The Sun's large-scale magnetic field is regenerated cyclically: sunspot emergence migrates equatorward over an approximately 11-year activity cycle, the polar field reverses every cycle, and the whole pattern repeats with a roughly 22-year magnetic polarity period. The physical mechanism responsible — which flows generate and transport the field, and what sets the period, emergence latitudes, tilt, and amplitude of the cycle — has not been identified. The leading candidate is a Babcock–Leighton type alpha-omega dynamo, in which differential rotation winds surface poloidal field into submerged toroidal field and the decay of tilted bipolar active regions regenerates poloidal field, but its details remain open. A directly coupled obstacle is the 'convective conundrum': global numerical simulations of solar convection predict large-scale (giant-cell) flow amplitudes up to one to two orders of magnitude stronger than upper bounds from helioseismic inversions, and different helioseismic techniques disagree among themselves, leaving the speed and structure of the deep flows that drive the dynamo undetermined. The problem remains open.

Background

The solar cycle is the quasi-periodic, roughly 11-year modulation of sunspots, irradiance, and surface magnetism, underlain by a ~22-year cycle in which the Sun's global dipolar (poloidal) magnetic field reverses polarity. Sunspot pairs emerge in the two hemispheres with opposite polarity orientation and at latitudes that drift toward the equator as the cycle progresses, producing the 'butterfly diagram' of sunspot coverage versus time and latitude. Bipolar sunspot groups also emerge tilted with respect to the east–west direction by an angle that grows with latitude (Joy's law). Explaining these robust regularities — the period, the latitude drift, the tilts, the polar reversals, and the cycle-to-cycle amplitude fluctuations including episodes of suppressed activity such as the Maunder minimum — is the solar dynamo problem (Aschwanden 2008 lists 'the solar magnetic field (dynamo, solar cycle, corona)' among the ten outstanding problems of solar physics).

Dynamo theory describes how a conducting fluid can sustain magnetic field against ohmic decay through inductive motions. An 'alpha-omega dynamo' combines two processes: the omega-effect, in which differential rotation (the observed variation of the Sun's rotation rate with latitude and depth) shears poloidal (north–south dipole-like) field into intense toroidal (east–west) field; and an alpha-effect, which converts toroidal field back to poloidal field. In the Babcock–Leighton scenario, named after two 1961 proposals, the alpha step occurs not throughout the turbulent convection zone but at the surface: tilted bipolar active regions, produced when toroidal flux ropes rise buoyantly through the convection zone, decay and disperse their flux (modulated by Joy's-law tilts and transported by surface flows and the poleward meridional circulation), rebuilding the poloidal field. Cameron and Schüssler (2015) showed that the net toroidal flux generated by differential rotation in a hemisphere is effectively determined by the observed surface field, evidence that the surface flux distribution controls the next cycle's reservoir. In 'flux-transport' variants, a deep equatorward return flow of the meridional circulation advects toroidal field and is invoked to set the cycle period. Reviewing this framework, Cameron, Dikpati and Brandenburg (2016) conclude that the arguments favor an alpha-omega dynamo of the Babcock–Leighton type, but that the main open questions remain: why flux emerges at the preferred low latitudes of the butterfly wings, why the cycle is about 11 years long, and what produces Joy's-law tilts — all tied to unresolved subsurface and deep-interior dynamics, along with how magnetic helicity conservation (the near-conservation, at high magnetic Reynolds number, of the field's twist-and-linkage measure, which quenches large-scale field growth in simulations) is circumvented in the Sun.

The convective engine underneath is itself in question. The outer ~30% by radius of the Sun is a convection zone in which energy is transported by turbulent convection at extraordinary parameters (Reynolds number of order 101410^{14}, Prandtl number 10−710^{-7}–10−410^{-4}). Global simulations of rotating spherical-shell convection have long reproduced the Sun's differential rotation, but helioseismology — the inference of interior structure and flows from the Sun's oscillation waves, e.g. by cross-correlating wave travel times between surface points (time-distance helioseismology) — yields upper bounds on deep, large-scale 'giant-cell' convective velocities one to two orders of magnitude below simulation predictions (Hanasoge, Duvall and Sreenivasan 2012; Hanasoge, Gizon and Sreenivasan 2016). This mismatch is the 'convective conundrum': either the simulations are wrong in a fundamental way, or the seismic inversions carry uncontrolled systematics; moreover, different helioseismic techniques and instruments disagree among themselves, and there are no high-latitude (polar) observations to close the picture (Featherstone et al. 2023). Because convection both generates the turbulent electromotive force and sustains the differential rotation and meridional circulation that organize the dynamo, this flow-structure uncertainty propagates directly into every part of the dynamo question — which is why the convection puzzle has been called a 'window into the dynamo' (Featherstone et al. 2023). Charbonneau and Sokoloff (2023), reviewing a century of solar and stellar dynamo theory, enumerate the still-unresolved 'tension points': the physical well-posedness of mean-field electrodynamics (the statistical closure used to model turbulent induction), magnetic helicity conservation, the role of differential rotation and meridional flows in flux-transport dynamos, the competition between Babcock–Leighton induction and alternative poloidal-field sources, and the ambiguous empirical precursors of cycle amplitude.

Problem Statement

Identify, physically and quantitatively, the mechanism by which the Sun generates and cyclically regenerates its large-scale magnetic field. Concretely: (1) determine whether the cycle operates as a Babcock–Leighton type alpha–omega (flux-transport) dynamo — with differential rotation winding poloidal into toroidal field and tilted bipolar active-region decay regenerating poloidal field — or by some competing inductive mechanism, and identify the flows and physics that set the still-unexplained features of the cycle: the ~11-year period, the confinement and equatorward drift of flux emergence latitudes seen in the butterfly diagram, the Joy's-law tilts of bipolar regions, cycle-amplitude modulation including grand minima, and the role of magnetic helicity transport; and (2) resolve the coupled deep-convection question on which (1) depends: establish the true speed and structure of the large-scale convective flows in the solar convection zone — in particular, explain why global convection simulations predict giant-cell amplitudes one to two orders of magnitude larger than helioseismic upper bounds, and why independent helioseismic inversions of these flows disagree among themselves. Completion, as the field frames it, is a self-consistent account in which the convective driving is consistent with helioseismic (and surface-flow) constraints and the resulting dynamo reproduces the observed spatiotemporal structure of the solar cycle, including its cycle-to-cycle variability.

References

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