1. Data for Helioseismology Testing Dali Georgobiani Michigan State University Presenting the results of Bob Stein (MSU) & Åke Nordlund (NBI, Denmark) with David Benson (Kettering University) Stanford, July 29, 2008

2. Numerical Method Staggered mesh Non-linear, fully compressible, 3D, explicit Spatial differencing: 6 th order centered finite difference Time advancement: 3 rd order Runge-Kutta

3. Size and Resolution Size of the domain: 96 Mm x 96 Mm x 20 Mm 1000 x 1000 x 500 grid points Grid information: dx = dy = 0.1 Mm dz = 0.012–0.075 Mm dt = 0.25 sec (saved every 60 sec)

4. Boundary Conditions Density: logarithmic extrapolation on top and bottom Velocity at the top is taken to be constant at its value at the last physical point Energy (per unit mass): top – slowly evolving average, bottom – fixed energy in inflows Initialization Start from existing 12x12x9 Mm simulation Extend adiabatically to 20 Mm and relax for a solar day to develop structures Double horizontally + small fraction of stretched fluctuations to remove symmetry Relax to develop large-scale structures

5. Radiation Treatment LTR Non-grey, 4 bin multigroup Equation of State Tabular EOS Includes ionization, excitation H, He, H 2, other abundant elements

6. Mean Atmosphere

8. Sound Speed

9. Vertical Velocity at 2.5 & 8 Mm depth Boxes show domain of earlier simulations at 6, 12, 24 & 48 Mm widths.

10. Vertical momentum at 0, 2, 4, 16 Mm

11. Vertical momentum vs depth

12. Velocity stream lines Courtesy Chris Henze (NASA)

13. Finite time Lyapunov exponent (proxy for vorticity) Courtesy Bryan Green (AMTI/NASA)

14. Available Datasets Website http://sha.stanford.edu/stein_simhttp://sha.stanford.edu/stein_sim (some info) Contact Bob Stein stein@pa.msu.edu (more info)stein@pa.msu.edu Simulated data are being ingested into the new SDO JSOC database Thanks to Rick Bogart for his extensive help with archiving!

15. Archived Data Description 9 variables: horizontal velocities Vx, Vz, vertical velocity Vy, temperature, density, pressure, internal energy, electron density, and  Each snapshot of a variable is stored in a separate file; 9 variables at each time step are combined to be retrieved together Data are in FITS format Duration 511 minutes (360 minutes recorded, WIP) A snapshot of a variable occupies approximately 2 GB of disk space First and third directions are horizontal, second direction is vertical Vertical grid is provided separately (The data will be available for retrieval soon – check with Rick)

16. Another Data Set 4 hour averages, with 2 hour overlap 6 variables: horizontal velocities V x, V z, vertical velocity V y, temperature, density, and sound speed Simultaneous surface velocities Stored in the IDL SAVE format at MSU Work in progress… initial 6 variables calculated and stored, now adding internal energy E

17. Units of Variables Length is in 10 8 cm = 1 Mm Time is in 10 2 s Velocities V x, V z, and V y are in 10 km/s Temperature is in K Density is in 10 -7 g/cm 3 Pressure is in 10 5 dynes/cm 2 Internal energy is in 10 5 ergs/cm 3 Electron density is log cm -3

18. Data Analysis Power spectrum Tests of time-distance methods Compare the results for the simulations and the SOHO/MDI high-res observations (211.5 Mm by 211.5 Mm patch, 512 min) The following work was performed with Junwei Zhao and Alexander Kosovichev

19. Power Spectra SimulationsMDI high-res data

20. Power Spectra SimulationsMDI high-res data

21. Power Spectra SimulationsHinode data

22. Velocity Spectra

23. sqrt [k P(k)]

24. Time-Distance Diagram

25. TD Diagrams at Various Depths

26. Exploring Simulated Surface Structures Spatial filtering Spectral analysis f-mode time-distance analysis Local correlation tracking

27. Large Structures

28. Time-Distance Analysis

29. Horizontal Flow Fields SimulationsInversions Depth range is 2-3 Mm. The longest arrow corresponds to 300 m/s

30. Local Correlation Tracking Correlation coefficient Is 0.99 But velocity amplitudes are under- estimated (~1.8 times lower than in simulations)

31. These simulations provide an excellent opportunity to validate various techniques, widely used in solar physics and helio- seismology for directly obtaining otherwise inaccessible properties (subsurface flows, structures etc.) On the other hand, these analysis techniques also help to examine how realistic the simulations are Conclusions