Flows in the Solar Convection Zone

1. Flows in the Solar Convection Zone David Hathaway NASA/MSFC National Space Science and Technology Center 2004 July 21

2. Outline • Non-Axisymmetric Flows – Convective Flows • Non-Axisymmetric Flows – Flows around Sunspots • Axisymmetric Flows – Differential Rotation • Axisymmetric Flows – Meridional Circulation • Solar Cycle Variability • Inter-relationships • Conclusions

3. Convective Flows Three layers of convection cells: 1801 Granules – Surface to 1000 km 1954 Supergranules – Surface to 30,000 km 1964 Giant Cells – Surface? to 200,000 km Granules Supergranules Giant Cells?

4. Granulation Granulation movies from the Swedish Vacuum Solar Telescope in La Palma illustrate the evolving granulation pattern. Typical cells are about 1000 km in diameter with lifetimes of about 20 minutes.

5. Granulation Simulations The numerical simulations of Stein & Nordlund reproduce the granulation pattern in most details. A “Cork” movie by Fausto Cattaneo shows magnetic elements might be advected into downdrafts.

6. Supergranulation Supergranulation is seen in Doppler velocity observations and in flow field constructed with time-distance helioseismology. Typical cells are about 30,000 km in diameter and have lifetimes of a couple days.

7. Supergranulation in the Interior Duvall et al. (Solar Phys. 1997) used time-distance helioseismology to show that the supergranulation flows extend several thousand kilometers into the sun.

8. Supergranulation Simulations Numerical simulations of supergranulation are not as mature as those for granulation. The mechanism that selects cells the size of supergranules is still uncertain. Data simulations can, however, provide important information about the properties of supergranules.

9. Supergranules and Magnetic Field Diffusion A Diffusivity constructed from the data simulation input spectrum (velocity x wavelength) gives a spectrum that is strongly peaked at ℓ~120 (supergranules).

10. Nordlund & Stein Simulations Correlation Tracking Results Data Simulation Input Data Simulation Observed The Photospheric Convection Spectrum The spectrum has two peaks: one at ℓ~120 (supergranules) and one at ℓ~4000 (granules). There is nothing to indicate an additional component (mesogranules).

11. Supergranulation as a Wave Recent 3D spectral analyses of MDI Dopplergrams suggest that there may be a wave-like property to supergranulation (Gizon, Duvall, & Schou, Nature 2003; Schou, ApJ 2003). Cells of different sizes rotate at different rates.

12. Giant Cells? A 3D spectral analysis of MDI Dopplergrams shows a ridge of power that extends down to the lowest wavenumbers. This represents large Doppler features rotating with the Sun. However, the characteristics of these Doppler features are inconsistent with actual flows and do not exhibit other characteristics expected from Giant cells.

13. Giant Cells as “Sub-Surface Weather?” Local helioseismology (time-distance: Zhao & Kosovochev, ApJ 2004; Ring-diagrams: Haber et al., ApJ 2002) shows large velocity features below the suns surface that are more representative of giant cells.

14. The Axisymmetric Flows

15. Photospheric Differential Rotation Sunspot motions and direct Doppler measurements had long ago revealed a rapidly rotating equator and more slowly rotation pole. Photospheric zonal velocity from GONG 1995.

16. Internal Differential Rotation Helioseismic determinations of the internal rotation rate show that the latitudinal differential rotation seen at the surface extends through the convection zone. Layers of strong radial shear are found near the surface and at the base of the convection zone (the tachocline).

17. Photospheric Meridional Flow The direction, the strength, and the structure of the meridional flow were uncertain prior to helioseismology. Photospheric Meridional flow from GONG 1995.

18. Internal Meridional Flow Local Helioseismology has revealed aspects of the internal structure of the Meridional Circulation. (Giles et al., 1997; Braun and Fan, 1998; Schou and Bogart, 1998; Basu, Antia, and Tripathy 1999) All of these investigations indicate a poleward meridional flow of about 20 m/s that persists with depth.

19. Deep Meridional Flow(Giles 2001) • Inversion of travel times with mass-conservation constraint through the whole convection zone (Giles PhD thesis). • For r/R>0.8 the mean meridional circulation is poleward in both hemispheres and peaks around 25 deg latitude. • The data are consistent with a 3 m/s return flow at the base of the convection zone. Fractional radius r/R

20. Latitude Drift of Sunspot Zones We examined the latitude drift of the sunspot zones by first separating the cycles where they overlap at minimum. We then calculated the centroid position of the daily sunspot area averaged over solar rotations for each hemisphere. [Hathaway, Nandy, Wilson, & Reichmann, ApJ 2003]

21. Drift Rate vs. Latitude The drift rate in each hemisphere and for each cycle (with one exception) slows as the activity approaches the equator. This behavior follows naturally from the characteristics of a deep meridional flow. The flow amplitude is about 2-3 m/s.

22. Variations over the Sun’s Activity Cycle Cyclicmagnetohydrodynamichelioseismology

23. Zonal Flow Variations Torsional Oscillations Torsional Oscillations in the rate of rotation were first observed at the surface. Early surface observations showed high latitude extensions (Snodgrass, ApJ 1985). More recent observations show detatched polar spin-ups at cycle maximum (Ulrich, ApJ 2001).

24. Torsional Oscillations – Internal Extensions Kosovichev & Schou (1997) found the torsional oscillation signal below the surface. Antia & Basu (2001) follow the equatorward drift in GONG data at 15 Mm depth and see high latitude spin up. Howe et al. (2000) see extensions to 60-70 Mm depth.

25. Tachocline Oscillations Howe et al. 2002 found that the shear across the tachocline grew and decayed with a period of about 18 months.

26. Cycle-to-Cycle Variations Sunspot Latitude Drift Rate The sunspot cycle period is anti-correlated with the drift velocity at cycle maximum. The faster the drift rate the shorter the period. R=-0.5 95% Significant

27. Drift Rate – Amplitude Correlations The drift velocity at cycle maximum is correlated to the cycle amplitude but a stronger and more significant correlation is with the amplitude of the second following (N+2) cycle. Both of these results were anticipated by the Dikpati & Charbonneau, ApJ 1999, dynamo paper. R=0.5 98% Significant R=0.7 99% Significant

28. Inter-Relationships: Solar Rotation, Convection, and Axisymmetric Flows The effects of the Sun’s rotation changes the shape and dynamics of the convection cells – cells elongated north-south drive a rapidly rotating equator (Miesch et al., ApJ 2000). The meridional flow is more complex.

29. Effects of Weak Rotation Solar Rotation (27d) is slow for supergranules (40h) and granules (20m). Foukal & Jokipii, ApJ 1975, suggested that with slow rotation fluid will tend to conserve angular momentum and produce a shear layer with rotation increasing inward. Simulations by Gilman & Foukal, ApJ 1979, and by Hathaway, Solar Phys. 1982, confirmed this for supergranulation. A poleward meridional flow at the surface is also produced.

30. Magnetic Features reveal the Flows

31. Conclusions • Granulation is well observed and simulated with numerical models. • Supergranulation still holds some surprises. – What drives it? Does it have wave-like properties? • Giant cells are still elusive. Can we observe their characteristics? Do they match the simulations? • Differential rotation and the meridional circulation throughout the bulk of the convection zone are probably driven by giant cells. • The surface shear layer and excess surface meridional flow is probably driven by supergranulation. • The Tachocline is driven by…? • Torsional oscillations may be driven by thermal shadows from rising flux tubes (Spriut, 2003). • Tachocline oscillations may be driven by…?