Open AccessThe analysis of indexed astronomical time series – VI. Covariances of amplitude ratios and phase differences estimated from multicolour photometry of a pulsating star
Author(s) -
Koen Chris
Publication year - 2000
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2000.03559.x
Subject(s) - amplitude , physics , photometry (optics) , series (stratigraphy) , phase (matter) , astrophysics , covariance , bootstrapping (finance) , wavelength , stars , statistics , optics , mathematics , paleontology , quantum mechanics , econometrics , biology
One of the tools used to identify the pulsation modes of stars is a comparison of the amplitudes and phases as observed photometrically at different wavelengths. Proper application of the method requires that the errors on the measured quantities, and the correlations between them, be known (or at least estimated). It is assumed that contemporaneous measurements of the light intensity of a pulsating star are obtained in several wavebands. It is also assumed that the measurements are regularly spaced in time, although there may be missing observations. The amplitude and phase of the pulsation are estimated separately for each of the wavebands, and amplitude ratios and phase differences are calculated. A general scheme for estimating the covariance matrix of the amplitude ratios and phase differences is described. The 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 different wavebands. Once the multivariate time‐series structure can be modelled, the covariance matrix can be found by bootstrapping. An illustrative application is described in detail.