The Acoustic Sun Simulator

Computing medium-l data

Shravan Hanasoge Thomas Duvall, Jr.

HEPL, Stanford University

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

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

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

Theoretical model

The linearized Euler equations with a Newton cooling type damping are solved

Viscous and conductive process are considered negligible (time scale differences)

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

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

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

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

Radial grid spacing

Boundary conditions

Absorbing boundary conditions on the top and bottom

Implemented using a ‘sponge’

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

Artificially stabilized model Convectively stable

Maintain cutoff frequencies

Smooth extension of the interior model S

Hydrostatic equilibrium

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.

Validation I – eigen-modes

Validation II – frequency shifts by constant rotation

Traveltimes

Acoustic Wave Correlations

Medium l data correlations Correlation from simulations

Note that signal-noise levels compare very well!

Problems with radial aliasing….

Linewidths and asymmetries

• Solar-like velocity asymmetry

• Asymmetry reduces at higher frequencies due to damping

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

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

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

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

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