Differential Rotation 15 degree patches 30-degree patches Radial variation of the mean rotation rate, shifted to give a zero rate at the surface, for global inversions (curves mark error bounds) of MDI data and local inversions of MDI (filled circles) and GONG (open diamonds) data at latitudes 0(top left), 15(top right), 30 (bottom left) and 45 (bottom right). Howe, R. et al., 2006, Solar Physics ,235,1.

North-South asymmetry • The latitudinal variation is most likely a consequence of the solar-cycle variation of the zonal flow, the torsional oscillation pattern. • The zonal flow is predominantly faster in the southern hemisphere that in the northern one. This differences increase with latitude about 25-degrees, and with depth. Zaatri, A. et al, 2006, Solar Physics, 236,227 Temporal variation of the zonal flow in the Northern (dark grey) and Southern (light grey) hemisphere at four latitudes and four depths. The surface rotation rate has been subtracted (Snodgrass, 1984). The line thickness represents about two standard deviations of the formal undertainty. The top row shows, for comparison, the time scale in Carrington Rotations.

Torsional oscillation from ring-diagram analysis: MDI-GONG combo that I showed at the AGU meeting. MDI before mid-2001, GONG after. The flows are averaged in depth over 4-10 Mm. Bands of faster (or slower) rotation move toward the equator. The fast band of cycle 24 appears before there is any surface activity present. The new fast band is stronger in the northern hemisphere indicating that the activity will be stronger in this hemisphere. Courtesy of R. Komm Torsional Oscillation (local helioseismology)

Meridional circulation: Surface Observations Meridional circulation derived from the motion of small magnetic features Komm, Horward & Harvey 1993, Solar Physics, 147, 207

Surface Observations Cycle variations of the meridional flows from surface observations of small magnetic features Komm, Horward & Harvey 1993, Solar Physics, 147, 207

Meridional Circulation Hathaway and Rightmire, 2010 “..kinematic dynamo simulations which demonstrate that a fast meridional flow in the first half of a cycle, followed by a slower flow in the second half, reproduces both characteristics of the minimum of sunspot cycle 23. Our model predicts that, in general, very deep minima are associated with weak polar fields. Sunspots govern the solar radiative energy and radio flux, and, in conjunction with the polar field, modulate the solar wind, the heliospheric open flux and, consequently, the cosmic ray flux at Earth.” Nandy, D., Muñoz-Jaramillo, A., Martens, P. C. H. 2011, Nature

Meridional circulation variation with the solar cycle Meridional flows obtainedfrom 34.5 Mm (solid curves)and 69 Mm (dash-dotted curves)for different Carringtonrotations. (b) Residual meridionalflows after the flowsof CR1911 have beensubtracted from each rotation.Shaded regions are thesame as Fig. 2. Theerror bars may beunderestimated, because the errorsfrom flows of CR1911 are not included. Zhao and Kosovichev, ApJ, 2004

Meridional Circulation variation with the solar cycle Temporal variation of the fitted polynomial to the meridional circulation observations at a depth of 5.8 Mm. A symmetrical plot averaging ring-diagram analysis of GONG data for both hemispheres is shown. Positive velocities are taken toward each respective pole. The B0 effect is clearly seen superimposed in the results, however the long term trend of the amplitude increase is not associated with this artifact [7]. González Hernández et al., 2010, ApJ

Meridional flow averaged over Carrington rotation 1909-1911 from MDI data (top) and CR 2076-2080 (bottom) from GONG data. TOP: minimum of cycle 22-23 BOTTOM: minimum of cycle 23-24 Flows appear stronger during the recent minimum than in the previous one. Comparison between the last two minima Courtesy of R. Komm

Meridional circulation countercell McDonald & Dikpati (2003) (Figure from Dikpati et al., 2010, Geophys. Research.) Haber et al., 2002, ApJ

Meridional circulation countercell Gonzalez Hernandez et al., 2006, ApJ. González Hernández et al, 2006

Meridional circulation countercell Dikpati, M. et al. 2010, GeoRL González Hernández et al, 2006

Motivation: Solar Dynamo Yearly results for the meridional circulation function. Each day throughout each year is treated independently with the averages and standard deviations being calculated from the set of daily results. The lines connect the average values while the error bars give the error of the mean based on the number of days in the annual set. Ulrich, R. 2010. ApJ

Meridional circulation at high latitudes Meridional Circulation with HMI (the B0 effect!) Results obtained by applying ring-diagram analysis technique to the HMI data averaged over Carrington rotation 2106 (HMI rings team) Results obtained by applying ring-diagram analysis technique to the HMI data averaged over Carrington rotation 2101 (HMI rings team)

Yearly averages of the meridional flow obtained by ring-diagram analysis of continuous GONG data at four different depths. The variation with the solar cycle clearly observed at the superficial layers is less pronounced at deeper layers. The extra circulation (bumps) is also clearly visible in the shallow layers. González Hernández, et al.. 2010, ApJ Extra circulation in the active belts Left: Longitudinal averages of surface horizonal flows. Solid lines: before excluding active region areas, dashed lines: after excluding active regions. Right: Sketch of surface flows around active regions Gizon, L. 2004, Solar Physics, 224, 217

Temporal variation of the meridional circulation residuals (or jets) at a depth of 5.8 Mm (bottom panel). Positive velocities are directed towards the poles. A symmetrical plot averaging both hemispheres is shown in the bottom panel [7]. The top panel shows the location and magnetic strength of the activity during the same period (calculated from MDI synoptic magnetograms). The existence of the residuals, or extra circulation, at medium-high latitudes before the onset of activity of solar cycle 24 confirmed previous results showing the persistence of such residuals after removing the contribution from active regions [6]. Extra circulation in the active belts: another component of the torsional oscillation? González Hernández et al., 2008, 2010

Speed of the antisymmetric component of the meridional flows plotted as a function of latitude and time at four depths. To make the plot symmetric, the sign of the flow has been reversed in the southern hemisphere. Thus, positive velocity points toward the poles in both hemispheres. Each data point is assumed to represent the time interval between the mid-points with neighboring sets. The actual time covered by each set (which is typically one Carrington rotation) is usually much smaller than the interval between the sets. Solar Cycle 23 meridional circulation residuals from MDI Basu & Antia, 2010, ApJ, 717, 488

Prospects for Detection of the Deep Solar Meridional Circulation Meridional travel time differences as a function of latitude and propagation depth (top). Measurements are averaged over the period 1995-2009. The increase of time differences at a depth of about 0.77RSun can be an indication of large perturbations of the meridional flow or some other properties of the deep convective zone. Inversions of these travel time differences are needed in order to get realistic estimations of the actual flows. The lower panel shows the precision of measurements. In this figure, the horizontal axis correspond to the same depths as the top panel, but has been labeled in units of separation distance for cross-correlation analysis. It should be noted that error bars for most measurements are smaller than 0.02 seconds [8]. Courtesy of S. Kholikov

Long-term surface observations Hathaway and Rightmire 2010, Science, 327, 1350

Recent Surface Observations Ulrich, R. 2010, ApJ, 725, 658 “…that the differences in surface meridional flow speed between the solar plasma and magnetic patterns can be explained as due to the effects of surface turbulent magnetic diffusion.” Dikpati, M., Gilman, P. and Ulrich, R. 2010, AstroPh

Multiwavelengthhelioseismology:HMI/AIA GONG/MOTH Subsurface flow maps for Jan 18, 2003(left) and Jan 19, 2003 (right). Blue arrows show flows obtained from the Ni line (~200km from base of photosphere) and red from the K line (~420 Km from base of photosphere). Differences Jain, K. et al, 2006

Supergranulation and “banana” cells Nagashima, K. et al. 2011, ApJ, 726L, 17: Noth-South aligment of the supergranulation in the polar regions using time-distance analysis (SOT/Hinode). Featherstone, N. A. et al, 2006/2007 (SPD/AAS): Helioseismic Searches for the Elusive Giant Cells of Convection Rudi Komm (private communication): Long term giant “banana” cell like structures in the subsurface layers Differences

Conclusions and future work • Solar cycle variation • Depth profile /deep meridional circulation • High latitudes • Meridional circulation countercells? • Polar branch of the torsional oscillation • Large cells and supergranulation (lot of work to be done!) • Understand the systematics in the different analysis methods • Global helioseismology inferences (Gough & Hindman)of mc • SDO: HMI/AIA • Different vantage points

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