Abstract
It is well known that the residuals of the multifrequency analysis of δ Scuti stars are correlated, giving rise to challenging features such as a plateau (HD 50844, HD 50870, HD 49434, …) of non-resolved frequencies with amplitude higher than the expected noise level. Several hypotheses have been advanced to explain these features: effective convection, rotation, non-linear interactions, etc. We have recently demonstrated that in some cases the underlying function describing the light variations of δ Scuti stars has not the property of being analytic. The strong consequence of this result is that the Fourier expansion on which the harmonic analysis is based could be not justified.In order to know the extension of this phenomenon among δ Scuti stars, we have used photometric data from CoRoT seismofield and a set of Kepler stars. The results show that this inconsistency in the application of harmonic analysis is almost ubiquitous to the δ Scuti pulsating stars.
Highlights
It is well known that the residuals of the multifrequency analysis of δ Scuti stars are correlated, giving rise to challenging features such as a plateau (HD 50844, HD 50870, HD 49434, . . . ) of non-resolved frequencies with amplitude higher than the expected noise level
It is not always guaranteed that a periodogram is an unbiased estimator of the spectral density, i.e. the discrete Fourier transform converges to the real frequency content of the time series
In [2] we proposed a method to study the analyticity of the underlying function of light curves through the “connectivities” in order to test whether the periodogram is an unbiased estimator of the spectral density
Summary
It is well known that the residuals of the multifrequency analysis of δ Scuti stars are correlated, giving rise to challenging features such as a plateau (HD 50844, HD 50870, HD 49434, . . . ) of non-resolved frequencies with amplitude higher than the expected noise level. To perform seismological studies of the stars it is essential to detect pulsational frequencies in their photometric or radial velocity time series. A periodogram ([1]) is a well defined and easy to calculate estimator of the spectral density of a time series.
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