| dc.description.abstract | The development of time-frequency analysis techniques made astronomers successfully deal with non-stationary time series that originated from unstable physical mechanisms. I applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), on two examples of non-stationary astrophysical phenomena: the superorbital modulation in a high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of a narrow-line Seyfert 1 active galactic nucleus (AGN) RE J1034+396.
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. A Hilbert spectrum that shows more detailed information in both the time and frequency domains was obtained using the light curve collected by the All-Sky Monitor onboard the Rossi X-ray Timing Explorer (RXTE). The RXTE observations show that the superorbital modulation period was mostly between ~50 days and ~65 days, whereas it changed to ~40 days around MJD 50,800 and MJD 54,000. Based on the instantaneous phase defined by the HHT, 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. A positive correlation between the mean period and the amplitude of the superorbital modulation, which is similair to that in Her X-1, was also discovered. With the superorbital phase defined by the HHT, a phase-resolved analysis of both the spectra and the orbital profiles was processed. From all the spectral parameters, I noticed that the relation between the equivalent width of iron line and the plasma optical depth 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. Furthermore, 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.
With the successful experience of dealing with the superorbital modulation of an X-ray binary system, we further applied the HHT to analyze the QPO of RE J1034+396 using the data collected by XMM-Newton in 2007. RE J1034+396, a narrow-line Seyfert 1 galaxy, is the first example of AGNs that exhibited a nearly coherent QPO. The ensemble empirical mode decomposition (EEMD) provides bandpass-filtered data that can be used in the O - C and correlation analysis. From the Hilbert spectrum and the O - C analysis, I suggested that it is better to divide the evolution of the QPO in this observation into three epochs according to their different periodicities. Besides the periodicities, the correlations between the QPO periods and corresponding mean count rates are also different in these three epochs. The change in periodicity and the relationships could be interpreted by the change in oscillation mode based on the assumption of diskoseismology model. Finally, 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, I presented a brief summary and pointed out possible future applications of the HHT on other astronomical time series, as well as the possible application of two-dimensional EEMD on morphological analysis.
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