The development of time-frequency analysis techniques allow astronomers to successfully deal with the non-stationary time series that originate from unstable physical mechanisms. We applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), to two non-stationary phenomena: the superorbital modulation in the high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of the AGN RE J1034+396. From the analysis of SMC X-1, we obtained a Hilbert spectrum that shows more detailed information in both the time and frequency domains. Then, a phase- resolved analysis of both the spectra and the orbital profiles was presented. From the spectral analysis, we noticed that the iron line production is dominated by different regions of this binary system in different superorbital phases. Furthermore, a pre-eclipse dip lying at orbital phase ~ 0.6 - 0.85 was discovered dur- ing the superorbital transition state. We further applied the HHT to analyze the QPO of RE J1034+396. From the Hilbert spectrum and the O - C analysis results, we suggest that it is better to divide the evolu- tion of the QPO into three epochs according to their different periodicities. The correlations between the QPO periods and corresponding uxes were also different in these three epochs. The change in periodicity and the relationships could be interpreted as the change in oscillation mode based on the diskoseismology model.

LMC X-4 is an eclipsing high-mass X-ray binary exhibiting a superorbital modulation with a period of ~ 30.5 days. We present a detailed study of the variations of the superorbital modulation period with a time baseline of ~ 18 years. The period determined in the light curve collected by the Monitor of All-sky X-ray Image (MAXI) significantly deviates from that observed by the All Sky Monitor (ASM) onboard the Rossi X-ray Timing Explorer (RXTE). Using the data collected by RXTE/ASM, MAXI, and the Burst Alert Telescope (BAT) onboard Swift, we found a significant period derivative, _P = (2.08±0.12) X 10-5. Furthermore, the O{C residual shows complex short-term variations indicating that the superorbital modulation of LMC X-4 exhibits complicated unstable behaviors. In addition, we used archive data collected by the Proportional Counter Array (PCA) on RXTE to estimate the orbital and spin parameters. The detected pulse frequencies obtained in small time segments were fitted with a circular orbital Doppler shift model. In addition to orbital parameters and spin frequency for each observation, we found a spin frequency derivative of v = (6.482 ± 0.011) X 10-13 Hz · s-1. More precise orbital and spin parameters will be evaluated by the pulse arrival time delay technique in the future.

We present our analysis results for an updated orbital ephemeris for the dipping low mass X-ray binary 4U 1624-49, using the light curve collected by the All Sky Monitor (ASM) on board the Rossi X-ray Timing Explorer (RXTE) and the Monitor of All-Sky X-ray Image (MAXI). To make clear dip profiles, the light curve from the ASM and the MAXI were divided into ten 500d segments and four 400d segments for ASM and MAXI light curves, respectively, and folded with the linear ephemeris proposed by Smale et al. (2001). The phases of dip centers were determined by the method adopted from Hu et al. (2008). The phase drift was then fitted with a linear function. We obtained an updated orbital period of 0.869896(1) d and a phase zero epoch of JD 2450088.6618(57). No clear orbital period derivative is detected with a 2-sigma upper limit of 1.4 X 10-6(yr)-1 from a quadratic curve fitting of the dip phase evolution.

X1822-371 is a low mass X-ray binary with an accretion disk corona exhibiting partial eclipses and pulsations in the X-ray band. We update its orbital ephemeris by combining new RXTE observations and historical records, with a total time span of 34 years. There were 11 RXTE observations in 2011 but the eclipsing prole can be seen in only 4 of them. The eclipsing center times were obtained by fitting the profile with the same model as previous studies. Combined with the eclipsing center times reported by Iaria et al. (2011), the O-C analysis was processed. A quadratic model was applied to fit the O-C results and produced a mean orbital period derivative of _Porb = 1.339(25) X 10-10s=s, which is slightly smaller than previous records. In addition to the orbital modulation from the orbital profile, we also present our preliminary results for measuring the orbital parameters using the orbital Doppler effect from the pulsation of the neutron star in X1822-371. The updated orbital parameters from eclipsing profiles will be further compared with the ones from pulsar timing.

We present the results from analysis of the Hilbert-Huang transform (HHT) for the 4 Hz quasi-periodic oscillations (QPO) around the black hole X-ray binary XTE J1550-564. The resultant Hilbert spectra demonstrate that the QPO is composed of a series of intermittent signals appearing occasionally. From the analysis of the HHT, we further found the distribution of the lifetimes for the intermittent oscillations and the distribution for the time intervals with no significant signal (the break time). The mean lifetime is 1.45 s and 90% of the oscillation segments have lifetimes less than 3.1 s whereas the mean break time is 0.42 s and 90% of break times are less than 0.73 s. We conclude that the intermittent feature of the QPO could be explained by the Lense-Thirring precession model and rules out interpretations of continual frequency modulation.

4U 1323-62, a low mass X-ray binary with an orbital period of 2.94 hr, exhibits periodic X-ray dips, which are due to absorption by the bulge of the outer accretion disk. The purpose of this study is to search for orbital period changes using archived X-ray data over a time span of 20 years. We present our preliminary results from analyzing light curves observed by RXTE, BeppoSAX, XMM-Newton and Suzaku. We used the method proposed by Hu et al. (2008) to estimate dip center time and adopted the Observed - Calculated method to measure changes in period. We obtained an orbital period of 2.941917(36) hr and a period derivative of _Porb=Porb = (-9.9 ± 3.5) X 10-7yr-1. The F-test result shows that the quadratic ephemeris is describes the evolution of the dip phases better than the linear ephemeris at a greater than 95% confidence level. More X-ray data collected from the early 80s will be included to further rfine the orbital ephemeris.

The Palomar Transient Factory is a project making use of a Schmidt 48 inch telescope located on the Palomar Mountain, which is surveying the sky with dynamical cadences. It was deployed in 2009 and the observed sky region is over 1200 square degrees. We have studied the long-term periodic variabilities of the known galactic cataclysmic variables (CVs). More than 20 of the sources had been found to have long term periodic signals, ranging from several tens of days to several hundreds of days. Some possible scenarios are proposed to explain the results, such as a magnetic field change of the companion star, precession of the accretion disk, triple systems and superoutburst cycles. Some preliminary discussion will be presented in this article.