Statistical Revision of the Moment Method

Abstract

The moment method is a well known technique, which uses a time series of the first 3 moments of a spectral line, to estimate the (discrete) mode parameters l and m. The method, contrary to Doppler imaging, also yields other interesting (real-valued) parameters such as the inclination angle i, or v sin i, during its identification procedure. In this paper, we are not only interested in the estimation of these real-valued parameters themselves but also in reliable estimates for their uncertainty. We designed a statistical formalism for the moment method based on the so-called generalized estimating equations (GEE). This formalism aims to estimate the uncertainty of the real-valued parameters taking into account that the different moments of a line profile are correlated and — more importantly — that the uncertainty of the observed moments depends on the pulsation parameters. The latter property of the moment method makes the least-squares technique a poor choice to estimate the uncertainty of the real-valued parameters. We implemented the GEE method and present an application to a high-resolution spectroscopic dataset of the slowly pulsating B star HD181558.