On Maximum Likelihood Estimation of averaged power spectra

Abstract

It is custom in helioseismology to assume that the power spectra of time series of solar radial velocity or of solar intensity have χ2 with 2 degrees of freedom statistics. This assumption is regularly used in helioseismology for using Maximum Likelihood Estimators for single power spectra with that assumed statistics. When independent power spectra are added, it is also custom to assume that the resulting power spectra can be approximated by a Gaussian distribution. Here we show that this approximation is irrelevant, and that the software code developed for fitting single power spectra can be used without any approximation after proper normalization of the added power spectra.