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The pattern rotation rate for the sun's magnetic field, determined by cross-correlating Mount Wilson full disk 5250.2 (Fe I) magnetograms spaced a full solar rotation apart, closely parallels at all latitudes the photospheric plasma rotation profile determined from the Doppler shifts of the same spectral line. When an 11-yr running mean is subtracted, a torsional oscillation is revealed, in the form of an equatorward-migrating pattern of fast and slow zones. Although the magnetic rotation torsional pattern is similar enough to its much-studied Doppler counterpart to provide confirmation, there are significant differences between the two - the magnetic pattern is strongest (about 20 m/s) at high latitudes, weakens at sunspot latitudes where the Doppler pattern is strongest, and is offset at all latitudes by about 10 deg toward the equator, so that its slow zones approximately coincide with the maximal shear zones of the Doppler pattern. These zones appear to be fore-runners to the wings of the magnetic flux (sunspot) butterflies of the activity cycle.
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Herschel B. Snodgrass (1991) studied this question.
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