Global 3D magnetohydrodynamic simulations that self-consistently generate magnetic cycles show the solar meridional circulation being actively driven and reshaped by the dynamo field: magnetic torques near the base of the convection zone modify the angular-momentum balance (gyroscopic pumping), producing a deep mid-latitude upwelling at the equatorward edge of the toroidal field bands that peaks at cycle maximum, a transient near-surface polar counter-cell near cycle minimum, and magnetic modulation of the baroclinic term in the meridional force balance (Passos, Miesch, Guerrero & Charbonneau 2017). If such magnetically driven dynamics operate in the Sun, the kinematic treatment of the meridional circulation at the heart of flux-transport dynamo models is fundamentally incomplete, and a specific, cycle-phased, deep flow signature should exist in helioseismic data. The problem is to determine whether these dynamics operate in the Sun: to detect or bound the predicted deep upwelling helioseismically with systematic errors controlled, to establish by simulation or theory whether the mechanism survives at solar conditions, and to quantify the consequences for kinematic cycle models. Nearly a decade later the deep meridional profile itself remains observationally ambiguous, the predicted signal lies at or below documented systematic errors, and no solar-parameter simulation yet combines a self-generated magnetic cycle with solar-like flows, so the question remains open.

Background

The Sun hosts, besides its differential rotation, a slow axisymmetric flow of a few tens of metres per second along meridians (north-south lines): the meridional circulation (MC), poleward at the surface in each hemisphere, with a return flow somewhere inside the convection zone (the outer roughly 30% by radius of the Sun, where the plasma is convectively unstable). Though weak, MC is a central ingredient of flux-transport dynamo models, the dominant paradigm for the 11-year sunspot cycle. In these models the poloidal (north-south) magnetic field, regenerated by the Babcock-Leighton mechanism (the statistical reorganization of decayed, tilted active-region fields into the global dipole), is carried poleward at the surface, while the toroidal (east-west) field is transported equatorward by the deep return flow; the MC speed therefore sets the cycle period in the advection-dominated regime, and its fluctuations modulate cycle amplitude. In the kinematic approximation the flow is prescribed and unaffected by the magnetic field, which is advected passively.

Large-scale flows in rotating convective envelopes are governed by angular-momentum transport. In the meridional plane the flow is established by gyroscopic pumping: the divergence of angular-momentum fluxes, carried by Reynolds stresses (correlations of turbulent convective velocities) and by Maxwell stresses when magnetic fields are present, drives localized upwelling or downwelling that a closed meridional cell then completes, with the flow sense fixed by the sign of the flux divergence. Three-dimensional simulations of rotating convection (Featherstone & Miesch 2015) showed that this mechanism naturally produces a single-cell MC. The axisymmetric meridional force balance also contains a baroclinic term (a latitudinal entropy gradient, often called the thermal-wind term), which magnetism can itself modulate by altering how convection transports heat (Cossette et al. 2017).

Helioseismology, which probes the solar interior through the Sun's acoustic oscillations (for example time-distance helioseismology, measuring differences in travel time between poleward- and equatorward-propagating waves), is the only observational access to the deep MC, but the target signal is at the metres-per-second level and beset by systematic errors. Observations show the surface MC varies in anti-phase with the activity cycle, conventionally attributed to inflows converging on active regions; that explanation, however, cannot operate at the high latitudes where a transient equatorward counter-cell is observed near cycle minima. Helioseismic inversions disagree on the deep structure: Zhao et al. (2013) reported a double-cell MC with a deep equatorward flow and a high-latitude counter-cell, while later analyses (Liang et al. 2018; Gizon et al. 2020) favour a single cell per hemisphere with the return flow near the base of the convection zone.

Passos, Charbonneau & Miesch (2015) and especially Passos et al. (2017) analysed MC dynamics in the EULAG-MHD millennium simulation, a global 3D convection simulation that self-consistently generates a magnetic cycle with polarity reversals on a multi-decadal timescale, although in a parameter regime far from solar conditions (active latitudes confined to roughly 45-85 degrees, lower Reynolds number, no near-surface shear layer — the strong radial gradient of rotation in the outermost few per cent of the Sun — and no active-region inflows). They found that the MC morphology and amplitude are strongly controlled by the dynamo field through magnetic torques concentrated at the base of the convection zone: gyroscopic pumping modulated by magnetism. Three features stand out. First, a prominent deep upwelling appears at mid latitudes at the equatorward edge of the toroidal field bands, waxing and waning in phase with the cycle and peaking at maximum. Second, a small clockwise (northern-hemisphere) near-surface polar cell appears around activity minimum, reminiscent of the observed high-latitude counter-cell, plausibly tied to the magnetic modulation of baroclinicity through heat-transport changes. Third, because the flow readjusts within a rotation or two while the field evolves over years, the system tracks a quasi-static sequence of force-balanced states, in stark contrast to the kinematic picture of a passive flow advecting a passive field. The unresolved target is whether any of this magnetically driven dynamics actually operates in the Sun.

Problem Statement

Do the magnetically driven meridional-circulation dynamics found in the cyclic convective dynamo simulation of Passos et al. (2017) operate in the Sun? The single overarching objective is to establish whether the Sun's meridional circulation is an actively magnetically driven, cycle-modulated component of the dynamo, rather than the passive, prescribable flow assumed in the kinematic flux-transport framework. Three linked facets jointly answer this one question: each facet is a required deliverable, and a complete answer must state which way the evidence points overall.

(1) Observational test. Search extant and future helioseismic data (from the MDI instrument on the SOHO spacecraft, the HMI instrument on SDO, and the ground-based GONG network; ideally spanning at least two activity cycles) for the predicted coherent upwelling in the deep convection zone at active latitudes, at the equatorward edge of the toroidal field bands, of order 1 m s−1^{-1} near 0.7-0.85 solar radii, building up over the cycle and peaking at cycle maximum. The required outcome is either a detection with the systematic errors that currently limit deep inversions (side lobes of the averaging kernels that encode an inversion's spatial sensitivity, centre-to-limb variation of the travel-time signal, surface magnetic effects, leakage from near-surface active-region inflows) quantified and controlled, or an observational bound stringent enough to exclude the simulated amplitude and cycle phase at those depths and latitudes.

(2) Physical viability at solar conditions. Establish by simulation and/or theory whether gyroscopic pumping driven by dynamo-generated magnetic torques near the base of the convection zone, and the associated magnetic modulation of baroclinicity through heat-transport changes, persist when the convective dynamo is pushed toward solar parameters (solar-like differential rotation with a near-surface shear layer, active latitudes, realistic convective power), including whether the small near-surface polar counter-cell at activity minimum is reproduced and corresponds to the observed solar counter-cell.

(3) Dynamical consequence. Quantify, through systematic comparison of matched kinematic and dynamically coupled models, whether and how magnetic feedback on the meridional circulation changes flux-transport predictions of cycle period, amplitude, and memory (the dependence of one cycle's properties on those of earlier cycles); that is, whether the kinematic approximation materially broke down.

The facets are connected by one scientific objective, and conclusions should be cross-supporting: an unambiguous detection in (1) would establish the magnetic driving and motivate the corrections in (3); a rigorous exclusion in (1), combined with a demonstration in (2) that the mechanism cannot reach observable strength at solar conditions, would refute the solar relevance of the simulated dynamics; (2) alone can establish viability in principle but cannot settle what the Sun actually does. A completion may accordingly be a supported overall verdict rather than a positive detection or exclusion: an explicit conclusion of 'currently inconclusive / not yet decidable' is acceptable, provided the answer reports the evidence, and any bound or limitation reached, for each of the three facets.

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