The Sun's meridional circulation, the large-scale flow that runs poleward at the photosphere and is thought to close via an equatorward return flow at depth, is a central ingredient of flux-transport solar dynamo models, yet how it varies in time and what that variability does to the dynamo remains unresolved. Helioseismic observations show its near-surface speed organizing into bands that migrate with the 11-year activity cycle, secondary circulation structure reported around the Cycle 24 maximum and into Cycle 25, and extended-cycle (roughly 22-year) and longer-term trends, while dynamo theory identifies the circulation as the agent that carries surface magnetic memory down to the tachocline and thereby underlies precursor-based cycle prediction. This record poses the open problem of characterizing the time-dependent meridional circulation as a function of latitude and depth over solar-cycle, extended-cycle, and multi-decade timescales, and of establishing quantitatively how this variability modulates cycle amplitude, period, and rise/decay asymmetry, and how it enables or limits solar-cycle predictability.

Background

The solar magnetic cycle, manifested in the roughly 11-year rise and fall of sunspot numbers, is driven by a magnetohydrodynamic dynamo operating in the Sun's convection zone. In the widely used Babcock–Leighton/flux-transport picture, the poloidal (north–south dipole-like) field is regenerated at the surface from the decay of tilted bipolar active regions, while the toroidal (azimuthal) field that produces sunspots is amplified by rotational shear in the tachocline, the thin shear layer at the base of the convection zone near 0.7 R⊙0.7\,R_{\odot}. The two branches are coupled by the meridional circulation: a slow (∼\sim 10–20 m/s) flow that runs poleward at the surface and is conventionally assumed to close by an equatorward return flow in the interior. In these models the circulation acts as a conveyor belt whose speed and geometry set the cycle period and strongly modulate cycle amplitude, so any time variation of the flow feeds directly into cycle behavior.

What the flow actually does inside the Sun is measured only indirectly, by helioseismology: inferring subsurface flows from the properties of the Sun's acoustic oscillations. Two local techniques dominate. Ring-diagram analysis tracks horizontal flows in the outer few percent of the radius by measuring shifts in the frequencies of acoustic modes trapped under small patches of the surface, while time-distance helioseismology measures the travel times of acoustic waves between surface points and inverts them for deeper flows. Both are limited by known systematic errors, most prominently an unexplained center-to-limb travel-time effect (a systematic signal that varies with position across the solar disk and can masquerade as, or hide, a true meridional flow), and they disagree in part on the deep circulation: time-distance inversions found evidence for a double-cell (poleward cell over an equatorward counter-cell) circulation, while other analyses favor a single cell, and even the static deep profile remains disputed.

The time dimension is even less settled. Time–latitude maps of the near-surface meridional flow show alternating bands of faster and slower flow that migrate toward the equator with the activity cycle, in step with the torsional oscillations (alternating bands of faster and slower rotation) and the extended solar cycle, the roughly 22-year pattern of migrating flow and weak magnetic activity that starts near the poles well before each sunspot maximum. More recent long-baseline analyses trace extended-cycle variations of the meridional flow itself, report secondary circulation components converging on the active latitudes that became prominent around the Cycle 24 maximum and into Cycle 25, and combine multi-instrument records from the Global Oscillation Network Group (GONG), the Michelson Doppler Imager (MDI), and the Helioseismic and Magnetic Imager (HMI) to search for secular multi-decade trends. On the theoretical side, idealized experiments with stochastic forcing have shown that a tachocline-based mean-field dynamo has surface-field predictive skill (the basis of polar-field precursor schemes for forecasting the next cycle) only when meridional circulation is included, because only then is the surface poloidal field submerged and carried to the tachocline where the next cycle's toroidal field is built. Whether the observed time variability of the circulation is deterministic (e.g., Lorentz-force feedback from the magnetic field) or stochastic, how it propagates into cycle amplitude, period, and shape, and how much of cycle predictability rests on it, are unresolved questions that current dynamo-based forecasts explicitly acknowledge as missing physics.

Problem Statement

Determine how the Sun's internal meridional circulation varies in time - as a function of latitude and depth, on the 11-year solar-cycle and the roughly 22-year extended-cycle timescales, including any longer-term multi-decade trends - and establish quantitatively what this time dependence does to the solar dynamo.

Concretely, a resolution must characterize, over the available multi-instrument helioseismic record (GONG/MDI/HMI, Solar Cycle 23 onward) and acknowledging the baseline and cross-calibration limitations of that record: (1) the migrating bands of enhanced and reduced meridional-flow speed and their relation to the torsional-oscillation and magnetic-activity belts; (2) the appearance, latitude–depth structure, growth, and decay of secondary or counter-circulation cells, including those reported around the Cycle 24 maximum and into Cycle 25; and (3) any secular trends in the flow over the available multi-instrument record. On this basis, it must also establish the dynamo consequences of the variability: how time-varying meridional circulation modulates cycle amplitude, period, and rise/decay asymmetry; whether the observed variability is deterministic (e.g., Lorentz-force feedback), stochastic, or a combination of the two in origin; and what fraction of solar-cycle predictability - in particular the skill of polar-field and tachocline-based precursor schemes, which exists in interface dynamos (tachocline-based dynamos whose toroidal-field amplification is concentrated in the thin shear layer at the base of the convection zone) only when meridional circulation couples the surface field back down to the tachocline - is attributable to, or limited by, the circulation's time variability. A resolution requires all of these parts jointly - the observational characterizations (1)-(3) and all three dynamo consequences are each necessary - and must address the predictability consequence by stating how much of the variance or forecast uncertainty in the relevant cycle property (e.g., the next cycle's polar field or amplitude) is attributable to the circulation's time variability; this part is satisfied by a quantitative estimate of that fraction - a value or an explicit bound at the tightest precision the evidence supports, each accompanied by a quantified uncertainty and the basis for the estimate. The characterizations (1)-(3) must be established by synthesizing the multi-instrument record rather than by restating any single cited study, and the dynamo consequences must be argued from that synthesis together with explicit dynamo-theory or simulation results; a resolution is judged complete only when it provides (i) a single latitude-depth-time synthesis of the circulation that, for each of (1)-(3), reports the latitude and depth range and the instrument(s) that constrain the feature and states what the record establishes and what it leaves unconstrained, (ii) a quantitative statement, as a value or an explicit bound at the tightest precision the evidence supports, each with a quantified uncertainty and stated basis, of how the variability modulates cycle amplitude, period, and rise/decay asymmetry, (iii) a determination of the origin of that variability - deterministic, stochastic, or a stated combination - with the evidence for it, and (iv) the predictability fraction meeting the standard stated above.

References

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