T.L. Duvall Jr.1, S.M. Hanasoge2,3, S. Chakraborty4
1Solar Physics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD
2Tata Institute of Fundamental Research, Mumbai, India
3Max-Planck-Institut fur Sonnensystemforschung, 3, Gottingen, Germany
4HEPL, Stanford University, Stanford, USA
Figure 1|(a) The supergranular velocity vectors that best match observations are shown. Blue arrows represent the direction and amplitude of the flow. (b) The vertical flow amplitude vz is shown as a function of depth, z, for the position corresponding to the dashed red line location in panel (a). Note that the vertical flow peaks at –2.30 Mm with an upflow of 240 m s–1. (c) The horizontal flow amplitude vx is shown as a function of depth, z, for the position corresponding to turquoise line in panel (a). Note the peak horizontal flow amplitude is 700 m s–1 at z=–1.6 Mm and x=7 Mm.
Supergranulation, first seen as a 30 Mm cellular pattern of horizontal flows detected by Doppler shifts in the solar photosphere, continues to puzzle investigators. Recent work attempts to understand supergranulation by revealing its subsurface structure using local helioseismology .
Detailed radiative-hydrodynamic simulations of the outer convection zone and atmosphere show no excess flow signal at the supergranular scale in the photosphere, in contrast to the observational results . These simulations, which match the observations of the solar granulation so well, would seem to have all of the ingredients required to reproduce supergranulation, but do not. In particular, that the He II ionization could give rise to supergranulation, is tested by the simulations with a null result. One possibility remaining to be tested is the simulation of magnetic field, which is known to be present along cell boundaries.
We analyze 60,000 supergranules using HMI data from 64 12–hour intervals (10 June 2010–10 July 2010). This work is a continuation of a previous supergranule study  using HMI data and simulations. However, our methods are improved and the supergranular flow profiles that are recovered have less uncertainty. Cross-correlation maps were constructed for each 12–hour period for the in and out-annulus signals and for the four quadrant signals (quadrants are eastward, westward, northward and southward wave direction) for 16 distance ranges. Travel times were computed for each set of cross correlations and differences. An average of the travel-time differences is made about the supergranular center. Features at different latitudes are treated equally due to using a Postel’s coordinate system centered on the feature. The details of the analysis can be found in .
A convectively stabilized solar model is employed with a vertical-flow features with flow peaking at a depth of –2.3 Mm with a vertical Gaussian depth profile with a width of 0.82 Mm and horizontal Gaussian width of 5.1 Mm. This is a forward model with prescribed flows in order to test the reliability of our analysis procedures to recover flows. A global simulation of wave propagation is performed with wave sources near the surface. Center to annulus travel-time differences were measured from the simulations results as a function of the annulus radius.
Our results support the conclusions from the previous paper that supergranules have an upflow velocity much larger than the surface upflow of 10 m s–1, possibly as large as 240 m s–1 and a peak flow 2–3 Mm below the surface as seen in Fig 1. The disagreement between the present work and the smaller flows reported previously has somewhat disappeared with the work of Svanda5. He used f-modes and small separation p-modes and finds flows similar to ours.
The question remains: What sets the supergranularsize-scale in the Sun? And why aren’t the radiative-hydrodynamic simulations able to reproduce a similar feature?
 Gizon, L., Birch, A.C., Spruit, H.C., 2010, Ann. Rev. Astron. Astrophys., 48, 289.
 Nordlund, A., Stein, R.F., Asplund, M., 2009, Living Rev. Solar Phys., 6, 2.
 Duvall Jr., T.L., Hanasoge, 2013, Solar Phys, 287, 71.
 Duvall Jr., T.L., Hanasoge, S.M, Chakraborty, S., 2014, Solar Phys., see: http://arxiv.org/abs/1404.2533
 Svanda, M., 2012, Astrophys. J., 759, L29.