CINDERELLA: comparison of INDEpendent RELative least-squares amplitudes

Abstract

Context. The identification of smaller and smaller signals from objects observed with a non-perfect instrument in a noisy environment poses a challenge for a statistically clean data analysis. Aims. We compute the probability that frequencies determined in various data sets are related or not, which cannot be answered with a simple comparison of amplitudes. Our method provides a statistical estimator for whether a given signal with different strengths in a set of observations is of instrumental origin or is intrinsic. Methods. Based on the spectral significance as an unbiased statistical quantity in frequency analysis, Discrete Fourier Transforms (DFTs) of target and background light curves are compared. The individual False-Alarm Probabilities are used to deduce a conditional probability of a peak in a target spectrum being real in spite of a corresponding peak in the spectrum of sky background or of comparison stars. Alternatively, we can compute joint probabilities of frequencies to occur in the DFT spectra of several data sets simultaneously but with different amplitude, leading to composed spectral significances. These are useful to investigate a star observed in different filters or during several observing runs. The composed spectral significance is a measure of the probability that none of the coinciding peaks in the DFT spectra under consideration are due to noise. Results. CINDERELLA is a mathematical approach to a general statistical problem. Its potential reaches beyond photometry from ground or space to all cases where a quantitative statistical comparison of periodicities in different data sets is desired. Examples of the composed and the conditional CINDERELLA mode for different observation setups are presented.