9.3 Recent results
As more data accumulated, the signature of the torsional oscillation pattern in the helioseismic
observations became clearer. Vorontsov et al. (2002) 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
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
Figure 23: Contour diagrams of constant rotation velocity residuals at , obtained using
two dimensional RLS inversion of the GONG data, from Basu and Antia (2003) (reproduced by
permission of the AAS).
Figure 24: Zonal flow pattern derived from MDI -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 23.
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. (2005, 2006b), 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 25, 26, and 27 show the variations in rotation rate, based on the results and figures in Howe
et al. (2005, 2006b), 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. (2000a) and
the other related papers. Figure 28 shows the phase and amplitude profiles for 11-year sine functions fitted
to the rotation variations.
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).
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).
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)
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).