T he A coustic S un S imulator Computing medium- l data

1. The Acoustic Sun Simulator Computing medium-l data Shravan Hanasoge Thomas Duvall, Jr. HEPL, Stanford University

2. Why artificial data? • Validation of helioseismic techniques • Improve understanding of wave interaction with flow structures, sunspot-like regions etc. – the need for controlled experiments • Improving existing techniques based on this understanding

3. generating the data… • Acoustic waves are excited by radially directed stochastic dipoles • Waves propagate through a frozen background state that can include flows, temperature perturbations etc. • The acoustic signal is extracted at the photospheric level of the simulation

4. Computation of Sources • Granulation acts like a spatial delta function, exciting all medium-l the same way. • Use a Gaussian random variable to generate a uniform spherical harmonic-spectrum and frequency limited series in the spherical harmonic – frequency space • Transform to real space to produce uncorrelated sources

5. Theoretical model • The linearized Euler equations with a Newton cooling type damping are solved • Viscous and conductive process are considered negligible (time scale differences)

6. Computational model • Horizontal derivatives computed spectrally • Radial derivatives with compact finite differecnces • Time stepping by optimized 5 stage LDDRK (Hu et al. 1996) • Parallelism in OpenMP and MPI • Model S of the sun as the al.) background state (Christensen-Dalsgaard, J., et

7. Horizontal variations • Spherical Harmonic decomposition of variables in the horizontal direction • Horizontal derivatives are calculated in Spherical Harmonic space (expensive) • Gaussian collocated grid points in latitude and equally spaced in longitude

8. Crazy density changes… • 11 scale heights between r = 0.26 and r = 0.986 • 13 scale heights between r = 0.9915 and r =1.0005 • Grid allocation method is a combination of log-density and sound-speed

9. Radial variations • Interior radial collocation: constant acoustic travel-time between adjacent grid point • Near surface collocation: constant in log density • Sixth order compact finite differences in the radial direction

10. Radial grid spacing

11. Boundary conditions • Absorbing boundary conditions on the top and bottom • Implemented using a ‘sponge’

12. Convective instabilities • The outer 30% of the sun is convectively unstable • The near-surface (0.1% of the radius) is highly unstable – start of the Hydrogen ionization zone • Modeling convection is infeasible • Instability growth rates around 5 minutes; corrupt the acoustic signal • Solution: altered the solar model to render the model stable

13. Artificially stabilized model • Convectively stable • Maintain cutoff frequencies • Smooth extension of the interior model S • Hydrostatic equilibrium

15. Log power spectrum – 24 hour data cube. Simulation domain extends from the outer core to the evanescent region. Banded structure due to limited excitation spectrum.

16. Validation I – eigen-modes

17. Validation II – frequency shifts by constant rotation

18. Traveltimes

19. Acoustic Wave Correlations Medium l data correlations Correlation from simulations Note that signal-noise levels compare very well!

20. Linewidths and asymmetries • Solar-like velocity asymmetry • Asymmetry reduces at higher frequencies due to damping

21. Computational efficiency • The usefulness of this method limited by the rapidity of the computation • Currently, 2 seconds of computational time to advance solar time by 1 second (at high l ) • The hope is to push this ratio to 1:1 or perhaps even better

22. Interpreting the data… • Motivation guiding the effort: differential studies of helioseismic effects • Datum: a simulation with no perturbations • Differences in helioseismic signatures of effects are expected to be mostly insensitive to the neglected physics

23. Capabilities at present • L < 200 (spherical harmonic degree) –OpenMP • Tested for L ~ 341 (works efficiently) with the MPI version • Can simulate acoustic interaction with: • Arbitrary flows • Sunspot type perturbations (no magnetic fields) • Essentially, perturbations in density, temperature, pressure and velocities

24. Current applications • Can we detect convection? • Far-side imaging: validation • Solar rotation: how good are our estimates? • Tachocline studies • Meridional flow models: validation • Line of Sight projection effects

25. References for this work • Computational Acoustics in spherical geometry: Steps towards validating helioseismology, Hanasoge et al. ApJ 2006 (to appear in September) • Computational Acoustics, Hanasoge, S. M. 2006, ILWS proceedings

26. Want artificial data? Email: shravan@stanford.edu