Imaging Solar Tachocline Using Numerical Simulations and SOHO/MDI Data

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Imaging Solar Tachocline Using Numerical
Simulations and SOHO/MDI Data

• Junwei Zhao1, Thomas Hartlep2, Alexander G.
  Kosovichev1, Nagi N. Mansour2

1. W.W.Hansen Experimental Physics Laboratory,
   Stanford University, Stanford, CA94305-4085
2. NASA Ames Research Center, Moffett Field, CA94035

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Tachocline Imaging Using Numerical Simulation Data
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Simulation Model
Sound-speed perturbation of 0.6 is placed at
0.7R, with a latitudinal dependence, and with a
Gaussian shape. Its symmetric along the equator.
The simulation used here is 1024 minutes.
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Measurement Scheme Surface Focusing

• We use surface-focusing scheme, also averaging
  around annulus. Annulus radii range from 6 to 86
  degrees, and annulus width is 1 pixel size, i.e.,
  0.6 degree Postels projection is used.
• No any filtering is used except that filtering
  out f-modes and convection
• The central pixel location ranges from -60 to 60
  degrees in both latitude and longitude
• After all measurements, collapse all pixels of
  the same latitude into one
• In the end, we have 200 numbers in latitude and
  131 numbers in annulus radii.

R
0.45R
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Measured Travel Times
Measured travel times are displayed after a
reference profile is subtracted. The reference
profile is measured from a simulation that Thomas
Hartlep made without perturbations.
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Inversion

• Inversion kernels were made based on
  ray-approximation
• Inversion was performed by use of Multi-Channel
  Deconvolution, which was a code easier to write
  than other least square inversion techniques.
• Regularization was only used in vertical
  direction.
• In the radial direction, the resolution we used
  was 5Mm/pixel.

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Inversion Result
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Comparing Inversion Result with Model

• The inversion result seems not well localized,
  the perturbation is widely spread into all other
  areas.
• Seems a feature at 0.6R equator was something
  brought down by the ray path.

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Comparing Inversion Result with Model
1D result that was averaged from all latitudes
once again show that inversion was not well
localized. Averaging kernels should be computed
to see how localized our inversions are.
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Measurement Scheme Deep Focusing

• I also use deep-focusing scheme, averaging
  around annulus as well. Annulus radii also range
  from 6 to 86 degrees, and annulus width is 1
  pixel size, i.e., 0.6 degr
• No any filtering is used except that filtering
  out f-modes and convection
• The central pixel location ranges from -60 to 60
  in both latitude and longitude
• After all measurements, collapse all pixels of
  the same latitude into one
• In the end, I have 200 numbers in latitude and 66
  numbers in annulus radii.

R
0.45R
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Measured Travel Times
Travel times are displayed after the reference is
subtracted. The reference is from measuring quiet
Sun simulation as well. Some Gaussian smoothing
was done to reduce noises.
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Deep Focusing Inversion Result

• Results are not so good as surface focusing
  results.
• One reason is that measurement noises are quite
  high.

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Deep Focusing Inversion Result
Once again, the inverted profile seems not well
localized.
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Tachocline Imaging Using Observational Data
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Applying the Analysis on Observations

• 1440-minute (1 day) medium-l datasets are used
• To infer one tachocline image, I used one
  Carrington rotations simulation to average,
  i.e., 27 datasets.
• EXACTLY the same measurement and inversion
  procedure was applied to the real observation as
  used in simulated data
• Note that the reference profile is also the same
  as that is used in simulated data, i.e., travel
  times measured from quiet Sun simulation.

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Measurements from Real Sun Surface Focusing
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Results from Real Sun Surface Focusing

• Structures are not hemisphere symmetric.
• Tachocline is clearly seen, pretty much
  latitudinal dependent.

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Measurements from Real Sun Deep Focusing
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Results from Real Sun Deep Focusing

• Again, structures are not hemisphere symmetric.
• Tachocline is also clearly seen, latitudinal
  dependent.

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Results Comparing with Global Helioseismology
Result

• Red and pink curves are from surface- and
  deep-focus, respectively.
• Tachocline is surprisingly in good agreement!
• Should keep in mind the experiments using
  simulated data show that results are not well
  localized.

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Tachocline Variations with Solar Cycle
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I kept some Stanford computers running
continuously for about 3 months, and obtained 11
years far-side images, 11 years interior sound
speed images, 11 years interior rotations, and
11 years meridional flow priofiles, all from
time-distance technique, and all from MDI
medium-l data.
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Tachocline Variations from August 1996 to August
2007
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Results Are Not Exciting, But Rather,
Disappointing
Seems that results are very much instrument
sensitive. When SOHO rotates upside-down due to
the key-hole issue, inverted results are also
upside-down.
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All previous analyses were wrong.
Even if we neglect the instrument effect, the
travel time variations are caused by interior
sound-speed perturbation together with the
interior magnetic field. I should not invert
without the magnetic field term.
Even if I had inverted with both terms, how about
surface effects?
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Correlation with Magnetic Field
I am facing the same problem as Rachel in her
frequency shift analysis. Is the interior sound
speed perturbation caused by interior magnetic
field, or is it just caused by surface effect?
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Summary

• Local Helioseismology is useful to get global
  results
• It is interesting that we can get the sound-speed
  bump at the location of tachocline by use of both
  surface and deep-focusing
• It is quite annoying that seems MDI instrument
  can bring lots of troubles in the analysis
• It is not known, but certainly worth further
  studying to understand the correlation of
  sound-speed perturbation with the magnetic field.
• Can we infer the interior magnetic field from
  such an analysis?