Rotational radial shear in the low solar photosphere. Direct detection from high-resolution spectro-imaging

TL;DR

The paper tackles the problem of depth-dependent solar rotation in the low photosphere by introducing a direct spectro-imaging approach that samples different heights via line-wing formation. Using high-resolution, AO-corrected observations of Fe I 630.15 nm and Ca I 616.2 nm, and a cross-spectrum phase analysis across 25 line chords, the authors deduce formation heights and measure height-resolved differential rotations via shifts between consecutive scans. They find a parabolic decrease in azimuthal rotation with height up to about $z=80$ km, with roughly $-0.3$ km s$^{-1}$ of differential rotation at the top of the probed layer, and no significant meridional gradient or latitudinal differences within uncertainties. These results provide empirical constraints on the low photosphere’s dynamical behavior, informing boundary conditions for solar convection simulations and highlighting consistency and tensions with recent independent measurements near $z\sim70$ km.

Abstract

Radial differential rotation is an important factor in stellar dynamo theory. In the Sun, helioseismology has revealed a near surface shear layer in the upper 5 to 10% of the convection zone. At low to midlatitudes, the rotation velocity gradient decreases sharply near the surface. A depth gradient in rotational velocity was recently detected in the low photosphere using a differential interferometric method on spectroscopic data. Granular structures at different depths in the FeI 630.15 nm line showed a systematic retrograde shift compared to continuum structures, suggesting a height-related decrease in angular velocity, dependent on the assumed granulation coherence time. We use a more direct approach to measure the differential rotational velocity at different photospheric heights. We performed spectroscopic scans of the same granular region in FeI 630.15 nm and CaI 616.2 nm lines and measured displacements of images at different line chords between consecutive scans. These observations require excellent seeing, stable adaptive optics, and scanning times shorter than the granulation lifetime. Adaptive optics stabilizes continuum images but not higher-altitude rotation differences. We used THEMIS and HINODE SOT FeI data to measure formation height differences via perspective shifts observed away from the disk center with the slit radially oriented. Measurements at disk center and $\pm$25° latitude along the central meridian show a parabolic decrease in rotational velocity with height, reaching about 16% slower rotation at 80 km above the continuum. No significant difference is found between the equator and $\pm$25° latitudes. The low photosphere is a transition zone between the convective and radiative layers. Our measurements provide new constraints on its dynamical behavior and valuable boundary conditions for numerical simulations of the Sun s upper convection zone.

Figures (9)

• Figure 1: Phase of the cross-spectrum of the images at the reference level and at line chord 15 in the Fe I 630.15 nm line as function of the spatial frequency. The spectrograph slit is oriented along the north-south axis at $\cos\theta= 0.81$. Red (blue) symbols: THEMIS data in the southern (northern) hemisphere. Green symbols: HINODE data at the same heliocentric angle in both hemispheres.
• Figure 2: Same as Fig. \ref{['fig1']} but for level 15 of the Ca I 616.2 nm line. No HINODE data is available for this line.
• Figure 3: Formation heights (in kilometers) of the images at the different line chords derived from the perspective effect in both hemispheres. Positive values are obtained in the northern hemisphere where the perspective displacement is toward the north, and negative values in the southern hemisphere. Blue symbols: Fe I 630.15 nm line. Red symbols: Ca I 616.2 nm line.
• Figure 4: Phase of the cross-spectra of images at two successive scans at line-chord level 12 (green symbols) and at the continuum level (blue symbols).
• Figure 5: Differential rotation velocity measured at the center of the solar disk in the Fe I 630.15 nm line as a function of the formation height of the line-chord images up to line chord 10. The green line shows the linear fit obtained in Paper I for $0 < z < 32$ km, the blue line is a parabolic fit for $0 < z < 80$ km.