9.4 Local helioseismology and the torsional oscillation
The torsional oscillation pattern, at least at lower latitudes and closer to the surface, is also suitable for
measurements using the techniques of local helioseismology, in which short-wavelength, short-lived waves
are used to infer the structure and dynamics of localized areas of the Sun. Because these waves do not
penetrate very far below the surface, such techniques are restricted to the outer few megameters of the solar
envelope, but this region can be studied in much greater detail and with shorter averaging times than is
possible with global helioseismology.
Figure 30: Zonal flows since 1986, from Mount Wilson Doppler measurements (top), global
helioseismic measurements from BBSO and MDI (middle) and MDI ring-diagram analysis (bottom).
The color scale is in nHz.
Basu and Antia (2000) detected the zonal flow migration using MDI data and the ring-diagram
technique (Hill, 1988), in which the displacement of three-dimensional acoustic power spectra
derived from small areas of the solar disk is used to infer horizontal flows in both the zonal
and meridional directions. Later, Haber et al. (2002) measured both the zonal flows and a
corresponding modulation of the meridional flow pattern, as seen in Figure 29 (left). Beck
et al. (2002), using the time-distance technique, which considers the correlations between oscillations at
spatially separated locations, also found bands of meridional flow away from the activity belts
associated with the zonal flow bands. Chou and Dai (2001) and Chou and Ladenkov (2005),
using data from the Taiwan Oscillations Network [TON]), also found diverging meridional flows
associated with the activity belts. Zhao and Kosovichev (2004) measured the zonal (Figure 29
right) and meridional flows with the time-distance technique, and reported meridional flow
converging on the activity belts above a depth of 12 Mm, with diverging flows below 18 Mm,
forming circulation cells around the activity belts. The presence of inflows into the activity
belts was also observed at the surface by Komm et al. (1993b) and Komm (1994). Komm
et al. (2005) studied the flows in about a year of high-resolution GONG (“GONG+”) data, and
concluded that the overall flow pattern existed whether or not active regions were included in
the analysis; in other words, the zonal flow bands and their associated converging/diverging
meridional flows appear to exist independently of the flows in the immediate vicinity of strong active
Howe et al. (2006a) compared the results from ring-diagram analysis of the MDI data, global analysis of
MDI and GONG data, and the Mount Wilson Doppler observations. They found very similar results for the
north–south symmetrized flow pattern close to the surface in all three observations. Both the global and
local helioseismic data indicated that the strength of the flow pattern did not fall off steeply below the
It should be noted that the local helioseismic observations are somewhat prone to systematic errors,
some of which follow the changing angle, or tilt of the solar rotation axis relative to the observer, as
shown for example by Zaatri et al. (2006). This can result, for example, in a pronounced and almost
certainly non-solar north–south variation of the zonal flow measurements, which is generally corrected for
by subtracting suitable averages.
Some further features of the torsional oscillation pattern as we know it from a full cycle of
observations from GONG and MDI (and nearly two cycles of surface Doppler observations) are worth
- The exact appearance of the pattern is quite sensitive to the background term that is subtracted.
For example, compare the -mode results shown in Figure 24, which were plotted as the
difference from a smooth 3-term expansion of the rotation rate, with the plots in Figure 25,
which were plotted by subtracting the temporal mean at each location.
- Although the pattern repeats – of course not precisely – with each (approximately) 11-year
activity cycle, each equatorward-migrating flow band exists for about eighteen years, emerging
at mid-latitudes soon after the maximum of one cycle and finally disappearing at the equator
a couple of years after the minimum of the following cycle; thus, the band of faster rotation
associated with the activity of cycle 22 was still visible at the beginning of GONG and MDI
observations in early cycle 23, and the band that is expected to accompany cycle 24 became
visible around 2002 (if we look at the mean-subtracted residuals), or 2005 – 2006 (if we use the
smooth-function subtraction). On the other hand, each poleward-moving branch seems to last
only about nine years, appearing a year or so after solar minimum and moving to the pole
before the next minimum.
- Although the equatorward-migrating bands of faster rotation are clearly associated with the
migrating activity belts of the magnetic butterfly diagram, the relationship is not completely
straightforward. The new equatorward-propagating branch is clearly visible some years before
noticeable new cycle active regions begin to erupt, and the phase/latitude profiles of the
magnetic index and the velocity are very different. Also, as was noted by LaBonte and
Howard (1982) and by Howe et al. (2006a), the strength of the torsional oscillation signal has
not shown much change over the last few solar cycles, while the level of magnetic activity varies
much more from one cycle to another.
- Although the equatorward branch of the zonal flow migration pattern shows some relationship
to the pattern of enhanced activity in the Fe xiv corona going back to 1973 (Altrock, 1997), the
“extended solar cycle” seen in these observations starts at a much higher latitude, apparently
about 70°, before migrating to the equator over about eighteen years; thus even the equatorward
edge of these coronal activity bands seems to be at higher latitude than the observed new
branch in the zonal flows that starts at about the same time.
- Finally, we note that because the angular velocity changes associated with the torsional
oscillation signal are relatively small compared to the difference in angular velocity between
the surface and the bottom of the near-surface shear layer, while the amplitude of the signal
does not decrease rapidly with depth, the magnitude of the shear at a given location varies by
only a fraction of its value during the solar cycle. However, the fractional change in the shear
is much greater than the fractional change in the rotation rate.