Data for Helioseismology Testing:
Large-Scale Stein-Nordlund
Simulations
Dali Georgobiani
Michigan State University
Presenting the results of
Bob Stein (MSU) &
Åke Nordlund (Denmark)
with
David Benson (MSU)
Stanford, August 6, 2007
Stein–Nordlund RHD Simulations
• Conservative compressible 3D (M)HD equations
• LTR non-gray radiation transfer
• Realistic EOS and opacities

    u
t
20
Mm
u u 
 ui
 
j
i
ui u j  Pij   



x
 gi  J  Bi
t

x

x


 j
i 

 j 
2
u u 
e
i
   eu  P  u   
 j 
 J 2  Qrad


t
x j x i 
48 Mm
B
   E, E  u  B  J, J    B / 0
t
 No free parameters (except for diffusion model).
 Wave excitation and damping occur naturally.
 There is an excellent correspondence between the code results and observations.
Simulations
• Supergranulation scale:
48 Mm x 48 Mm x 20 Mm
• Resolution:
100 km horizontal, 12–75 km vertical
• Numerical method: staggered variables
Spatial differencing:
6th order centered finite difference
Time advancement:
3rd order Runge-Kutta
Vertical
velocity
Horizontal
velocity
divergence
Vertical
velocity,
horizontal
slices at
various
heights
Vertical velocity, vertical slice
Image of the vertical momentum showing a granule 30
Mm across. This is a snapshot at a depth of 16.8 Mm.
96 Mm by 96 Mm
wide simulations
Vertical Velocity at 2.5 & 8 Mm depth
Boxes show domain of earlier simulations at 6, 12, 24 & 48 Mm widths.
Available Datasets
Simulated data are being ingested into the new SDO JSOC database
• Website http://sha.stanford.edu/stein_sim
(some info)
• Contact Bob Stein stein@pa.msu.edu
(more info)
• 2 datasets:
8.5 hr (511 min) solar time, no rotation
58.5 hr, with rotation
Thanks to Rick Bogart for his extensive help with archiving!
Archived Data Description
•
•
•
•
Data are in FITS format
Temporal cadence is 1 minute
3D spatial grid is 500x500x500
A snapshot of a variable occupies
approximately 500 MB of disk space
• First and third directions are horizontal
• Second direction is vertical
• Vertical grid is provided separately
Data Set 1
• Duration: 511 minutes, or 8.517 hours
• No rotation
• 5 variables: horizontal velocities Vx, Vz,
vertical velocity Vy, temperature, density.
• Each variable is stored in a different
directory, each snapshot in a separate file.
Every 20 minutes of data are in one subdirectory.
Data Set 2
• Duration: 58 hours 29 minutes
• Uniform background rotation
• 9 variables: horizontal velocities Vx, Vz,
vertical velocity Vy, temperature, density,
pressure, internal energy, electron density
and G1
• Each snapshot of a variable is stored in a
separate file; 9 variables at each time step
are combined to be retrieved together
(The data will be available for retrieval soon – maybe, in September)
Units of Variables
• Length is in 108 cm = 1 Mm
• Time is in 102 s
•
•
•
•
•
•
Velocities Vx, Vz, and Vy are in 10 km/s
Temperature is in K
Density is in 10-7 g/cm3
Pressure is in 105 dynes/cm2
Internal energy is in 105 dynes/cm2
Electron density is log cm-3
These simulations provide an excellent
opportunity to validate various techniques,
widely used in solar physics and helioseismology for directly obtaining otherwise
inaccessible properties (subsurface
flows, structures etc.)
On the other hand, these analysis
techniques also help to examine
how realistic the simulations are
Data Analysis
• Power spectrum
• Tests of time-distance methods
Compare the results for the simulations and
the SOHO/MDI high-res observations
(211.5 Mm by 211.5 Mm patch, 512 min)
Power Spectra
Simulations
MDI high-res data
Time-Distance Diagram
TD Diagrams at Various Depths
Exploring Simulated Surface
Structures
•
•
•
•
Spatial filtering
Spectral analysis
f-mode time-distance analysis
Local correlation tracking
Large Structures
Time-Distance Analysis
Time-Distance Analysis
Local Correlation Tracking
Correlation
coefficient
Is 0.99
But velocity
amplitudes
are underestimated
(~1.8 times
lower than in
simulations)
These and other results of the simulated data analysis were published in
Georgobiani, D.; Zhao, J.; Kosovichev, A.; Benson, D.; Stein, R.; Nordlund, A.
"Local Helioseismology and Correlation Tracking Analysis of Surface Structures
in Realistic Simulations of Solar Convection"
Astrophysical Journal 2007, Vol. 657, p.1157
Zhao, J.; Georgobiani, D.; Kosovichev, A.; Benson, D.; Stein, R.; Nordlund, A.
"Validation of Time-Distance Helioseismology by Use of Realistic Simulations of
Solar Convection"
Astrophysical Journal 2007, Vol. 659, p.848
Summary - Advantages
 Large domain – supergranulation scale
 Deep - includes lower turning points
 Fast code (parallelizes well)
Future Plans




More Time – Distance calculations?
Acoustic holography?
MHD: sunspot simulations (Nordlund)
Spectra? Mode asymmetries?