1. Numerical Simulations of Supergranulation and Solar Oscillations Åke Nordlund Niels Bohr Institute, Univ. of Copenhagen with Bob Stein (MSU) David Benson, Dali Georgobiani Sasha Kosovichev, Junwei Zhao (Stanford)

2. Experiment settings: Code Staggered mesh code conservative, with radiative transfer fast – about 5 CPU-microseconds / mesh-update includes 4-bin radiative transfer massively parallel OpenMP up to about 250 CPUs MPI up to thousands of CPUs (just developed) Hybrid MPI/OMP for clusters with shared mem. nodes  e.g. DCSC/KU: 118 nodes x dual-CPUs x dual core AMD = 472 cores (corresponds to ~90 million zone-updates / sec)

3. Stagger Code: Scaling on Columbia (Altix) With OpenMP With MPI Size N-cpuµsec/pnt 125x500x1251 5.9 250x500x250648.6 500x500x500647.8 500x500x5001259.3 500x500x50025011.9 Size N-cpuµsec/pnt 250x500x2501 4.3 250x500x250504.7 500x500x500505.3 500x500x5001006.1 500x500x5002506.7

4. Supergranulation Simulation 48 Mm wide x 20 Mm deep  63 hours (1.3 turnover time)  f-plane rotation (surface shear layer)  No magnetic field (yet)  Low resolution: 100 km horizontal, 12-70 km vertical

5. Mean Atmosphere: Ionization of Hydrogen and Helium

6. What can we learn? Use the model and data as a test bed SOHO/MDI synthetic data what does SOHO/MDI actually measure, and how well? Local helioseismology what do the various methods measure, and how well? Nature of the flow field What is ‘supergranulation’? How does it fit in with larger & smaller scales?

7. Data sets available on Stanford Helioseismology Archive

8. Upflows at surface come from small area at bottom (left) Downflows at surface converge to supergranule boundaries (right)

9. Animation

10. Time evolution at various depths

11. Velocity at the same depths

12. The solar velocity spectrum Power spectra are often plotted log-log, which means the power per unit x-axis is really k P(k), rather than just P(k)!

13. Solar velocity spectrum MDI doppler (Hathaway) TRACE correlation tracking (Shine) MDI correlation tracking (Shine) 3-D simulations (Stein & Nordlund) V ~ k V~k -1/3 Velocity spectrum: v(k) = (k P(k)) 1/2

14. Rotation subtracted solar Doppler image

15. Ni 6768 response function

16. simulationMDI k-  Diagram

17. Sub-sonic filtering ~ 7 km/s

18. P-mode power (red), convective power (black) – time average (blue) Hi-res MDI Note that it matters very much how one computes power spectra

19. Velocity spectrum only distinct scale is granulation V horiz (sim) V z (sim) V MDI - - - - convection …. oscillations

20. A continuous solar velocity spectrum! Supergranulation may stand out a little But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size

21. A Nearly Scale Free Spectrum! Doppler Image of the Sun (SOHO/MDI)

22. Solar horizontal velocity (observed) Scales differ by factor 2 – which is which? 400 Mm 200 Mm 100 Mm 50 Mm

23. Solar horizontal velocity (model) Scales differ by factor 2 – which is which? 24 Mm12 Mm 6 Mm3 Mm

24. Solar velocity spectrum

25. Time-Distance Diagram

26. f-mode Travel Times vs Simulated Flow Fields (divergence) Right side image shows the f-mode outgoing and ingoing travel time differences, and the left side image shows the divergence computed from simulation. (From Junwei Zhao)

27. f-mode Travel Times vs Simulated Flow Fields (Horizontal) Right side image shows the f-mode north-going and south-going travel time differences, and the left side image shows the V n-s averaged from simulation. (From Junwei Zhao & Aaron Birch)

28. Local Correlation Tracking

29. Sunspots

30. Sunspot, initial time evolution

31. Sunspot, time evolution (rep.)

32. Temperature, hor. & vert. magn. field, hor. & vert. velocity, surface intensity

33. Velocity, as seen by VAPOR (top perspective)

34. Sunspot, log magnetic pressure

35. Sunspot, field lines with density iso-surface (~solar surface)

36. Field line detail

37. Key result: A continuous solar velocity spectrum Supergranulation may stand out a little But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size

38. Data sets available on Stanford Helioseismology Archive

39. Experiments: Forthcoming AR magnetic fields add B from MDI magnetogram (as in Gudiksen & Nordlund) Quiet Sun magnetic fields advect initially horizontal field from the bottom b.c. Rise of magnetic flux tube Insert flux tube near bottom, study emergence through surface Coronal & chromospheric heating similar to Gudiksen & Nordlund, but “real driving”

40. The End