Helioseismic Evidence That the Solar Dynamo Originates near the Tachocline

Abstract

The exact location of the solar dynamo remains uncertain--whether it operates primarily in the near-surface shear layer, throughout the entire convection zone, or near the tachocline, a region of sharp transition in the solar rotation, located at the base of the convection zone, approximately 200,000 km beneath the surface. Various studies have supported each of these possibilities. Notably, the solar magnetic "butterfly" diagram and the pattern of zonal flows ("torsional oscillations") exhibit strikingly similar characteristics, suggesting a link between magnetic field evolution and solar flows. Since magnetic fields cannot be measured directly in the deep solar interior, torsional oscillations and rotation gradients are employed as diagnostic proxies. Our analysis reveals that the gradient of rotation displays "butterfly"-like behavior near the tachocline, which is similar to the magnetic butterfly diagram at the surface. This result supports the idea that the solar dynamo has a deep-seated origin, likely operating either near the tachocline or throughout the convection zone, thereby disfavoring the recent scenario of a shallow, near-surface dynamo. This finding may also have important implications for understanding how stellar dynamos operate in general.

Figures (4)

• Figure 1: We show $\partial\Omega/\partial\theta$, with Southern Hemisphere values multiplied by $-1$ to enforce hemispheric symmetry, as it naturally reverses sign across the equator. The analysis is based on $4 \times 72$-day GONG datasets (left panel) and combined MDI and HMI observations (right panel). The results are shown at three depths, $0.78$, $0.75$, and $0.6\ R_\odot$. At $0.78\,R_\odot$ and $0.75\,R_\odot$, the error in $\partial\Omega/\partial\theta$ is $1.2\,\mathrm{nHz\,rad^{-1}}$, rising to $3\,\mathrm{nHz\,rad^{-1}}$ at $0.6\,R_\odot$. To enhance the visibility of latitudinal patterns, the results are multiplied by $\sin\theta$. Magnetic-field contours for the same period are overlaid to highlight the correlation between the evolution of the toroidal magnetic field and $\partial\Omega/\partial\theta$.
• Figure 2: The left panel shows $\partial\Omega/\partial r$ as a function of the solar cycle. The right panel presents the dimensionless radial gradient, $\nabla_r\Omega$, at three depths $0.78$, $0.75$, and $0.6 R_\odot$, obtained from GONG $4 \times 72$-day data. The uncertainty in $\partial\Omega/\partial r$ is $6\times10^{-9}$ at depths of $0.78\,R_\odot$ and $0.75\,R_\odot$, increasing to $1.5\times10^{-8}$ at $0.6R_\odot$.
• Figure 3: Upper left panel: zonal flows at several depths (indicated in each panel title), overlaid with the magnetic butterfly diagram to highlight the phase lag between flows at different depths and the magnetic pattern, using combined MDI and HMI datasets. Velocity measurements from the inversion have an accuracy of $0.4\,\mathrm{m\,s^{-1}}$ at $0.8\,R_\odot$, rising to $0.9\,\mathrm{m\,s^{-1}}$ at $0.6\,R_\odot$. Figure 14 of our previous work mandal_25 also presents error bars in the velocity measurement on a radius–latitude grid as a 2D plot. Top right panel: torsional oscillation variations with depth at selected latitudes (indicated in each panel title). At low latitudes, the signal emerges from the tachocline with a time lag before reaching the surface, whereas at high latitudes (near $50^\circ$) it appears first at the surface. This behavior is characteristic of a dynamo wave–like signature in solar torsional oscillations. Bottom left panel: we plot the jump in radial profile obtained from the inversion of $a_3$ coefficient between depths of $0.8\,R_\odot$ and $0.6\,R_\odot$. The dashed vertical line indicates the cycle minimum, while the solid vertical line marks the cycle maximum. The variation in sunspot number over the same period is shown by the solid light-blue line. Bottom right panel: Averaging kernels at selected depths (listed in the legend) are shown, with different colors representing different depths.
• Figure 4: We calculate the average $a$-coefficients (shown by black markers, with black error bars) for modes with turning points between $0.7$ and $0.8,R_\odot$ and plot them alongside the sunspot number (light blue line). The variation of the $a$-coefficients is further smoothed with a Gaussian filter and shown as a red solid line. The plot is based on the combined MDI and HMI $4\times 72$-day datasets.