A NEW TECHNIQUE FOR THE DETECTION OF PERIODIC SIGNALS IN COLORED POWER SPECTRA

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 p eriodic modulation over the frequency range in which these ''colored'' noise components are dominant has proved a very complex task. Commonl y used methods rely upon spectral smoothing or incoherent summation of sample spectra in order to decrease the variance of the power estimat es. The consequent reduction in frequency resolution also causes a red uction of sensitivity to periodic signals. We develop here a technique aimed at detecting periodicities in the presence of ''colored'' power spectrum components, while maintaining the highest Fourier frequency resolution. First, we introduce a simple approximation to the statisti cal properties of the ''colored'' 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. This involves averaging the spectral estimate s adjacent to each frequency over a suitably chosen interval in order to follow steep red noise features and produce estimates that are loca lly unaffected by the possible presence of a sharp peak. By dividing t he sample spectrum by the smoothed one, a white noise-like spectrum is obtained, the approximate probability distribution of which is derive d. A search for coherent pulsations is then carried out by looking for peaks in the divided spectrum, the chance probability of which is bel ow a given detection threshold. If no significant peaks are found, an upper limit to the amplitude of a sinusoidal modulation is worked out for each searched frequency. The technique is tested and its range of applicability determined through extensive numerical simulations. We p resent also an application to the X-ray light curves of V0332+53, a hi ghly variable accreting X-ray pulsar, and GX 13+1, a bright and variab le accreting source in the Galactic bulge.