本篇論文是利用鹿林一米望遠鏡 (LOT) 在2008及09年期間對黑洞雙星系統Swift J1753.5-0127及A0620-00進行可見光波段的觀測，並進行光變的分析。
Swift J1753.5-0127於2005年的爆發後才被發現，至今其可見光波段的仍十分明亮。Zurita et al. (2008) 藉由其複雜的光變曲線而認為3.24小時的光變是由superhump所造成。然而，只從光變曲線做判斷不夠嚴謹，應再討論其他軌道性質如週期變化率 。A0620-00自1975年爆發後，迄今其X光波段仍處在沉靜期 (quiescent state)，但Cantrell et al. (2008) 提出在其可間光波段的顏色－星等關係圖 (color-magnitude diagram) 可能有一個約30天的週期變化，若此現象是由吸積盤的進動所造成，那麼A0620-00可能存在著superhump的現象。因此，我們藉由對Swift J1753.5-0127及A0620-00的時間分析來研究這兩個系統是否有superhump現象存在。
我們制定了一套取得光變曲線的流程，除了基本的資料校正 (data reduction)外，並探討傳統標準星校正法在數學邏輯上的問題，重新設計出合理的擬合過程。並將此概念融入較差測光 (differential photometry) 中，以減少大氣質量及消光效應對後續時間分析的影響。
在對每天光變曲線進行趨勢移除 (trend removal) 後，利用Lomb-Scargle (LS) peirodogram與Phase dispersion minimization (PDM)方法計算出光變最有可能的訊號。接著使用Period04對光變曲線進行正弦函數的擬合，得到光變模型。再對其殘餘量 (資料點扣除模型) 進行LS periodogram與PDM的分析，檢查是否有其他的週期訊號存在。解析出所有的訊號後，Swift J1753.5 -0127並沒有發現任何與3.24小時相近的週期；而A0620-00也呈現單純的橢圓光變，沒有其他週期訊號存在。將三個波段所求出的週期做加權平均後得到Swift J1753.5 -0127的平均週期為3.2442 ±0.0002小時，與Zurita et al. (2008) 所提出R波段的結果3.2454±0.0080小時一致；A0620-00的平均週期為7.75229 ±0.00004小時，亦與McClintock & Remillard (1986) 提出的7.75234 ±0.00010小時一致。
從窗函數的分析中，我們發現Swift J1753.5-0127殘餘量的週期訊號可能皆為3.24小時的頻率與窗函數耦合的而成的結果。另外我們使用O-C方法試圖找出 ，而過大的觀測空窗期使得分析結果的可信度並不高，因此在我們的研究中仍無法決定出3.24小時究竟是superhump或是軌道週期。A0620-00其30天的週期也並不是由superhump現象所造成，而是可能來自於其他未知的原因。

In this thesis, I report the observations and analysis results for black hole binaries Swift J1753.5-0127 and A0620-00 for their timing properties with Lulin One-meter Telescope (LOT) during 2008 and 09.
Swift J175.5-0127 was first observed after its 2005 outburst, and its optical band remains bright to date. Zurita et al. (2008) claimed that the 3.24 hrs modulation is the superhump period from its complex modulation profile. However, it is not conscientious enough to determine only by the modulation profile except other properties, i.e. period change . A0620-00 stayed in X-ray quiescent state after its 1975 outburst, but Cantrell et al. (2008) proposed a 30-days period is shown in the color-magnitude diagram. If this is caused by the disk precession, the superhump phenomenon may exist in this system. Therefore, we analyzed the variations of Swift J1753.5-0127 and A0620-00 to verify if these two systems exist superhump phenomena.
We set up a procedure to get the light curves, including the fundamental data reduction and reexamining the problem for the traditional standard star calibration, and reconstructing a reasonable fitting process. We also applied this concept into the differential photometry to minimize the effect of airmass and extinction as we do timing analysis.
After removing the daily trend, we performed Lomb-Scargle (LS) Periodogram and Phase Disperiosn Minimization (PDM) to calculate the most probable periods of modulation. Then we used Period04 to do multi-sinusoidal fitting and derive the model of modulation. After removing the ~3.2 hrs modulation, no clear side-band was found in the spectra of Swift J1753.5-0127’s residual light curves. A0620-00 showed pure ellipsoidal modulation, and no other significant signal was detected after removing its orbital variation. The best period of Swift J1753.5-0127 evaluated from this method is 3.2440 ±0.0002 hrs, consistent with the one proposed by Zurita et al. (2008) (3.2454±0.0080 hrs). The same analysis technique was applied for A0620-00 and yielded a period of 7.75229±0.00004 hrs, also consistent with the orbital period proposed by McClintock & Remillard (1986) ( 7.75234±0.00010 hrs).
From the analysis of window function, we found the residual signals of Swift J1753.5 -0127 may be the coupling of 3.24 hrs period and window function. We attempted to evaluate the period derivative from O-C method. But the large observation gaps also made the O-C results not significant. Therefore, we still cannot determine the 3.24 hrs period is the orbital period or the superhump one. The 30-day period of A0620-00 is unlikely caused by superhump phenomenon, but from other unknown origins.

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