A New Technique for the Detection of Periodic Signals in ``Colored'' Power Spectra

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Abstract
The light curves from a variety of celestial objects display aperiodic variations, often giving rise to red-noise components in their power spectra. Searching for a narrow power spectrum peak resulting from a periodic modulation over the frequency range in which ``coloured'' noise components are dominant has proven a very complex task. We develop here a technique aimed at detecting periodicities in the presence of ``coloured'' power spectrum components, while mantaining the highest Fourier frequency resolution. First we introduce a simple approximation to the statistical properties of the ``coloured'' power spectra from celestial objects, based on a few examples and the theory of linear processes. We then estimate the continuum components in the power spectrum through an ad hoc smoothing technique. By dividing the sample spectrum by the smoothed one, a white-noise like spectrum is obtained, the approximate probability distribution of which is derived. A search for coherent pulsations is then carried out by looking for peaks in the divided spectrum, the chance probability of which is below a given detection threshold. The technique is tested and its range of applicability determined through extensive numerical simulations. We present also an application to the X-ray light curves of V0332+53, a highly variable accreting X-ray pulsar, and GX13+1, a bright and variable accreting source in the galactic bulge.
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