Reversibility of time series: Revealing the hidden messages in X-ray binaries and cataclysmic variables

We explore the non-linear, high-frequency, aperiodic variability properties in the three cataclysmic variables MV Lyr, KIC 8751494 and V1504 Cyg observed with Kepler, as well as the X-ray binary Cyg X-1 observed with RXTE. This is done through the use of a high-order Fourier statistic called the bispectrum and its related biphase and bicoherence, as well as the time-skewness statistic. We show how all objects display qualitatively similar biphase trends. In particular, all biphase amplitudes are found to be smaller than p/2, suggesting that the flux distributions for all sources are positively skewed on all observed time-scales, consistent with the lognormal distributions expected from the fluctuating accretion disc model. We also find that for all objects, the biphases are positive at frequencies where the corresponding power spectral densities display their high-frequency break. This suggests that the noise-like flaring observed is rising more slowly than it is falling, and thus not time-reversible. This observation is also consistent with the fluctuating accretion disc model. Furthermore, we observe the same qualitative biphase trends in all four objects, where the biphases display a distinct decrease at frequencies below the high-frequency break in their respective power spectral densities. This behaviour can also be observed in the time skewness of all four objects. As far as we are aware, there is no immediate explanation for the observed biphase decreases. The biphase decreases may thus suggest that the fluctuating accretion disc model begins to break down at frequencies below the high-frequency break.