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.

ABSTRACT
1. INTRODUCTION
2. OBSERVATIONS
3. RESULTS
    3.1. The Lomb-Scargle Periodograms
    3.2. The Long-Term Evolution of the Superorbital Modulation
    3.3. The Orbital Parameters
4. SUMMARY & FUTURE WORK
REFERENCES

• Chin-Ping Hu(Graduate Institute of Astronomy, National Central University)
• Ching-Ping Lin(Graduate Institute of Astronomy, National Central University)
• Yi Chou(Graduate Institute of Astronomy, National Central University)
• Ting-Chang Yang(Graduate Institute of Astronomy, National Central University)
• Yi-Hao Su(Graduate Institute of Astronomy, National Central University)
• Hung-En Hsieh(Graduate Institute of Astronomy, National Central University)
• Po-Sheng Chuang(Graduate Institute of Astronomy, National Central University)
• Nai-Hui Liao(Graduate Institute of Astronomy, National Central University)