⊙R_\odot denoting the solar radius; this is the base of the convection zone, where the strong overshoot-and-shear layer called the tachocline sits), so the question concerns the whole shell below the well-measured near-surface shear layer (the outer approximately 5% by radius where rotation rate changes rapidly with depth). The answer matters because virtually all modern flux-transport (Babcock–Leighton type) dynamo models — the leading explanations of the 11-year sunspot cycle — use the MC as the transport belt that carries poloidal magnetic field poleward at the surface and toroidal-flux-related components equatorward at depth. Whether this belt is a single cell closing at the base of the convection zone, or two (or more) cells stacked in radius with the return flow at mid-depth (approximately 0.8R⊙0.8R_\odot), changes where the dynamo loop closes, the cycle's memory and duration, and the predicted latitude drift of sunspot emergence. Getling and Kosovichev (2025), analyzing time–distance flow maps in the top approximately 21 Mm from 2010–2024, note that "the detailed spatial structure of meridional flows is a matter of debate, especially for large depths, due to the low velocity of the flows", citing as competing evidence Zhao et al. 2013 and Gizon et al. 2020; these shallow measurements do not reach the debated depths.

Problem Statement

Determine the detailed spatial structure of the Sun's meridional circulation — the large-scale flow that is poleward near the surface in each hemisphere with a compensating equatorward return flow at depth — in the convection zone below the well-measured near-surface layers, from about 0.95R⊙0.95R_\odot down to the base of the convection zone at about 0.71R⊙0.71R_\odot: (i) the number of circulation cells stacked in radius in each hemisphere — a cell being a layer of meridional flow of one direction (poleward or equatorward) in the meridional plane, so that cells stacked in radius correspond to sign reversals of the flow direction with depth — stated as a function of latitude wherever the structure is latitude-dependent (single cell, double cell, or a more complex multi-layer structure); (ii) the depth or depths and latitudes at which the poleward near-surface flow returns equatorward; (iii) the amplitude and latitudinal profile of the deep flows; and (iv) how this structure varies over the 11-year and extended 22-year activity cycles. A satisfactory determination must control the known helioseismic systematic effects — the center-to-limb effect (a travel-time shift that depends only on the measurement's position on the solar disk and not on interior flows), near-surface magnetic-activity contamination, and averaging-kernel side-lobe leakage of surface flows into the deep interior — at sub-m/s accuracy, below the few-m/s amplitude of the expected deep return flow.

References

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