Imaging Solar Tachocline Using Numerical Simulations and SOHO/MDI Data

1. Imaging Solar Tachocline Using Numerical Simulations and SOHO/MDI Data Junwei Zhao1, Thomas Hartlep2, Alexander G. Kosovichev1, Nagi N. Mansour2 • W.W.Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA94305-4085 • NASA Ames Research Center, Moffett Field, CA94035

2. Tachocline Imaging Using Numerical Simulation Data

3. Simulation Model Sound-speed perturbation of 0.6% is placed at 0.7R, with a latitudinal dependence, and with a Gaussian shape. It’s symmetric along the equator. The simulation used here is 1024 minutes.

4. 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; Postel’s 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

5. 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.

6. 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.

7. Inversion Result

8. 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.

9. 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.

10. 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

11. 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.

12. Deep Focusing Inversion Result • Results are not so good as surface focusing results. • One reason is that measurement noises are quite high.

13. Deep Focusing Inversion Result Once again, the inverted profile seems not well localized.

14. Tachocline Imaging Using Observational Data

15. Applying the Analysis on Observations • 1440-minute (1 day) medium-l datasets are used; • To infer one tachocline image, I used one Carrington rotation’s 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.

16. Measurements from Real Sun: Surface Focusing

17. Results from Real Sun: Surface Focusing • Structures are not hemisphere symmetric. • Tachocline is clearly seen, pretty much latitudinal dependent.

18. Measurements from Real Sun: Deep Focusing

19. Results from Real Sun: Deep Focusing • Again, structures are not hemisphere symmetric. • Tachocline is also clearly seen, latitudinal dependent.

20. 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.

21. Tachocline Variations with Solar Cycle

22. 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.

23. Tachocline Variations from August 1996 to August 2007

24. 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.

25. 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?

26. 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?

27. 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?