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Enhancing Helioseismic Insights through Acoustic Sun Simulation Techniques

This research explores the development of an artificial acoustic simulator to improve the understanding of solar wave interactions, particularly in regions akin to sunspots. By validating helioseismic techniques through controlled experiments, the study utilizes stochastic dipoles to excite acoustic waves that propagate in a modeled solar environment. The methodology involves complex spectrally computed derivatives and utilizes advanced computational techniques for efficient simulations. The findings aim to enhance the accuracy of solar models and deepen our insight into solar dynamics, including convective instabilities and acoustic signal properties.

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Enhancing Helioseismic Insights through Acoustic Sun Simulation Techniques

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  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 differences • 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

  14. 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.

  15. Validation I – eigen-modes

  16. Validation II – frequency shifts by constant rotation

  17. Traveltimes

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

  19. Problems with radial aliasing….

  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, 1 seconds of computational time to advance solar time by 1.3 second (at l~127 ) • The hope is to achieve this ratio at high l

  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

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