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Motivated by the recent proposal that one can obtain quasi-periodicoscillations (QPOs) by photon echoes manifesting as non-trivial features in theautocorrelation function (ACF), we study the ACFs of the light curves of threeaccreting black hole candidates and a neutron star already known to exhibitQPOs namely, GRS 1915+105, XTE J1550-564, XTE J1859+226 and Cygnus X-2. Wecompute and focus on the form of the ACFs in search of systematics or specifictemporal properties at the time scales associated with the known QPOfrequencies in comparison with the corresponding PDS. Even within our smallobject sample we find both similarities as well as significant and subtledifferences in the form of the ACFs both amongst black holes and between blackholes and neutron stars to warrant a closer look at the QPO phenomenon in thetime domain: The QPO features manifest as an oscillatory behavior of the ACF atlags near zero; the oscillation damps exponentially on time scales equal to theinverse QPO width to a level of a percent or so. In black holes thisoscillatory behavior is preserved and easily discerned at much longer lagswhile this is not the case for the neutron star system Cyg X-2. The ACF of GRS1915+105 provides an exception to this general behavior in that its decay islinear in time indicating an undamped oscillation of coherent phase. We presentsimple ad hoc models that reproduce these diverse time domain behaviors and wespeculate that their origin is the phase coherence of the underlyingoscillation. It appears plausible that time domain analyses, complementary tothe more common frequency domain ones, could impose tighter constraints andprovide clues for the driving mechanisms behind the QPO phenomenon.

QPOs in the Time Domain: An Autocorrelation Analysis