The solar dynamo begins near the surface

This study investigates whether the Sun’s global dynamo is driven by a near-surface magneto-rotational instability (MRI) operating in the near-surface shear layer (NSSL), rather than by processes in the deeper tachocline. Key observational constraints include: the butterfly diagram of sunspot emergence migrating from ∼30° latitude to the equator on an ∼11-year timescale; torsional oscillations that track sunspot migration; a poloidal field of ∼1 G at the photosphere that lags sunspots by a quarter cycle and reaches ∼100 G below the surface; the hemispheric current-helicity sign rule (negative in the north, positive in the south); and the presence of strong inwardly increasing differential rotation in the outer 5–10% of the Sun revealed by helioseismology. Prior deep-seated dynamo models struggle with these constraints. The authors hypothesize that the axisymmetric MRI, triggered by inwardly increasing rotation and a background poloidal field in the NSSL, initiates the solar cycle near sunspot minimum, producing the observed torsional oscillations and generating toroidal field. They ask whether MRI-based near-surface dynamics can quantitatively account for the spatiotemporal scales and amplitudes of the observed flows and fields.

Traditional interface/tachocline dynamos tend to produce high-latitude fields and predict shear disruptions inconsistent with observations. Mean-field dynamos provide qualitative insights but lack first-principles foundations and conflict with observed meridional circulations. Global convection-zone simulations often require unrealistic conditions and misalign with key solar observations. Previous proposals considered a distributed or near-surface dynamo shaped by the NSSL without invoking MRI, while some kinematic studies dismissed NSSL relevance by excluding full MHD instabilities. Local MRI analyses in a solar context have focused on small scales, and recent advances in large-scale MRI physics have not been applied to the solar dynamo. Helioseismology pins the low-latitude torsional oscillations to the NSSL, suggesting near-surface processes. The Babcock–Leighton paradigm addresses poloidal regeneration but does not by itself specify where instability originates. This work builds on MRI theory from accretion disks (and laboratory confirmation) to propose an NSSL MRI as the engine of the global solar cycle.

The authors use a combination of analytic estimates and global linear eigenmode calculations of the MRI in a solar-like near-surface shell to assess feasibility and predict observables.

• Instability criterion and scaling: They adopt the axisymmetric MRI condition ω_A = 2ΩS > ω_λ, with ω_A = B_0 k / (4πρ_0) the local Alfvén frequency, S = −r⁻¹ dΩ/dr the shear, Ω the rotation rate, and k ≈ π/H_r the smallest radial wavenumber fitting in the layer of depth H_r. In the adiabatic convection zone, buoyancy effects on the linear criterion are negligible. Empirical NSSL values give S ≈ Ω ≈ 2π per month, and early-phase torsional oscillation timescales (2–12 months) imply modest MRI growth rates (γ on the order 10⁻³–10⁻¹ of Ω), consistent with mildly nonlinear dynamics.
• Numerical model: They solve for eigenstates of the linearized anelastic MHD equations in spherical polar coordinates (r, θ, φ) using the Dedalus spectral framework. Domain spans r/R_⊙ ∈ [0.89, 0.99] to isolate the NSSL while avoiding the photospheric layer where compressibility, partial ionization, radiative transfer, and vigorous convection complicate dynamics. The anelastic approximation with an adiabatic background captures strong density stratification (∼100× density contrast across the NSSL producing ∼10× variation in Alfvén speed) and removes acoustic modes; entropy perturbations are small and decoupled.
• Background profiles: Density ρ_0(r) is a polynomial fit to Model S, accurate to <1% over the domain. Differential rotation is Ω(r, θ) = Ω_0 R(h) Θ(μ), with Ω_0 = 466 nHz, R(h) = 1 + 0.02h − 0.01h² − 0.03h³ (h the normalized radius), and Θ(μ) = 1 − 0.145μ² − 0.148μ⁴ (μ = cos θ), matching helioseismic constraints below 60° latitude. The background magnetic field is a confined poloidal configuration constructed from a vector potential with B_0(r) ∝ (r/r_)⁻³ − (r/r_)⁻², yielding predominantly horizontal near-surface field with RMS |B| ≈ 180 G and subsurface strengths consistent with inferences (∼50–150 G poloidal). The configuration is in MHD force balance. Pure dipole and mixed cases were also tested with similar outcomes.
• Eigenmode analysis and saturation estimates: Global MRI eigenmodes are computed to identify growth rates, spatial structure (fast and slow branches), and confinement to the NSSL (surface down to r/R ≈ 0.90–0.95). Quasi-linear theory is used to estimate saturation by background shear modification, leading to an analytical estimate for torsional oscillation amplitude Ω′ from a balance dominated by shear feedback (their equation (3)). Using the full numerical eigenstates, quasi-linear saturation amplitudes are computed for representative modes.
• Observational cross-checks: Helioseismic rotation profiles quantify shear (latitudinal 400–600 nHz on average in the NSSL, peaks ∼1,200 nHz; tachocline shear much smaller), torsional oscillation patterns and amplitudes (∼nHz level), and spatial scales (horizontal aspect ratio ∼4:1, NSSL thickness ∼5% of R_⊙). Alfvén speeds v_A ≈ 200–2,000 cm s⁻¹ (0.1–1.0 R_⊙ per year) are inferred to match MRI requirements and observed subsurface field strengths (poloidal ∼100–200 G; toroidal ∼300–1,000 G within the NSSL).

• Near-surface MRI feasibility: Simple scaling with observed NSSL shear (S ≈ Ω ≈ 2π per month) and torsional oscillation timescales (2–12 months) implies MRI growth rates in the mildly nonlinear regime, consistent with regular solar cycles. The observed horizontal aspect ratio (∼4:1) and layer thickness (∼5% of R_⊙, k ≈ 70/R_⊙) match MRI mode geometry in the NSSL.
• Field strengths: Required Alfvén speeds (v_A ≈ 200–2,000 cm s⁻¹) correspond to internal poloidal fields of ∼100–200 G given NSSL densities (ρ_0 ≈ 3×10⁻²–3×10⁻¹ g cm⁻³), consistent with helioseismic/magnetic inferences. MRI can operate up to latitudinal toroidal field strengths ≈1,000 G, with subsurface toroidal fields ∼300–1,000 G confined to the NSSL.
• Global MRI eigenmodes: Two branches are identified and confined to the NSSL (surface to r/R ≈ 0.90–0.95): • Fast branch: direct growth with γ/Ω ≈ 6×10⁻², e-folding time t ≈ 60 days; spatial pattern with roughly one wave between equator and 20° latitude, resembling torsional oscillations. • Slow branch: γ/Ω ≈ 6×10⁻³, e-folding t ≈ 600 days, oscillation frequency ω/Ω ≈ 7×10⁻³ (period P ≈ 5 years); pattern spans equator to ∼20–30° latitude. Additional modes: 34 other fast purely growing modes, two additional oscillatory modes, and one intermediate exceptional mode were found.
• Torsional oscillations and saturation: Analytical shear-modification estimate (their equation (3)) gives Ω′ ≈ 7 nHz for S = Ω_0 − ω, consistent with observed torsional oscillation amplitudes. Quasi-linear saturation from full eigenstates yields Ω′ ≈ 6 nHz (fast branch) and Ω′ ≈ 3 nHz (slow branch), both comparable to observations.
• Helicity hemispheric rule: Slow-branch current helicity H ∝ (∇×b)·b exhibits H < 0 in the north and H > 0 in the south, reproducing the observed hemispheric sign rule and suggesting rotationally constrained dynamics (low Rossby number) for this branch.
• Dynamo picture: The axisymmetric subsurface field and torsional oscillations constitute a nonlinear MRI traveling wave. Saturation proceeds by radial transport of mean magnetic flux and angular momentum, relaxing the instability criterion. MRI-driven dynamics provide a pathway for poloidal-to-toroidal conversion; additional MHD instabilities (helical/3D MRI, clamshell, Babcock–Leighton) likely contribute to poloidal regeneration.

The results directly address the central question by demonstrating that MRI operating in the NSSL can reproduce key observed properties of the solar cycle. The inferred growth rates, spatial confinement to the outer 5–10% of the Sun, and saturation amplitudes match torsional oscillation timescales, geometry, and nHz-scale flow amplitudes. The required subsurface field strengths (∼100–200 G poloidal; ∼300–1,000 G toroidal) are consistent with helioseismic and magnetic inferences. The slow-branch eigenmodes naturally encode the hemispheric current-helicity sign rule, providing a mechanistic explanation tied to rotational constraint. In contrast to tachocline-centric models, the near-surface MRI avoids issues of unrealistically strong deep shear and high-latitude field preference, and it links the observed NSSL shear directly to the dynamo engine. The framework predicts correlated evolution of subsurface flows and magnetic fields; time-resolved helioseismic inversions could test these correlations. As a nonlinear, self-sustaining process acting on a finite background poloidal field at solar minimum, the MRI paradigm also offers a route to explain intermittent weak cycles and grand minima by imperfect regeneration, with noise potentially restoring normal cycles, analogous to delayed-oscillator behavior in ENSO.

This work proposes and supports a near-surface, MRI-driven solar dynamo. Analytical scaling and global anelastic MHD eigenmode calculations in a realistic NSSL shell produce fast and slow MRI branches whose growth rates, spatial structure, and saturation amplitudes match observed torsional oscillations and inferred subsurface magnetic fields. The model reproduces the hemispheric current-helicity sign rule and frames torsional oscillations as a nonlinear MRI traveling wave. By shifting the dynamo engine from the tachocline to the NSSL, the framework offers improved prospects for predicting magnetic cycles and space weather. Future work should incorporate additional physics (buoyancy/magnetic buoyancy, baroclinicity, fully compressible low-Mach formulations), turbulent convection and nonlinear feedbacks, explore high-latitude/deeper MRI branches, and pursue joint helioseismic inversions of flows and magnetic fields to test predicted correlations and refine constraints on subsurface field strengths.

The numerical eigenmode study isolates MRI by design and employs reduced physics: anelastic approximation with adiabatic background, neglect of magnetic buoyancy/baroclinicity, small-scale convection, and nonlinear dynamo feedbacks. The computational domain excludes the outermost 1% of the Sun where additional complex processes (partial ionization, radiative transfer, strong convection) are important. Background differential rotation is a low-order fit constrained primarily below 60° latitude; high-latitude rotation is less certain. The subsurface magnetic field configuration and strength are among the least constrained inputs, and different realizations across cycles are possible. Strong turbulence could, in principle, modify or damp large-scale dynamics. As a linear analysis with quasi-linear saturation estimates, fully nonlinear interactions among multiple modes and feedback on background profiles are not captured.