Mausumi Dikpati
High Altitude Observatory, Boulder, CO 80301, USA

Accurate knowledge of the Sun’s meridional circulation profile, speed and its time variation from observations and theory is necessary for solar dynamo models and successful predictions of solar cycle features. It is even more necessary now, given that the advection-dominated dynamo models, assuming a single cell meridional circulation in each hemisphere, led to a high solar cycle 24 amplitude, which is unlikely to be validated.

New helioseismic inversion methods and new data from HMI are providing the first pictures of meridional circulation below the photosphere. Using HMI data, Zhao et al.¹ found evidence of a second meridional flow cell with depth (see Figure 1). Using SoHO/MDI data Schad et al.² found as many as four meridional circulation cells with latitude in each hemisphere, all of which extend to the bottom of the convection zone. Surface Doppler data indicated two or sometimes just one cell with latitude in the photosphere³, and assuming that the flow goes all the way down to the bottom of the convection zone a two-celled flow pattern in the convection zone can be inferred.

Figure 1 | Inferred meridional circulation pattern by Zhao et al.¹

The differences among results in Ref 1, 2, and 3 need to be understood and hopefully reconciled. The helioseismic data were from different time periods and all three data sets were analyzed using different methods.

The Zhao et al results especially create a new challenge for both solar dynamo models and meridional circulation models, because it is not only difficult to calibrate a dynamo for the Sun with two flow cells in depth, but even more so to generate two flow cells in depth by meridional circulation models, as those models favor cells going all the way down to the convection zone bottom.

Dikpati⁴ has shown that the radial and latitudinal Coriolis forces from the helioseismicly well-known differential rotation are very strong for the Sun, and the meridional circulation driven by these Coriolis forces contains two cells in latitude (see Figure 2), the cells going all the way to the bottom of the adiabatically stratified convection zone. For solar-type turbulent viscosity, the resulting poleward flow speed in the primary cell is two orders of magnitude larger than observed. These results indicate that there must be some other force within the convection zone that brakes the meridional circulation flow speed to produce a solar-like amplitude. Thermal forcing originating from a negative buoyancy and/or nonviscous turbulent stresses are the likely candidates for braking.

Figure 2 | (a) Solar-like differential rotation pattern as observationally inferred by Corbard et al.⁵ ; (b) meridional circulation pattern produced by this differential rotation and turbulent viscous Reynolds stresses.

The Sun’s meridional circulation is most likely mechanically driven and thermally braked, roughly opposite to the driving mechanism of the Hadley cell in the Earth’s atmosphere, which is thermally driven by differential heating from the Sun and mechanically braked by Coriolis forces from the Earth’s troposphere differential rotation.

Because gravity in the Sun is so large, the non-radial fluid density variations needed to produce a negative buoyancy force of required magnitude need not be very large. Thus it creates a challenging future investigation for what buoyancy patterns can produce a second meridional circulation cell in depth as found by Zhao et al. and four cells in latitude as found by Schad et al, and whether such patterns appear in short term as transients or persist for longer time scales, such as decadal time scales.

References

[1] Zhao, J., Bogart, R. S., Kosovichev, A. G., Duvall, T. L., Jr., Hartlep,T. 2013, ApJL, 774, L29
[2] Schad, A., Timmer, J., Roth, M. 2013, ApJL, 778, L38
[3] Ulrich, R. K., 2010, ApJ, 725, 658
[4] Dikpati, M., 2014, MNRAS, in press
[5] Corbard, T., Thompson, M. J., 2002, Solar Phys., 205, 211