Junwei Zhao1, R. S. Bogart1, A. G. Kosovichev1, T. L. Duvall Jr.2, and T. Hartlep1
1. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA
2. Solar Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
It is widely believed that meridional circulation plays an important role in solar dynamo by transporting magnetic flux in the Sun. However, although it has long been recognized that the meridional flow is poleward at the surface and in shallow interior to at least a depth of 30 Mm with a speed of about 20 m s-1, the detailed profile of the interior meridional circulation is still not clear. Earlier helioseismic inversion with a mass-conservation constraint put the equatorward return flow near the bottom of the convection zone with a speed of 2 m s-1 (ref. 1). Many flux-transport dynamo models adopt this single-cell circulation picture. Recently, Hathaway claimed the equatorward flow was shallow at a depth of about 50 Mm by tracking motions of supergranules2. This remains to be confirmed by helioseismic analyses.
2. Data Analysis and Results
Figure 1 | Comparison of the measured acoustic travel-time differences, δτSN, from the HMI and MDI data after removal of the systematic center-tolimb effect, together with the δτSN calculated from the interior velocity inverted from the HMI measurements. Error bars for the green dashed curves are similar to those for the black curves. (b) Comparison of the δτSN from the HMI and MDI quiet-period observations before the removal of the systematic effect.
Two years of full-disk HMI Doppler velocity data, from 2010 May 1 through 2012 April 30, are used in this analysis. For each observing day, the data were tracked with a uniform Carrington rotation rate and remapped using Postel’s projection with a spatial sampling rate of 0.18° pix-1. Acoustic travel times were measured along north-south directions, in the areas within 15° from the central meridian, for distances ranging from 2.16° to 44.64°. These measurement distances cover a depth from the surface to approximately 0.70 R⊙ according to acoustic ray theory.
Acoustic travel times along the east-west directions, in the areas within 15° from the equator, were also measured using the same north-south measurement geometry for the purpose to remove the systematic center-to-limb effect that was recently found in helioseismic analysis3. The exact cause of the center-to-limb effect is not clearly known, but recent works using different helioseismic analysis methods have shown that this effect exists in many methods and must be removed.
Measurements at selected latitudes, for both before and after the removal of the center-to-limb effect were shown in Figure 1. Also shown were measurements using MDI Dynamic Campaign data for selected quiet periods. Despite the different amplitude of the systematic effect, the measurements after the effect removal were in reasonable agreement.
Figure 2 | Meridional flow profile, obtained by inverting the measured acoustic travel times. Panel (a) shows a cross-section view of the meridional-flow profile, with the positive velocity directing northward. Panels (b) and (c) show the inverted velocity as functions of latitude averaged over several depth intervals. Panels (d) and (e) show the velocity as functions of depth averaged over different latitudinal bands.
Inversions are performed using ray-path approximation sensitivity kernels. Figure 2 shows the inversion results. Basically, the interior meridional circulation shows a double-cell profile (a schematic plot is shown in Figure 3), with the equatorward flow extending from approximately 0.92 R⊙ to 0.83 R⊙ with a speed of about 10 m s-1. The poleward flow covers depths of 0.92–1.0 R⊙ as well as 0.75–0.83 R⊙. Our measurements are too noisy to derive flows deeper than 0.75 R⊙. Longer observation and further development of measurement technique may help in this regard.
Our analysis using newly available helioseismic data from HMI reveals a double-cell meridional circulation inside the Sun, with the equatorward flow located in a relatively shallow interior between 0.83 and 0.92 R⊙.This new circulation profile, consistent with some global convection simulations (e.g., ref. 4), provides new opportunities in further advancing our understanding of the solar dynamo. For more, please refer to our full paper5.
 Giles, P. 1999, Ph.D. Thesis, Stanford University
 Hathaway, D. H. 2012, ApJ, 760, 84
 Zhao, J., Nagashima, K., Bogart, R. S., Kosovichev, A. G., Duvall, T. L., Jr. 2012, ApJL, 749, L5
 Miesch, M. S., Brun, A. S., Toomre, J. 2006, ApJ, 641, 618
 Zhao, J., Bogart, R. S., Kosovichev, A. G., Duvall, T. L., Jr., Hartlep, T. 2013, ApJL, 774, L29