Junwei Zhao1, A. G. Kosovichev2, & R. S. Bogart1
1. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085
2. Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314-9672
Solar global-scale flows, i.e., differential rotation and meridional flow, are closely related to solar dynamo and solar cycles. These flows also display cycle-related variations. Differential rotation exhibits faster- and slower-rotating zonal bands, known as torsional oscillation, which migrate together with the activity belts toward the equator. The shallow meridional-flow profile also changes with the phase of solar cycles. It was found that the residual meridional flow, after a mean flow profile was removed from profiles obtained from different time period, exhibits a converging flow toward the activity belts, and they migrate together toward the equator as the cycle evolves.
Here, by use of the first 3.7 years of HMI continuous observations, we study the torsional oscillation and meridional flow in more details, and disclose more information for the rising period of Cycle 24. The magnetic field data used in this study are HMI line-of-sight magnetic field, and the subsurface flow fields are from HMI time-distance data-analysis pipeline . The analysis covers the period from 2010 May 1 through 2014 January 14, a total of 50 Carrington rotations.
Figure 1 | (a) Butterfly diagram of net magnetic field, obtained by averaging over all longitudes for each Carrington rotation, for the analysis period. (b) Same as panel (a) but for unsigned magnetic field. (c) Background image is the same as in (b), and contours show levels of 10, 15, 20, 25, and 30 Gs. For all panels here and in Figure 2, the lower horizontal axis labels years and the upper horizontal axis labels
Carrington rotation numbers.
Figure 1 shows the longitudinally averaged net magnetic field strength and unsigned magnetic field strength. For cycle 24 the leading polarity is negative (positive) in the northern (southern) hemisphere, and in each hemisphere more following-polarity magnetic flux is transported poleward than leading-polarity flux. Figure 1 also shows that the northern hemisphere had its maximum activity during September through December 2011, and the activity in the southern hemisphere was reaching its maximum during October 2013 through January 2014, nearly 2 years behind the maximum of the northern hemisphere.
Figure 2 | Upper rows show torsional oscillation for the depths of (a) 0 – 1 Mm, (b) 3 – 5 Mm, and (c) 17 – 21 Mm. The lower row shows residual meridional flow profiles for the depths of (d) 0 – 1 Mm, (e) 3 -5 Mm, and (f) 10 – 13 Mm. The flow in the southern hemisphere is plotted with a reversed sign for a better visualization. Positive flow is poleward and negative flow is equatorward. White contours in panels are the same as those in Figure 1c.
The upper row of Figure 2 shows results on torsional oscillation. The torsional oscillation shows little change with depth up to 21 Mm into the interior. Both the width and strength of the torsional oscillation change with time, e.g., the faster bands became weak and narrow after the activity maximum of the northern hemisphere close to the end of 2011. The torsional oscillation exhibits a hemispheric asymmetry. Throughout the analysis period, the faster band in the equatorward-migrating torsional-oscillation branch is on average approximately 3° closer to the equator in the northern hemisphere than in the southern hemisphere. Moreover, the faster band in the northern hemisphere extended past the equator into the southern hemisphere near the end of the analysis period.
The lower row of Figure 2 shows results on residual meridional flow, after a 3.0-yr mean profile is removed from the flow profile of each rotation. The residual meridional flow converges toward the activity belts in both hemispheres, but only up to 13 Mm in depth. Compared with the torsional oscillation, the residual meridional-flow bands are more fragmented and wider, with the maximum speed ~2 m/s faster than the maximum torsional oscillation speed.
Figure 3 | (a) Black curves are meridional-flow velocity at the depth of 0 – 1 Mm, as a function of time, averaged from the latitude 35° – 40°N. Red curves are magnetic field from the same latitudinal bands. (b) Same as in panel (a) but for the latitude 40° – 45°S. Note that the meridional flow speed increases with the vertical axis in panel (a) but decreases in panel (b).
Remarkably, the meridional-flow speed above 35° latitude shows an anti-correlation with the magnetic flux that are transported poleward. Figure 3 illustrates this relation. The general trend for the meridional flow is that the speed decreases with the rise of magnetic activity; however, superimposing on this general trend is a component of that the flow speed is anti-correlated with the net magnetic field. That is, the poleward flow speed is faster when the leading-polarity field is transported toward the pole and slower when the following-polarity flux is transported. Since the following-polarity is transported poleward to cancel the existing magnetic field there and cause the polarity reversal, its anti-correlation with the meridional flow speed is expected to slow down the magnetic field cancellation and the polarity reversal.
To summarize, we confirm the previous result of that the residual meridional flow converges toward the activity belts, and we also find that above 30° latitude, the magnetic flux strength shows an anti-correlation with the meridional flow speed. For more details of this work, please refer to Ref .
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 Zhao, J., Couvidat, S., Bogart, R. S., Parchevsky, K. V., Birch, A. C., Duvall, T. L., Jr., Beck, J. G., Kosovichev, A. G., & Scherrer, P. H. 2012, Solar Phys., 275, 375
 Zhao, J., Kosovichev, A. G., & Bogart, R. S. 2014, ApJ Lett, 789, L7