Band-limited interpolation applied to the time series of rapidly oscillating stars

Abstract

We reconstruct the temporal Fourier spectra obtained from incomplete records of the luminosities of rapidly oscillating stars. This reconstruction involves a deterministic procedure related to ‘band-limited interpolation’. We show that the stability of the underlying deconvolution process is governed by the choice of the frequency intervals over which the restoration has to be achieved. A ‘time–frequency analysis’ provides a progressive constructive process allowing us to choose these intervals, to measure the frequencies and the fine structure of the driven modes of the star, and to control the error propagation. The method, which is the first step towards multisite deconvolution, is described in detail, and numerical examples for the DAV white dwarf GD 154 are presented to illustrate the application of the algorithm. The restored frequencies are compared with data obtained during a Whole Earth Telescope campaign.