The solar meridional circulation — the large-scale poleward flow observed at the surface, which must close via a return flow somewhere in the interior — is a central uncertain ingredient of flux-transport models of the solar cycle. From 3D magnetohydrodynamic (MHD) global convection simulations that develop solar-like magnetic cycles, Passos, Charbonneau & Miesch (2015) predicted an equatorward return flow near the base of the convection zone at mid-to-high latitudes, below the depth reachable by helioseismic measurements at the time (about 0.75 R⊙0.75\,R_{\odot}), and posed its confirmation or refutation as an explicit challenge to future helioseismology; they further found that the circulation's topology changes as the magnetic cycle unfolds, and were expanding their own analysis of the physical mechanisms of this magnetic modulation. A decade of subsequent helioseismic analyses has produced mutually conflicting results — double-cell profiles with the return flow in the mid-convection zone versus a single cell closing at the base — and re-analyses show the same data admit either profile, while identified observational systematics can mimic the disputed deep signal. The problem remains open: determine the deep meridional flow profile of the real Sun, in particular whether an equatorward return flow operates near the base of the convection zone, together with the related open question of the physical mechanism by which the cyclic large-scale magnetic field reshapes the circulation topology.

Background

The Sun's surface shows a slow (about 15 m s−115\,{\rm m\,s^{-1}}) flow from the equator toward each pole, called the meridional circulation (MC). Because mass cannot pile up at the poles, this flow must close through an equatorward return flow at some depth inside the convection zone (the outer ~30% by radius of the Sun, r≳0.7 R⊙r\gtrsim0.7\,R_{\odot}, which is convectively unstable), but helioseismology — the inference of the Sun's internal structure and flows from the frequencies and travel times of acoustic oscillation modes — has only partially mapped this return flow. The MC matters because in the flux-transport dynamo (FTD), the dominant framework for modeling the solar cycle, the MC advects magnetic flux: poloidal field generated near the surface by the decay of tilted active regions (the Babcock–Leighton process) is carried poleward, while the depth at which the MC returns equatorward sets where the toroidal field belt is transported toward the equator, and hence the cycle period, the shape of the butterfly diagram, and the model's memory. Whether the MC is a single cell closing at the base of the convection zone or a stack of two (or more) cells, with the equatorward return in the middle of the convection zone, is therefore a decisive input for FTD modeling. In 2013, time-distance helioseismology (a local-helioseismology technique measuring the difference in acoustic travel time between waves propagating northward and southward, hence sensitive to flows along the path) by Zhao et al. (2013) found a double-cell MC: poleward flow down to 0.91 R⊙0.91\,R_{\odot}, equatorward flow between 0.820.82 and 0.91 R⊙0.91\,R_{\odot}, and poleward flow again below 0.82 R⊙0.82\,R_{\odot}, i.e. no equatorward return at the base. Passos, Charbonneau & Miesch (2015) analyzed the meridional circulation emerging in a 3D MHD global simulation of solar convection (the EULAG-MHD code, an implicit large-eddy simulation — ILES, meaning the subgrid-scale dissipation is handled implicitly by the numerical scheme rather than by an explicit turbulence model) that self-consistently produces large-scale magnetic cycles. Comparing a simulated cycle with the Zhao et al. measurements, they argued on dynamical grounds (angular momentum and mass conservation constrain where the return flow can close) that the real Sun should possess an equatorward flow at mid-to-high latitudes near the base of the convection zone, below the 0.75 R⊙0.75\,R_{\odot} depth then probed, and posed this as 'a challenge to future helioseismic measurements which will eventually refute or confirm this result'. The same simulations showed that the MC undergoes substantial cyclic changes in morphology: the large-scale toroidal magnetic field modulates the turbulent Reynolds stresses (the correlations of convective velocity fluctuations that transport momentum, e.g. ⟨ur′uθ′⟩\langle u'_r u'_\theta\rangle) and the convective overshoot (the penetration of flows beneath the unstable zone, relevant to the tachocline — the shear layer at the base of the convection zone), reshaping the circulation. The authors stated they were expanding their analysis to understand these mechanisms, and noted that this two-way coupling between field and flow challenges the kinematic approach (prescribed flows, unaffected by the magnetic field) used in most FTD simulations. Two systematic effects complicate the observational side: the center-to-limb effect (a travel-time shift artifact that varies with disk position, which must be separated from the flow signal), and extended side lobes of the helioseismic averaging kernels (the spatial weight functions that relate measured travel times to the flow at each interior point), which can contaminate weak deep-flow inversions with signal from the much stronger surface flows.

Problem Statement

Determine the dynamical behavior of the solar meridional circulation in the deep convection zone, as posed by Passos, Charbonneau & Miesch (2015) from 3D MHD global convection simulations: the observational confirmation or refutation — via deeper helioseismic probing or other diagnostics — of the predicted equatorward return flow near the base of the solar convection zone at mid-to-high latitudes, below the roughly 0.75 R⊙0.75\,R_{\odot} depth reachable by measurements available in 2015; that is, establishing the actual deep topology of the meridional circulation, with the systematic effects (center-to-limb effect, averaging-kernel side lobes, inversion non-uniqueness) controlled well enough to discriminate between candidate profiles. The source's prediction is not a binary choice between a single cell closing at the base and a multi-cell stack with its equatorward return in the mid-convection zone: in the predicting simulations, an equatorward flow near the base of the convection zone generally occurs even if the circulation in the bulk of the convection zone is multi-celled, and an equatorward return flow in the mid-convection zone does not necessarily rule out an additional equatorward flow at the base; the deep topology may also change over the course of the solar cycle. This observational deliverable is resolved by the sign of the time-averaged meridional flow in the mid-to-high-latitude band at depths below about 0.75 R⊙0.75\,R_{\odot}: it is confirmed by a systematics-controlled determination that this deep flow is equatorward, refuted by a comparably controlled determination that it is poleward or consistent with zero, and is not settled merely by a double-cell profile in the bulk of the convection zone, since an equatorward mid-convection-zone return and an equatorward near-base return can coexist. A verdict that the deep signal cannot yet be separated from the named systematics resolves the deliverable only if that inability is demonstrated rather than asserted — for instance by showing that the candidate profiles are indistinguishable under the averaging kernels — and it states the observational advance that would decide between them. The same simulations also raise a second open question that this task requires answering: the physical mechanism by which the cyclic large-scale toroidal magnetic field modulates the turbulent Reynolds stresses and convective overshoot depth so as to reshape the meridional circulation topology over the solar cycle. An adequate account must identify the causal pathway from the cyclic large-scale field to the modulation of the turbulent Reynolds stresses and of the convective overshoot depth and hence to the change in circulation topology, and must state which links in that pathway the existing simulations establish and which remain open; a report of the topology change without an identified causal pathway does not complete this deliverable.

References

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