Current Status and Future Prospects of High-Degree Ridge Fitting

1. Current Status and Future Prospects of High-Degree Ridge Fitting Johann Reiter, Edward Rhodes, and Jesper Schou HMI Science Team Meeting Monterey, CA February 16, 2006

2. Recent Progress in Ridge-Fitting • We have Made Progress in the Fitting of both un-averaged and m-averaged power spectra. • Un-averaged spectra can now be fit for degrees between 45 and 1000. • Averaged spectra now include n-leaks in fitted profile and have been fit up to degrees of 1467. • Frequency errors have been greatly diminished in the fitting of un-averaged spectra.

3. Overview of Current Ridge-Fitting Methods • The method which fits m-averaged spectra is our Windowed, Multiple-Peak, Averaged-Spectrum (WMLTP) Method • This method requires that splitting coefficients be specified in the generation of the m-averaged spectra • This method employs m-averaged leakage matrices • The current version uses wide leakage matrices corrected for latitudinal differential rotation • This method can use symmetric or asymmetric profiles • This method produces frequencies, widths, amplitudes, asymmetries and their associated errors

4. Differential Rotation Correction Requires Input of Rate Coefficients

5. Overview of Current Ridge-Fitting Methods (cont.) • The method which fits un-averaged spectra is our Multiple-Peak, Tesseral-Spectrum (MPTS) Method • This method employs zonal, sectoral, and tesseral power spectra rather than Fourier Transforms • This method employs wide, unaveraged leakage matrices which are also corrected for latitudinal differential rotation • This method can also employ symmetric or asymmetric profiles • This method produces frequencies, widths, amplitudes, asymmetries and their associated errors • This method also produces rotational frequency-splitting coefficients and their associated errors

6. Problems which Affect Both WMLTP and MPTS Methods

7. Recent Improvements in WMLTP Fitted Profiles

8. Examples of WMLTP Method Fits for Modes and Ridges

9. Set of WMLTP Frequencies from 5.7-Day MDI Time Series Using Nigam and Kosovichev Asymmetric Profile for April 7-12, 2002

10. Chronological History of Multiple-Peak Tesseral-Spectrum Method Production Runs Using JPL SGI Origin 2000 Supercomputers

11. Recent Comparison of Frequencies Computed from m-averaged and Un-averaged Power Spectra Using WMLTP and MPTS Methods

12. Recent Improvements in Rotational Splitting Coefficients Computed Using MPTS Method

13. Rotational Inversion of High-Degree P-Mode Splitting Coefficients for Degrees up to 500 Computed Using Multiple-Peak Tesseral-Spectrum Fitting Method (Dec. 2004 run) Inner Turning-Point Radius Dependence of Newer Set Of P-Mode Splitting Coefficients Computed Using Multiple-Peak Tesseral-Spectrum Method for Degrees up to 1000 (July 2005 run)

14. Improvements in MPTS Frequencies Between 2001 and 2005 Reduction in MPTS Frequency Errors Between 2001 and 2005

15. Improvements Currently Underway in WMLTP Code • Non-linear expansions of amplitude and widths of sidelobes versus degree must be completed • Inclusion of n-leaks in theoretical profiles must be completed • Code needs to be ported to Stanford pipeline

16. Improvements Currently Underway in MPTS Code • Non-linear expansions of frequency, amplitude, and width of sidelobes versus degree must be implemented • N-leaks must be included in theoretical profiles • Theoretical Profiles Must be Convolved with Temporal Window Functions • Adjustment of input values must be automated • Code needs to be ported to Stanford pipeline

17. Future Issues for Both WMLTP and MPTS Methods • Un-averaged power spectra must be re-computed with corrections for: 1) improved model of MDI instrumental distortion, 2) a fixed error in MDI position angle, and 3) possible errors in the Carrington rotation elements • Un-averaged leakage matrices need to have corrections included for instrumental point-spread function and finite pixel size • Woodard’s 1989 theory for distortion from differential rotation needs to be refined • An improved asymmetric profile formula is essential

18. Conclusions • High-degree modes are fundamental to improving our knowledge of the solar interior • Current local helioseismic techniques are not valid substitutes for fits of spherical harmonic power spectra • We have demonstrated two fitting methods which can fit both narrow modal peaks and broad power ridges • We will soon be able to test MDI and GONG Fits • Both of these methods hold great promise for use in the HMI Software Pipeline

19. Manual Selection is Currently Required in Choice of Input Parameters