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

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.

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

Differential Rotation Correction Requires Input of Rate Coefficients

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

Problems which Affect Both WMLTP and MPTS Methods

Recent Improvements in WMLTP Fitted Profiles

Examples of WMLTP Method Fits for Modes and Ridges

Set of WMLTP Frequencies from 5.7-DayMDI Time Series Using Nigam and KosovichevAsymmetric Profile for April 7-12, 2002

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

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

Recent Improvements in Rotational Splitting Coefficients Computed Using MPTS Method

Rotational Inversion of High-Degree P-Mode Splitting Coefficients forDegrees up to 500 ComputedUsing Multiple-Peak Tesseral-Spectrum Fitting Method (Dec. 2004 run)

Inner Turning-Point RadiusDependence of Newer SetOf P-Mode Splitting CoefficientsComputed Using Multiple-PeakTesseral-Spectrum Method forDegrees up to 1000 (July 2005 run)

Improvements in MPTSFrequencies Between 2001 and 2005

Reduction in MPTSFrequency Errors Between 2001 and 2005

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

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

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

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

Manual Selection is Currently Required in Choice of Input Parameters