The analysis of indexed astronomical time series - VI. Covariances of amplitude ratios and phase differences estimated from multicolour photometry ofa pulsating star

One of the tools used to identify the pulsation modes of stars is a compari son of the amplitudes and phases as observed photometrically at different w avelengths. Proper application of the method requires that the errors on th e measured quantities, and the correlations between them, be known (or at l east estimated). It is assumed that contemporaneous measurements of the lig ht intensity of a pulsating star are obtained in several wavebands. It is a lso assumed that the measurements are regularly spaced in time, although th ere may be missing observations. The amplitude and phase of the pulsation a re estimated separately for each of the wavebands, and amplitude ratios and phase differences are calculated. A general scheme for estimating the cova riance matrix of the amplitude ratios and phase differences is described. T he first step is to fit a time series to the residuals after pre-whitening the observations by the best-fitting sinusoid. The residuals are then cross -correlated to study the interdependence between the errors in the differen t wavebands. Once the multivariate time-series structure can be modelled, t he covariance matrix can be found by bootstrapping. An illustrative applica tion is described in detail.