8 The Near-Surface Shear

One persistent puzzle in the measurements of rotation at the photosphere had been that direct Doppler measurements consistently gave somewhat slower rotation rates than the measurements made by tracing surface features. For example, Brown et al. (1989) summarized the results of Snodgrass (19831984) as

Ωm--= 462 − 74μ2 − 53μ4nHz (26 ) 2π
for magnetic features and
Ωp- 2 4 2π = 452 − 49μ − 84μ nHz (27 )
for the surface plasma, respectively, where μ is the sine of the latitude. For an overview of such measurements, see Beck (2000). The usual explanation for the discrepancy is that while the Doppler techniques measure the velocity at the surface, the tracers such as sunspots are anchored in a faster-rotating layer deeper down. For example, Gilman and Foukal (1979) noted that the observations implied a subsurface shear layer and suggested that this might arise from angular momentum conservation in the supergranular layer.

An extremely early attempt to measure the subsurface rotation was made by Rhodes Jr et al. (1979), when the identification of the 5-minute oscillations with p modes was still a relatively recent discovery. These authors used high-degree modes, probing about the upper 20 Mm (0.03 R⊙) of the convection zone, and detected an inwards-increasing gradient. If these measurements are reliable, they represent the first detection of the subsurface shear. However, most of the early helioseismic measurements of the internal rotation profile were restricted to a degree range that did not allow the near-surface shear to be resolved in inversions. Rhodes Jr et al. (1990), attempting to measure the rotation in the bulk of the convection zone, also saw hints of a gradient, opposite to that seen at the base of the convection zone, below the surface, and Wilson (1992) used forward calculation techniques on the data of Brown and Morrow (1987) and Libbrecht (1989) to deduce that the rotation rate must increase inward immediately below the surface. We should remember, however, that at this time the picture of the internal rotation profile was not as clear as it is today, and it is not always obvious whether interpretation of the observations as gradients of rotation refers to the near-surface shear, the shear at the base of the convection zone, or some unresolved amalgamation of the two. Wilson, for example, was not arguing for a near-surface shear layer but against the model with rotation constant along radii.

With the advent of GONG and MDI, measuring modes to higher degrees than had previously been possible, the near-surface shear could be seen in global inversions; it is visible in the early results presented by Thompson et al. (1996) for GONG and by Kosovichev et al. (1997) for MDI, in both cases apparently changing sign at higher latitudes.

Schou et al. (1998) found clear evidence of the near-surface shear in inversions of MDI data. All the inversion methods agreed well on the shear at low latitudes, but at high latitudes the picture was complicated by the proximity of the submerged “jet” feature and the methods agreed less well. The disagreement may have been partly due to systematic errors in the splitting coefficients. In the comparisons of MDI and GONG data and analysis carried out by Schou et al. (2002), the high-latitude reversal of the shear is seen only in data analyzed with the “CA” pipeline; this may be partly because the “AZ” pipeline mostly fails to recover the splittings of the (narrow, low-amplitude) f-mode peaks, but the reversal persists in the MDI data even for the restricted common mode set.

The near-surface shear (down to about 15 Mm) was studied in detail by Corbard and Thompson (2002), using f modes from MDI data. They measured the slope of the rotation rate, close to the surface at low latitudes, as about –400 nHz/R⊙, decreasing to a very small value by about 30° latitude and possibly reversing in sign at higher latitudes (though this result, seen in only the outer 5 Mm, was dependent on only the highest-degree modes, those with l ≥ 250). The low-latitude rotation rate was found to vary almost linearly with depth in the subsurface region, while if angular momentum was conserved in parcels of fluid moving with respect to the rotation axis, it would be expected to vary with the inverse square of the distance from the axis.

The near-surface shear is also accessible to the methods of local helioseismology, at least for latitudes below 50 – 60°. Basu et al. (1999Jump To The Next Citation Point) and Howe et al. (2006aJump To The Next Citation Point) compared results from local ring-diagram analysis and global inversions and found, at latitudes ≤ 30°, quite good agreement between the dΩ∕dr values obtained from local and global inversion results. However, although the slope from local measurements does show some variation with latitude (Figure 22View Image), it by no means vanishes at 52.5°, the highest latitude at which the measurement is made. The ring-diagram results allow us to consider the northern and southern hemispheres separately, but Basu et al. (1999) found very little difference in the shear between the two hemispheres.

View Image

Figure 22: Radial variation of the mean rotation rate after subtraction of the tracking rate, for global inversions (blue) and north – south averaged local inversions of MDI (green) and GONG (red) data at latitudes 0° (a), 15° (b), 30°(c), and 45° (d); similar to Howe et al. (2006aJump To The Next Citation Point).

Some attempts have been made to use the near-surface shear to drive or at least contribute to a solar dynamo, for example by Brandenburg (2005), but Dikpati et al. (2002) showed that any dynamo contribution from the shear of the outer layers could only provide a fraction of the effect needed to power the solar cycle.

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