The Acoustic Sun Simulator Computing medium-l data

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The Acoustic Sun Simulator Computing
medium-l data

• Shravan Hanasoge
• Thomas Duvall, Jr.
• HEPL, Stanford University

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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

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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

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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

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Theoretical model

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

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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

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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

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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

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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

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Radial grid spacing
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Boundary conditions

• Absorbing boundary conditions on the top and
  bottom
• Implemented using a sponge

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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

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Artificially stabilized model

• Convectively stable
• Maintain cutoff frequencies
• Smooth extension of the interior model S
• Hydrostatic equilibrium

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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.
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Validation I eigen-modes
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Validation II frequency shifts by constant
rotation
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Traveltimes
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Acoustic Wave Correlations
Medium l data correlations
Correlation from simulations
Note that signal-noise levels compare very well!
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Problems with radial aliasing.
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Linewidths and asymmetries

• Solar-like velocity asymmetry
• Asymmetry reduces at higher frequencies due to
  damping

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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 l127 )
• The hope is to achieve this ratio at high l

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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

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Capabilities at present

• L lt 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

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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

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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