LMC X-4 為一高質量 X 光食雙星，由中子星與大質量的早型星所組成，從作為伴星的早型>星供給物質，落到中子星周圍被吸積而產生 X 光輻射。雙星的軌道週期為 1.4 天，以及 13.5 秒的脈衝週期，並且有著因進動中的吸積盤而週期地遮掩的 30.5 天的超軌道週期。
我們使用 HEASARC 資料庫上的開放資料，分析 RXTE 1996-1999 年與 XMM-Newton 2003 年 對 LMC X-4 進行觀測的數據，先以軌道都卜勒效應分析的結果作為基礎，再經由相位分析>來得出各年觀測的最佳中子星自轉與軌道參數，之後利用 O-C 方法對過去文獻中與我們所>得的 $T_{\pi/2}$ 來測得 LMC X-4 的軌道週期變化率 $\dot{P}_{orb}/P_{orb} = (-9.13\pm0.68) \times 10^{-7} \, {yr}^{-1}$ ，並制定其星曆表；同時也收集過去測得的中子 星自轉頻率值，分別對中子星頻率歷經減速、加速與再減速等時期測量自轉頻率變化率： $\dot{\nu}_{spin} = (-2.87\pm0.20) \times 10^{13} \, Hz \cdot s^{-1}$ 、 $\dot{\nu}_{spin} = (6.90\pm0.83) \times 10^{13} \, Hz \cdot s^{-1}$ \& $\dot{\nu}_{spin} = (-5.37\pm0.16) \times 10^{13} \, Hz \cdot s^{-1}$ 。考量在 LMC X-4 上由潮汐>交互作用與恆星風所致的質量流失機制來探討理論上的軌道週期變化率大小，我們得到由恆 星風所致的質量流失機制不足以描述我們所測得的軌道週期變化率，最後以 \citet{2000ApJ...541..194L} 在過去所提出的潮汐交互作用做為主要的解釋成因。 ;LMC X-4 is a high-mass eclipsing X-ray binary consisting of an early type star and a neutron star as an accretor. The orbital period of the binary is 1.4 days. The pulsation period of neutron star is 13.5 $s$. It also has a superorbital modulation of period of 30.5 days caused by the precession of accretion disk periodically obscuring the X-ray emissions from the neutron star.
To study orbital and spin parameter evolutions of LMC X-4, we analyzed archival data collected by Proportional Counter Array on broad Rossi X-ray Timing Explorer in 1996-1999 and XMM-Newton/pn camera in 2003. All archival data were downloaded from the wed site of High Energy Astrophysics Science Archive Reserch Center. Using the orbital Doppler shift of the pulsation, we derived the preliminary orbital and spin parameters. More precision parameters were further refined by pulse arrival time delay technique. Combined with the historical reported values, we adopted O-C method to trace the evolution of $T_{\pi/2}$ and obtained an the orbital period derivative of $\dot{P}_{orb}/P_{orb}=(-9.13\pm0.68)\times10^{-7}$ $yr^{-1}$, and updated the orbital quadratic ephemeris of LMC X-4. We also examined the all reported spin frequencies of LMC X-4 and found that the neutron star experienced spin-down, and up and down epochs with spin frequency derivatives of $(-2.87\pm0.20)\times10^{13}$ $Hz \cdot s^{-1}$, $(6.90\pm0.83)\times10^{13}$ $Hz \cdot s^{-1}$, $(-5.37\pm0.16)\times10^{13}$ $Hz \cdot s^{-1}$ since 1988. About orbital period derivative of LMC X-4, we consider mechanisms of the tidal interaction and the mass-loss causing by stellar wind of companion star. We found that the contribution of mass-loss mechanism is insufficient to account for the measured orbital period derivative. Therefore, the remained mechanism of tidal interaction proposed by \citet{2000ApJ...541..194L} is still considered as the majority mechanism to explain the large orbital period derivative of LMC X-4.
