[en] RE J1034+396, a narrow-line Seyfert 1 active galactic nucleus (AGN), is the first example of AGNs that exhibited a nearly coherent quasi-periodic oscillation (QPO) for the data collected by XMM-Newton in 2007. The spectral behaviors and timing properties of the QPO have been studied since its discovery. We present an analysis of the QPO in RE J1034+396 based on the Hilbert-Huang transform. Comparing with other time-frequency analysis methods, the Hilbert spectrum reveals the variation of the QPO period in great detail. Furthermore, the empirical mode decomposition provides bandpass-filtered data that can be used in the O – C and correlation analysis. We suggest that it is better to divide the evolution of the QPO in this observation into three epochs according to their different periodicities. In addition to the periodicities, the correlations between the QPO periods and corresponding mean count rates are also different in these three epochs. Further examining the phase lags in these epochs, we found no significant phase lags between the soft and hard X-ray bands, which is also confirmed in the QPO phase-resolved spectral analysis. Finally, we discuss the indications of current models including a spotted accretion disk, diskoseismology, and oscillation of shock according to the observed time-frequency and spectral behaviors.

[en] We present time-frequency analysis results based on the Hilbert–Huang transform (HHT) for the evolution of a 4-Hz low-frequency quasi-periodic oscillation (LFQPO) around the black hole X-ray binary XTE J1550–564. The origin of LFQPOs is still debated. To understand the cause of the peak broadening, we utilized a recently developed time-frequency analysis, HHT, for tracking the evolution of the 4-Hz LFQPO from XTE J1550–564. By adaptively decomposing the ∼4-Hz oscillatory component from the light curve and acquiring its instantaneous frequency, the Hilbert spectrum illustrates that the LFQPO is composed of a series of intermittent oscillations appearing occasionally between 3 and 5 Hz. We further characterized this intermittency by computing the confidence limits of the instantaneous amplitudes of the intermittent oscillations, and constructed both the distributions of the QPO’s high- and low-amplitude durations, which are the time intervals with and without significant ∼4-Hz oscillations, respectively. The mean high-amplitude duration is 1.45 s and 90% of the oscillation segments have lifetimes below 3.1 s. The mean low-amplitude duration is 0.42 s and 90% of these segments are shorter than 0.73 s. In addition, these intermittent oscillations exhibit a correlation between the oscillation’s rms amplitude and mean count rate. This correlation could be analogous to the linear rms-flux relation found in the 4-Hz LFQPO through Fourier analysis. We conclude that the LFQPO peak in the power spectrum is broadened owing to intermittent oscillations with varying frequencies, which could be explained by using the Lense–Thirring precession model

[en] The high-mass X-ray binary SMC X-1 is an eclipsing binary with an orbital period of 3.89 days. This system exhibits a superorbital modulation with a period varying between ∼40 days and ∼65 days. The instantaneous frequency and the corresponding phase of the superorbital modulation can be obtained by a recently developed time-frequency analysis technique, the Hilbert-Huang transform (HHT). We present a phase-resolved analysis of both the spectra and the orbital profiles with the superorbital phase derived from the HHT. The X-ray spectra observed by the Proportional Counter Array on board the Rossi X-ray Timing Explorer are fitted well by a blackbody plus a Comptonized component. The plasma optical depth, which is a good indicator of the distribution of material along the line of sight, is significantly anti-correlated with the flux detected at 2.5-25 keV. However, the relationship between the plasma optical depth and the equivalent width of the iron line is not monotonic. There is no significant correlation for fluxes higher than ∼35 mCrab but clear positive correlation when the intensity is lower than ∼20 mCrab. This indicates that the iron line production is dominated by different regions of this binary system in different superorbital phases. To study the dependence of the orbital profile on the superorbital phase, we obtained the eclipse profiles by folding the All Sky Monitor light curve with the orbital period for different superorbital states. A dip feature, similar to the pre-eclipse dip in Her X-1, lying at orbital phase ∼0.6-0.85, was discovered during the superorbital transition state. This indicates that the accretion disk has a bulge that absorbs considerable X-ray emission in the stream-disk interaction region. The dip width is anti-correlated with the flux, and this relation can be interpreted by the precessing tilted accretion disk scenario

[en] The high-mass X-ray binary SMC X-1 exhibits a superorbital modulation with a dramatically varying period ranging between ∼40 days and ∼60 days. This research studies the time-frequency properties of the superorbital modulation of SMC X-1 based on the observations made by the All-Sky Monitor (ASM) onboard the Rossi X-ray Timing Explorer (RXTE). We analyzed the entire ASM database collected since 1996. The Hilbert-Huang transform (HHT), developed for non-stationary and nonlinear time-series analysis, was adopted to derive the instantaneous superorbital frequency. The resultant Hilbert spectrum is consistent with the dynamic power spectrum as it shows more detailed information in both the time and frequency domains. The RXTE observations show that the superorbital modulation period was mostly between ∼50 days and ∼65 days, whereas it changed to ∼45 days around MJD 50,800 and MJD 54,000. Our analysis further indicates that the instantaneous frequency changed to a timescale of hundreds of days between ∼MJD 51,500 and ∼MJD 53,500. Based on the instantaneous phase defined by HHT, we folded the ASM light curve to derive a superorbital profile, from which an asymmetric feature and a low state with barely any X-ray emissions (lasting for ∼0.3 cycles) were observed. We also calculated the correlation between the mean period and the amplitude of the superorbital modulation. The result is similar to the recently discovered relationship between the superorbital cycle length and the mean X-ray flux for Her X-1.