Calculating the GONG Leakage Matrix
Abstract
Since spherical harmonics do not form a complete orthonormal basis set over a portion of a sphere, helioseismic spectra computed for a specific target mode with degree ellt and azimuthal degree mt also contain modes with nearby ell'' and m''. These spatial leaks greatly increase the complexity of the observed spectrum, complicating the spectral fitting and degrading the resulting mode parameter estimates. This is particularly true where the target mode and the leaks have similar frequencies. Some strategies for fitting helioseismic spectra explicitly include the leakage matrix which estimates the relative strength of a mode (ell'' and m'') in the spectrum at (ellt,mt). Since the fitting methods assume that the matrix is correct and apply it as a constraint, an inaccurate matrix introduces systematic errors in the estimated mode parameters. It is thus important to have as accurate a matrix as possible. Here we report on the calculation of the leakage matrix for the GONG observations. The matrix elements are essentially the integrals (over the observed portion of the solar surface) of the crossproducts of the two spherical harmonics. However, several effects have been included to increase the accuracy of the matrix. These include the projection factor of the observable (velocity, intensity, modulation), the spatial apodization applied to the data, the finite rectangular pixel dimensions of the observations, and possible errors in the estimated image geometry. Other factors to be incorporated are the observed MTF, the merging of the GONG images, and the horizontal components of the oscillatory velocity field. We will compare the latest calculation with the observed spectrum and assess the relative importance of the input factors. We will also compare the leakage matrices for velocity and intensity to estimate their contribution to the large apparent differences in the helioseismic spectra obtained from these observables.
- Publication:
-
Structure and Dynamics of the Interior of the Sun and Sun-like Stars
- Pub Date:
- 1998
- Bibcode:
- 1998ESASP.418..225H