The art of tting p-mode spectra I. Maximum likelihood estimation

Abstract. In this article we present our state of the art of tting helioseismic p-mode spectra. We give a step by step recipe for tting the spectra: statistics of the spectra both for spatially unresolved and resolved data, the use of Maximum Likelihood estimates, the statistics of the p-mode parameters, the use of Monte-Carlo simulation and the signicance of tted parameters. The recipe is applied to synthetic low-resolution data, similar to those of the LOI, using Monte-Carlo simulations. For such spatially resolved data, the statistics of the Fourier spectrum is as-sumed to be a multi-normal distribution; the statistics of the power spectrum is not a 2 with 2 degrees of free-dom. Results for l = 1 shows that all parameters describ-ing the p modes can be obtained with negligible bias and with minimum variance provided that the leakage matrix is known. Systematic errors due to an imperfect knowl-edge of the leakage matrix are derived for all the p-mode parameters. Key words: methods: analytical; data analysis