The art of fitting p-mode spectra - II. Leakage and noise covariance matrices

In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using "Maximum Likelihood Estimators". In this article, hereafter Part II, we sinew how to use the theory developed in Part I for fitting real data. We introduce 4 new diagnostics in helioseismology: the (m, nu) echelle diagram, the cross echelle diagram, the inter echelle diagram, and the cross spectrum ratio. These diagnostics are extremely powerful to visualize and understand the covariance matrices of the Fourier spectra; and also to find bugs in the data analysis code. The diagrams are used to verify the computation of the leakage matrices; and also to measure quantitatively these matrices. Cross spectrum ratios are used to obtain quantitative information on the noise covariance matrices. Numerous examples using the LOI/SOHO a,nd GONG data are given.