Numerical Simulations of Supergranulation and Solar Oscillations

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Numerical Simulations of Supergranulation and
Solar Oscillations

• Åke Nordlund
• Niels Bohr Institute, Univ. of Copenhagen
• with
• Bob Stein (MSU)
• David Benson, Dali Georgobiani
• Sasha Kosovichev, Junwei Zhao (Stanford)

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Experiment settings Code

• Staggered mesh code
• conservative, with radiative transfer
• fast about 5 CPU-microseconds / mesh-update
• includes 4-bin radiative transfer
• massively parallel
• OpenMP up to about 250 CPUs
• MPI up to thousands of CPUs (just developed)
• Hybrid MPI/OMP for clusters with shared mem.
  nodes
• e.g. DCSC/KU 118 nodes x dual-CPUs x dual core
  AMD 472 cores (corresponds to 90 million
  zone-updates / sec)

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Stagger CodeScaling on Columbia (Altix)

• With OpenMP
• With MPI

Size     N-cpu µsec/pnt
125x500x125 1 5.9
250x500x250 64 8.6
500x500x500 64 7.8
500x500x500 125 9.3
500x500x500 250 11.9
Size     N-cpu µsec/pnt
250x500x250 1 4.3
250x500x250 50 4.7
500x500x500 50 5.3
500x500x500 100 6.1
500x500x500 250 6.7
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Supergranulation Simulation48 Mm wide x 20 Mm
deep

• 63 hours (1.3 turnover time)
• f-plane rotation (surface shear layer)
• No magnetic field (yet)
• Low resolution
• 100 km horizontal,
• 12-70 km vertical

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Mean Atmosphere Ionization of Hydrogen and Helium
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What can we learn?

• Use the model and data as a test bed
• SOHO/MDI synthetic data
• what does SOHO/MDI actually measure, and how
  well?
• Local helioseismology
• what do the various methods measure, and how
  well?
• Nature of the flow field
• What is supergranulation?
• How does it fit in with larger smaller scales?

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Data sets available onStanford Helioseismology
Archive
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Upflows at surface come from small area at bottom
(left)Downflows at surface converge to
supergranule boundaries (right)
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Animation
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Time evolution at various depths
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Velocity at the same depths
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The solar velocity spectrum

• Power spectra are often plotted log-log, which
  means the power per unit x-axis is really k
  P(k), rather than just P(k)!

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Solar velocity spectrum
Velocity spectrum v(k) (k P(k))1/2
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Rotation subtracted solar Doppler image
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Ni 6768 response function
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k-w Diagram
simulation
MDI
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Sub-sonic filtering
7 km/s
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P-mode power (red), convective power (black)
time average (blue)
Note that it matters very much how one computes
power spectra
Hi-res MDI
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Velocity spectrumonly distinct scale is
granulation
- - - - convection
Vhoriz (sim)
Vz(sim)
. oscillations
V MDI
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A continuous solar velocity spectrum!

• Supergranulation may stand out a little
• But the flow is nearly scale-invariant
• amplitudes scale inversely with size
• lifetimes scale with the square of the size

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A Nearly Scale Free Spectrum!Doppler Image of
the Sun (SOHO/MDI)
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Solar horizontal velocity (observed)Scales
differ by factor 2 which is which?
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Solar horizontal velocity (model)Scales differ
by factor 2 which is which?
24 Mm
12 Mm
6 Mm
3 Mm
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Solar velocity spectrum
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Time-Distance Diagram
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f-mode Travel Times vs Simulated Flow Fields
(divergence)
Right side image shows the f-mode outgoing and
ingoing travel time differences, and the left
side image shows the divergence computed from
simulation. (From Junwei Zhao)
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f-mode Travel Times vs Simulated Flow Fields
(Horizontal)
Right side image shows the f-mode north-going and
south-going travel time differences, and the left
side image shows the Vn-s averaged from
simulation. (From Junwei Zhao Aaron Birch)
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Local Correlation Tracking
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Sunspots
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Sunspot, initial time evolution
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Sunspot, time evolution (rep.)
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Temperature, hor. vert. magn. field,hor.
vert. velocity, surface intensity
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Velocity, as seen by VAPOR(top perspective)
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Sunspot,log magnetic pressure
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Sunspot, field lines with density iso-surface
(solar surface)
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Field line detail
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Key result A continuous solar velocity spectrum

• Supergranulation may stand out a little
• But the flow is nearly scale-invariant
• amplitudes scale inversely with size
• lifetimes scale with the square of the size

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Data sets available onStanford Helioseismology
Archive
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ExperimentsForthcoming

• AR magnetic fields
• add B from MDI magnetogram (as in Gudiksen
  Nordlund)
• Quiet Sun magnetic fields
• advect initially horizontal field from the bottom
  b.c.
• Rise of magnetic flux tube
• Insert flux tube near bottom, study emergence
  through surface
• Coronal chromospheric heating
• similar to Gudiksen Nordlund, but real driving

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The End