4U 1820-30是位於球狀星團NGC 6624中心附近的低質量X光雙星系統，由一顆中子星與一顆白矮星所組成，具有目前已知低質量X光雙星最短的685秒軌道週期。Rappaport et al. (1987)根據理論計算得出4U 1820-30的軌道週期變化率應為正值，但相關的觀測結果卻顯示軌道週期變化率為負值，此理論值與觀測值不符合的現象可能由球狀星團中的重力加速度引起。本論文目標為探討4U 1820-30之軌道週期演化。我們使用2017至2022年NICER的觀測數據，以Peuten et al. (2014)提出的線性星曆表(linear ephemeris)做疊合得到疊合光變曲線(folded light curve)，並以一階諧波擬合求得波峰對應之軌道相位值，結合1976至2011年過往之研究結果，得出時間跨度(time span)長達46.3年的軌道相位演化曲線，利用二階多項式擬合軌道相位演化曲線得出觀測到的軌道週期$P=685.011968\pm0.000021 s$及軌道週期變化率$\dot{P}/P=(-5.206\pm0.134)\times10^{-8} yr^{-1}$。而在三階多項式擬合中，在$|\ddot{P}|<5.48\times10^{-22} ss^{-2}$的2σ上限內並未明顯檢測到二階軌道週期變化率。我們進一步討論了可能的系統內在軌道週期變化率，由於其中存在太多不確定性，我們認為觀測到的軌道週期變化率不適合用於推斷NGC 6624中4U 1820-30的重力加速度。此外，我們在NICER收集到的X光光變曲線中還檢測到了$691.6\pm0.7 s$週期的光變(periodic modulation)，與Wang & Chakrabarty (2010)利用哈伯太空望遠鏡在遠紫外線波段中發現的superhump週期一致，我們認為此週期光變很可能是由於低質量X光雙星系統的$0.8\pm0.1$天吸積盤進動週期所引起。;4U 1820-30, a low mass X-ray binary (LMXB), located near the center of the globular cluster NGC 6624, consists of a neutron star and a white dwarf. It has the shortest orbital period of 685s in all of the known LMXBs. For its orbital period derivative, the theoretical value evaluated by Rappaport et al. (1987) should be positive, but the observational results showed that it is negative. This discrepancy is possible due to the gravitational acceleration in the globular cluster. The motivation of this thesis is to investigate the orbital period evolution and superhump modulation of 4U 1820-30. We used light curves collected by NICER from 2017 to 2022. The orbital modulation profiles were obtained by folding the light curves with the linear ephemeris proposed by Peuten et al. (2014) and the maximum of the profiles, evaluated by fitting a single sinusoidal function, were selected as the fiducial point of the orbital phases. Combined with previous results from 1976 to 2011, we obtained the orbital phase evolution with a time span of 46.3 years. Using a quadratic function to fit the orbital phase evolution, we obtained the observed orbital period of $P=685.011968\pm0.000021 s$ and the orbital period derivative of $\dot{P}/P=(-5.206\pm0.134)\times10^{-8} yr^{-1}$. From the fitting of a cubic function, we found there is no second order orbital period derivative is significantly detected with 2σ upper limit of $|\ddot{P}|<5.48\times10^{-22} ss^{-2}$. We further discuss the possible intrinsic orbital derivative and argue that the observed orbital period derivative is improper to infer the gravitational acceleration of 4U 1820-30 in NGC 6624 because there are too much uncertainty in it. Furthermore in the X-ray light curve collected by NICER, we detected a periodic modulation with a period of $691.6\pm0.7 s$, which is consistent with the superhump period discovered by Wang & Chakrabarty (2010) using the Hubble Space Telescope in the far-ultraviolet band. We believe that such periodic modulation is likely caused by a period of $0.8\pm0.1$ day the precession of accretion disk.
