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.
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Figure 29: Local helioseismic inferences of zonal flows close to the surface, from Haber et al. (2002Jump To The Next Citation Point) (left) and Zhao and Kosovichev (2004Jump To The Next Citation Point) (right) (reproduced by permission of the AAS).
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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 29View Image (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 29View Image 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 regions.

Howe et al. (2006aJump To The Next Citation Point) 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 surface.

It should be noted that the local helioseismic observations are somewhat prone to systematic errors, some of which follow the changing B0 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 noting:

  1. The exact appearance of the pattern is quite sensitive to the background term that is subtracted. For example, compare the f-mode results shown in Figure 24View Image, which were plotted as the difference from a smooth 3-term expansion of the rotation rate, with the plots in Figure 25View Image, which were plotted by subtracting the temporal mean at each location.
  2. 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.
  3. 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 (1982Jump To The Next Citation Point) 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.
  4. 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.
  5. 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.

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