Acoustic wave propagation in the solar subphotosphere

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Acoustic wave propagation in the solar
subphotosphere
S. Shelyag, R. Erdélyi, M.J. Thompson Solar
Physics and upper Atmosphere Research Group,
Department of Applied Mathematics, University of
Sheffield, Sheffield, UK
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Outline
We aim to develop a numerical toolbox for
helioseismological studies

• Numerical setup
• Harmonic source
• Local cooling event (non-harmonic source)
• Some analysis

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The simulation setup
Full 2-dimensional HD Cartesian geometry Total
Variation Diminishing spatial discretization
scheme Fourth order Runge-Kutta time
discretization The simulation domain 150 Mm
wide and 52.6 Mm deep, 600x4000 grid points The
upper boundary of the domain is near the
temperature minimum Two boundary regions of 1.3
Mm each at the top and bottom boundaries The
main part of the domain is 50 Mm deep
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The simulation domain
We look at the level 600 km below the upper
boundary The source is located 200 km below this
level
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The model profile
temperature
density
convection lt0 no gt0 yes
sound speed
Modified Christensen-Dalsgaard's standard Model,
pressure equilibrium.
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Convective instability
Convective instability is suppressed
?1const5/3
This approach has advantage, because the waves,
while propagating through the quiescent medium,
can be observed more clearly, undisturbed by
convective fluid motions far from the source.
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Source 1
Harmonic pressure perturbation (cf. Tong et al.
2003)
?p is the pressure perturbation amplitude t
real time T5.5 min
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Evolution of pressure perturbation 1
Consecutive snapshots of pressure deviation ?p in
the simulated domain after the harmonic
perturbation has been introduced. High order
acoustic modes produced by interference of the
lower ones can be noticed in the upper part of
the domain on the latest snapshots.
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Time-distance diagram 1
Synthetic time-distance diagram (the cut of ?p/p0
is taken at about 600 km below the upper
boundary of the domain).
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Source 2
Localized cooling event causing local convective
instability, mass inflow and sound waves
extinction
where timescale ?1120 s
Power spectrum of the source
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Velocity field around the source
The behavior of the source in time can be
understood as two stages. In the beginning, the
source creates expanding inflow and the pressure
and temperature drop. At the second stage, due to
an increased temperature gradient, two convective
cells surrounding the source are developed.
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Evolution of pressure perturbation 2
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Time-distance diagram 2
Time-distance diagram produced with the
non-harmonic source. The picture is covered by
the flows caused by the source.
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Time-distance diagram 2
Pressure cut with high-pass frequency filtering
applied. The filtering revealed seismic traces
similar to the ones shown for the harmonic source.
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Single non-harmonic source, some analysis
The power spectrum of the time-distance diagram
generated by a single perturbation source. The
p-modes are visible up to high orders. The
theoretically calculated p1 mode is marked by two
dashed lines.
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Multiple non-harmonic sources, some analysis
The power spectrum of a large number of sources
randomly distributed along a selected depth and
time. The features, connected with fluid motions
caused by these sources, and the high order
p-modes faint with the growth of the number of
random sources. The p1 mode is marked in the same
way as before.
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To-do list

• Better boundaries are necessary
• Non-uniform grid (and possibility of 3D)
• Magnetic field