9.3 Recent results

As more data accumulated, the signature of the torsional oscillation pattern in the helioseismic observations became clearer. Vorontsov et al. (2002Jump To The Next Citation Point) studied the evolution of the flows in MDI data from 1996 through 2001. They concluded that at least the high-latitude region of changing rotation involves the whole depth of the convection zone. The results on the radial extent of the flows at lower latitudes were less clear, with evidence that the bands of slower rotation might penetrate close to the base of the convection zone, while the bands of faster rotation appeared to reach about 0.9 R⊙ but no deeper. Another interesting feature of that paper was the introduction of the use of 11-year sinusoids to characterize the variation of the rotation rate at any given location. This innovation had the useful effect of clarifying the pattern, making obvious the poleward propagation of the high-latitude flows even with data from little more than half a cycle. The existence of a weak third-harmonic component to the 11-year cycle, however, was not confirmed in later work.
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Figure 23: Contour diagrams of constant rotation velocity residuals at 0.98 R⊙, obtained using two dimensional RLS inversion of the GONG data, from Basu and Antia (2003Jump To The Next Citation Point) (reproduced by permission of the AAS).
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Figure 24: Zonal flow pattern derived from MDI f-mode measurements, with smooth profile subtracted. Based on a figure from Schou (1999), updated and used by kind permission of J. Schou (2008, private communication.)

Basu and Antia (2003) found similar results in MDI and GONG data up to 2002, as seen in Figure 23View Image. These results also hint at another subtlety; at low latitudes, the phase of the flow pattern is not constant along radial lines. In fact, the variation in the lower part of the convection zone appears to lead that close to the surface by a year or two, with the low-latitude band of faster rotation following roughly the same 25° slant as the rotation contours. This tendency was further studied by Howe et al. (2005Jump To The Next Citation Point2006bJump To The Next Citation Point), who compared inversions of MDI and GONG data with forward-modeled profiles based on different flow configurations, including some derived from dynamo models. Although some detail was lost and distorted due to the resolution and uncertainties in the inversions, the authors were able to conclude that the low-latitude branch probably penetrates through much of the convection zone, but is sufficiently displaced in phase at greater depths that the correlation between the surface pattern and that deeper down almost vanishes. In this work, the 11-year sinusoid analysis showed evidence of a second-harmonic component rather than the third harmonic reported by Vorontsov et al. (2002).

Figures 25View Image, 26View Image, and 27View Image show the variations in rotation rate, based on the results and figures in Howe et al. (20052006bJump To The Next Citation Point), but brought up to date with the most recent GONG and MDI observations available at the time of writing. The plots were prepared using the same 2dRLS inversion codes for both MDI and GONG medium-degree data, and 2dSOLA for MDI, that were used for the work of Howe et al. (2000aJump To The Next Citation Point) and the other related papers. Figure 28View Image shows the phase and amplitude profiles for 11-year sine functions fitted to the rotation variations.

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Figure 25: Rotation rate after subtraction of a temporal mean at each location, as a function of latitude and time at selected depths, for OLA (top) and RLS (middle) inversions of MDI data, and for RLS inversions of GONG data (bottom).
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Figure 26: Rotation rate after subtraction of a temporal mean at each location, as a function of depth and time at selected latitudes. Latitudes are 0, 15, 30, 45, 60° from left to right; inversions are MDI OLA (top), MDI RLS (middle), and GONG RLS (bottom).
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Figure 27: Rotation rates at selected latitudes and depths as a function of time, after subtraction of a temporal mean. The results are from GONG RLS (black), MDI RLS (red), and MDI OLA (blue) inversions.
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Figure 28: Phase (left) and amplitude (right) of 11-year sine functions fitted to temporal variation of the rotation rate for OLA (top) and RLS (middle) inversions of around 11 years of MDI observations and for RLS inversions of GONG data (bottom).

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