The solar tachocline — the thin shear layer at the base of the Sun's convection zone where the radiative interior's near-uniform rotation gives way to latitudinal differential rotation — changes with the 11-year magnetic activity cycle, but no physical mechanism has been shown to account for how it changes. Thirty years of helioseismic data from the GONG network reveal that the jump in rotation rate across the tachocline varies significantly but without a simple correlation with activity, following different hysteresis-like branches in different cycles; the latitude at which this jump vanishes 'sloshes' with the cycle, dipping roughly three years after each activity peak; the tachocline's width is anticorrelated with activity, changing about four years after the 10.7 cm radio flux; and its midpoint has drifted secularly toward the convection-zone base at low latitudes over three decades. Existing theory explains the tachocline's steady-state thinness and shape (e.g. confinement by Maxwell stresses of a dynamo-generated field, or hydrodynamic thermal-wind balance) but not this temporal structure. The problem is to identify the dynamical coupling between the solar dynamo and the shear layer that produces the observed time dependence — including the multi-year phase lags and the cycle-to-cycle hysteresis — and to demonstrate quantitatively, in a self-consistent model or simulation, that it reproduces the measured phenomenology.

Background

The Sun does not rotate as a solid body: its convection zone rotates differentially (about 25 days at the equator versus about 35 days near the poles), while the radiative interior below rotates nearly uniformly. Helioseismology — the analysis of the Sun's global acoustic oscillation modes, observed as Doppler velocity variations at the surface — reveals this internal rotation because rotation splits the frequencies of modes of a given spatial degree into components with different azimuthal order; inverting these rotational splittings (using data from ground-based networks such as GONG, the Global Oscillation Network Group, and space instruments — the Michelson Doppler Imager (MDI) aboard the SOHO spacecraft and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO)) yields the rotation rate as a function of radius and latitude. These inversions show that the transition between differential and uniform rotation is confined to a thin layer, the tachocline, centered near the base of the convection zone at about 0.7 solar radii and only a few percent of the solar radius thick (Antia, Basu and Chitre 1998). The tachocline is central to theories of the solar dynamo — the mechanism that regenerates the Sun's magnetic field in an approximately 11-year cycle (the magnetic polarity cycle, the Hale cycle, being 22 years) — because it is the interface where the convection zone's large-scale flows can stretch poloidal (north–south) field into strong toroidal (east–west) field that is then stored in the stable stratification and eventually emerges as sunspots.

Magnetic fields and rotation in the Sun interact in both directions. In the convection zone, the observed 'torsional oscillations' — alternating bands of slightly faster and slower zonal rotation (amplitudes of a few meters per second) that migrate toward the equator in step with the activity cycle — are successfully explained by Lorentz-force feedback: the dynamo-generated magnetic force pulls on the flow, and mean-field flux-transport dynamo models with this feedback reproduce the observed surface zonal-flow pattern (Rempel 2007). At the tachocline itself, magnetic fields are the leading candidate for solving a second puzzle: without a counteracting stress, meridional circulation would burrow into the radiative interior and thicken the tachocline over the Sun's life (a process called radiative spreading), yet the layer is observed to be thin. Self-consistent global simulations (Matilsky et al. 2024; Matilsky, Korre and Brummell 2025) show that Maxwell stresses — the magnetic tension and pressure associated with a dynamo-generated, non-axisymmetric field — can confine the tachocline against spreading, and a long line of work (Spiegel and Zahn's hydrodynamic model onward, pursued recently by Garaud, Gough and Matilsky 2025, and by Dikpati and Gilman's magnetohydrodynamic shallow-water models 2026) addresses the layer's equilibrium thickness and shape. Balbus and Latter (2010) showed in a thermal-wind balance framework (a balance between latitudinal buoyancy and Coriolis torques that links temperature gradients to the rotation profile) that the latitude where the tachocline's rotation jump vanishes depends on the torque the tachocline exerts on the interior. All of this theory concerns the steady, time-averaged state.

Whether and how the tachocline itself varies with the activity cycle has been addressed observationally in stages. Corbard et al. (2001), analyzing six years of data from the LOWL helioseismology instrument (a single-site Doppler-imaging predecessor of GONG), found no compelling variation, which was a statement about sensitivity rather than absence: Howe et al. (2000) had reported a distinct quasi-biennial (~1.3-year) oscillation in rotation at the base of the convection zone that later data did not sustain (reviewed by Howe 2009), while the classical result that the interior rotation varies with the cycle was established for the convection zone and its base. With MDI and GONG data, Antia and Basu (2011) confirmed that the transition of the rotation rate across the tachocline, and to some extent its position, do vary with time. Basu, Andrade de Aguiar and Korzennik (2024) extended this through cycles 23, 24 and the rising phase of 25, finding that the rotation jump changes substantially but without a simple correlation with the cycle, and speculating that the tachocline varies on a period longer than the sunspot or magnetic cycle. Most recently, Basu, Korzennik and Tripathy (2026), using 30 years of GONG data, resolved the latitude dependence of these variations using the 10.7 cm solar radio flux (F10.7, a standard ground-based proxy for global magnetic activity) as the activity reference: the jump δΩ\delta\Omega shows hysteresis-like behavior with cycle-to-cycle differences (with speculation of a two-Hale-cycle period); the zero-crossing latitude θv\theta_v of the jump is lower at activity maxima, with its dips lagging activity peaks by a little more than three years; the width wdw_d is larger when activity is smaller, with changes in F10.7 leading changes in wdw_d by about four years; and the position rdr_d has drifted secularly toward the convection-zone base at latitudes below about 50 degrees over the past three decades, correlating with the long-term decline in the number of sunspots per sunspot group. The authors state explicitly that no current theoretical scenario explains the θv\theta_v behavior, and none of the confinement, shallow-water, or thermal-wind theories predicts the multi-year lags, the hysteresis, or the secular drift.

Problem Statement

Identify the physical mechanism — the dynamical coupling between the solar dynamo's magnetic fields and the shear layer at the base of the convection zone — that produces the observed time dependence of the tachocline, and demonstrate quantitatively that it accounts for the measured phenomenology. Concretely, the observed time dependence comprises four latitude-dependent temporal signatures established with 30 years of GONG helioseismology by Basu, Korzennik and Tripathy (2026), building on Basu et al. (2024): (1) the significant time variation of the rotation jump δΩ\delta\Omega across the tachocline, which does not correlate simply with activity and shows hysteresis-like, cycle-to-cycle differences (cycle 25 following cycle 24 rather than cycle 23, suggesting a possible two-Hale-cycle period); (2) the 'sloshing' of the zero-crossing latitude θv\theta_v of the jump — lower at activity maxima, with its dips lagging activity peaks by a little more than three years; (3) the anticorrelation of the tachocline width wdw_d with activity, with changes in the 10.7 cm radio flux leading changes in wdw_d by about four years, i.e. a thinner tachocline near activity maximum; and (4) the secular drift of the tachocline midpoint rdr_d toward the convection-zone base at latitudes below about 50 degrees over the past three decades. A satisfactory solution derives the coupling from established or explicitly justified physics — for example Lorentz-force or Maxwell-stress feedback of dynamo-generated fields on the stratified shear layer, or angular-momentum redistribution by meridional circulation, waves, or turbulent stresses — in a self-consistent model or simulation, shows quantitatively how it accounts for the measured lag, correlation, and hysteresis structure of these signatures, and states clearly which parts it does and does not explain. A solution is complete when it quantitatively reproduces, with their respective multi-year phase lags, at least signatures (2) and (3); the cycle-to-cycle hysteresis of the jump (signature 1) and the secular drift of the midpoint (signature 4) may be left as explicitly labeled open gaps. An answer must not narrow the target to a single parameter, latitude range, or cycle, nor merely re-describe the correlations without a dynamical cause.

References

  1. Basu, Sarbani; Korzennik, Sylvain G.; Tripathy, Sushanta C. (2026). 'Latitude-dependent Time Variations of the Solar Tachocline'. The Astrophysical Journal. DOI: 10.3847/1538-4357/ae4c50; arXiv:2603.02321. https://arxiv.org/abs/2603.02321
  2. Basu, Sarbani; Andrade de Aguiar, Wesley Antônio Machado; Korzennik, Sylvain G. (2024). 'Time Variation of the Solar Tachocline'. The Astrophysical Journal 975, 276. DOI: 10.3847/1538-4357/ad82e6; arXiv:2410.01895. https://arxiv.org/abs/2410.01895
  3. Antia, H. M.; Basu, Sarbani (2011). 'Revisiting the solar tachocline: Average properties and temporal variations'. The Astrophysical Journal Letters 735, L45. DOI: 10.1088/2041-8205/735/2/L45; arXiv:1107.1004. https://arxiv.org/abs/1107.1004
  4. Corbard, T.; Jiménez-Reyes, S. J.; Tomczyk, S.; Dikpati, M.; Gilman, P. (2001). 'The solar tachocline and its variation (?)'. ESA SP-464, 265. arXiv:astro-ph/0011367. https://arxiv.org/abs/astro-ph/0011367
  5. R. Howe; J. Christensen-Dalsgaard; F. Hill; R. W. Komm; R. M. Larsen; J. Schou; M. J. Thompson; J. Toomre (2000). 'Dynamic Variations at the Base of the Solar Convection Zone'. Science 287, 2456. DOI: 10.1126/science.287.5462.2456. https://doi.org/10.1126/science.287.5462.2456
  6. Rachel Howe (2009). 'Solar Interior Rotation and its Variation'. Living Reviews in Solar Physics 6, 1. DOI: 10.12942/lrsp-2009-1. https://doi.org/10.12942/lrsp-2009-1
  7. H. M. Antia; S. Basu; S. M. Chitre (1998). 'Solar internal rotation rate and the latitudinal variation of the tachocline'. Monthly Notices of the Royal Astronomical Society 298, 543. DOI: 10.1046/j.1365-8711.1998.01635.x. https://doi.org/10.1046/j.1365-8711.1998.01635.x
  8. Matthias Rempel (2007). 'Origin of Solar Torsional Oscillations'. The Astrophysical Journal 655, 651. DOI: 10.1086/509866. https://doi.org/10.1086/509866
  9. Loren I. Matilsky; Nicholas H. Brummell; Bradley W. Hindman; Juri Toomre (2024). 'Solar Tachocline Confinement by the Nonaxisymmetric Modes of a Dynamo Magnetic Field'. The Astrophysical Journal 962, 189. DOI: 10.3847/1538-4357/ad18b2; arXiv:2311.10202 (preprint title: 'Confinement of the Solar Tachocline by a Non-Axisymmetric Dynamo'). https://arxiv.org/abs/2311.10202
  10. Loren I. Matilsky; Lydia Korre; Nicholas H. Brummell (2025). 'Dynamo Confinement of a Radiatively Spreading Solar Tachocline Revealed by Self-consistent Global Simulations'. The Astrophysical Journal Letters 991, L1. DOI: 10.3847/2041-8213/adefe3. https://doi.org/10.3847/2041-8213/adefe3
  11. Steven A. Balbus; Henrik N. Latter (2010). 'The tachocline and differential rotation in the Sun'. Monthly Notices of the Royal Astronomical Society 407, 2565. DOI: 10.1111/j.1365-2966.2010.17086.x. https://doi.org/10.1111/j.1365-2966.2010.17086.x
  12. P. Garaud; D. O. Gough; L. I. Matilsky (2025). 'Toward a Self-consistent Hydrodynamical Model of the Solar Tachocline'. The Astrophysical Journal. DOI: 10.3847/1538-4357/adc72b. https://doi.org/10.3847/1538-4357/adc72b
  13. Mausumi Dikpati; Peter A. Gilman (2026). 'A Multilayer Magnetohydrodynamic Shallow-water Model of the Solar Tachocline: Equilibrium Shape and Thickness'. The Astrophysical Journal. DOI: 10.3847/1538-4357/ae314e. https://doi.org/10.3847/1538-4357/ae314e
  14. Sarbani Basu; Sylvain G. Korzennik (2025). 'The Shape of the Solar Tachocline'. The Astrophysical Journal 995, 91. DOI: 10.3847/1538-4357/ae1cc6; arXiv:2511.07534. https://arxiv.org/abs/2511.07534
  15. Sylvain G. Korzennik; Antonio Eff-Darwich (2026). 'Resolving the Tachocline Using Inversion of Rotational Splitting Derived from Fitting Very Long and Long Time Series'. The Astrophysical Journal. DOI: 10.3847/1538-4357/ae4026. https://doi.org/10.3847/1538-4357/ae4026
  16. Krishnendu Mandal; Alexander G. Kosovichev (2026). 'Helioseismic evidence that the solar dynamo originates near the tachocline'. Scientific Reports. DOI: 10.1038/s41598-025-34336-1. https://doi.org/10.1038/s41598-025-34336-1