臺灣博碩士論文加值系統

時頻分析技術的進展使天文學家們得以處理天文中非穩定機制所發出的非穩態訊號。本論文將「希爾伯．黃變換」(Hilbert-Huang transform, HHT) 這套近年發展的時頻分析方法，應用於天文中兩個非穩態現象的分析，分別是大質量X光雙星系統SMC X-1的超軌道運動，以及窄線西佛星系的活躍星系核 RE J1034+396 的準週期震盪 (QPO)。
大質量X光雙星系統 SMC X-1 擁有超軌道運動的現象，其週期於40天至60天之間變化。由Rossi X-ray Timing Explorer (RXTE) 上的 All-Sky Monitor 收集到的光變曲線，經過HHT分析所得到的希爾伯頻譜，我們可以在時間和頻率方面獲得非常詳盡的資訊。在 RXTE 的觀測中，SMC X-1 的超軌道運動週期大部份集中在50至65天，但在 MJD 50,800 和 MJD 54,000 時卻變為大約40天。利用HHT定義的瞬時相位，可以得到最佳的超軌道波型。由疊合光變曲線可得知它擁有一個不對稱的波型，其中在歷時約0.3週期的低強度時期，是幾乎沒有X射線輻射的。此外，在這個目標上，我們發現它的超軌道週期與振幅有著正相關性，這與另一個X光雙星系統Her X-1一致。
由於HHT可以得到完整定義的超軌道相位，因此我們可以針對軌道光變和光譜，進行超軌道的分相分析。由光譜分析所得的參數中，我們發現鐵線的等效寬度與電漿的光學深度之間有著極為複雜的關係。在X射線強度大於35 mCrab 時，兩者之間並沒有明顯的相關性，但在亮度小於20 mCrab 時卻有很強的正相關。這個發現指出了鐵線的輻射在不同的超軌道相位中是由不同的輻射機制所主導。另外，我們在高強度相位和低強度相位間的轉換相位中，找到類似Her X-1的掩食前光陷現象，座落於軌道相位0.6 – 0.85的位置。這個發現代表了在吸積流和吸積盤的交互作用區，有著一個隆起的結構。這個結構在特定的軌道相位會吸收部份由緻密天體所發射出來的X射線而造成光陷的現象。該光陷的寬度與超軌道週期中的X射線強度有著負相關，這也能用傾斜的吸積盤解釋。
有了分析X光雙星系統資料的經驗，我們更進一步地將HHT應用至一個活躍星系核 RE J1034+396的資料。該筆資料是由XMM-Newton於2007年所觀測。RE J1034+396是個I型窄線西佛星系，也是第一個被發現擁有QPO現象的活躍星系核。經驗模態分解可視為一個很好的帶通濾波器，將高頻訊號過濾之後的光變曲線可用於O-C分析以及相關性分析。由希爾伯頻譜以及O-C分析的結果可看出，在這段觀測中，QPO可以分成三個週期性明顯不同的演化階段。除了週期之外，這三個階段的QPO週期與X射線強度的關係也不同。利用吸積盤震動模型，週期以及相關性的改變可能是由於吸積盤震動模式的改變所造成的。最後，我們無法找到高能X射線和低能X射線間有相位延遲的現象，這點在分相光譜分析中也得到一致的結論。
最後，我將這些工作做個簡單的總結並指出未來HHT在其他的天文時間序列中的應用方向，以及討論二維經驗模態分解應用於天文影像中形態分析的可能性。

The development of time-frequency analysis techniques made astronomers successfully deal with non-stationary time series that originated from unstable physical mechanisms. I applied a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), on two examples of non-stationary astrophysical phenomena: the superorbital modulation in a high-mass X-ray binary SMC X-1 and the quasi-periodic oscillation (QPO) of a narrow-line Seyfert 1 active galactic nucleus (AGN) RE J1034+396.

The high-mass X-ray binary SMC X-1 exhibits a superorbital modulation with a dramatically varying period ranging between ~40 days and ~60 days. A Hilbert spectrum that shows more detailed information in both the time and frequency domains was obtained using the light curve collected by the All-Sky Monitor onboard the Rossi X-ray Timing Explorer (RXTE). The RXTE observations show that the superorbital modulation period was mostly between ~50 days and ~65 days, whereas it changed to ~40 days around MJD 50,800 and MJD 54,000. Based on the instantaneous phase defined by the HHT, a superorbital profile, from which an asymmetric feature and a low state with barely any X-ray emissions (lasting for ~0.3 cycles) were observed. A positive correlation between the mean period and the amplitude of the superorbital modulation, which is similair to that in Her X-1, was also discovered. With the superorbital phase defined by the HHT, a phase-resolved analysis of both the spectra and the orbital profiles was processed. From all the spectral parameters, I noticed that the relation between the equivalent width of iron line and the plasma optical depth is not monotonic. There is no significant correlation for fluxes higher than ~35 mCrab but clear positive correlation when the intensity is lower than ~20 mCrab. This indicates that the iron line production is dominated by different regions of this binary system in different superorbital phases. Furthermore, a dip feature, similar to the pre-eclipse dip in Her X-1, lying at orbital phase ~0.6-0.85, was discovered during the superorbital transition state. This indicates that the accretion disk has a bulge that absorbs considerable X-ray emission in the stream-disk interaction region. The dip width is anti-correlated with the flux, and this relation can be interpreted by the precessing tilted accretion disk scenario.

With the successful experience of dealing with the superorbital modulation of an X-ray binary system, we further applied the HHT to analyze the QPO of RE J1034+396 using the data collected by XMM-Newton in 2007. RE J1034+396, a narrow-line Seyfert 1 galaxy, is the first example of AGNs that exhibited a nearly coherent QPO. The ensemble empirical mode decomposition (EEMD) provides bandpass-filtered data that can be used in the O - C and correlation analysis. From the Hilbert spectrum and the O - C analysis, I suggested that it is better to divide the evolution of the QPO in this observation into three epochs according to their different periodicities. Besides the periodicities, the correlations between the QPO periods and corresponding mean count rates are also different in these three epochs. The change in periodicity and the relationships could be interpreted by the change in oscillation mode based on the assumption of diskoseismology model. Finally, we found no significant phase lags between the soft and hard X-ray bands, which is also confirmed in the QPO phase-resolved spectral analysis.

Finally, I presented a brief summary and pointed out possible future applications of the HHT on other astronomical time series, as well as the possible application of two-dimensional EEMD on morphological analysis.

Abstract ii
List of Figures vii
List of Tables ix
1 Introduction 1
1.1 Compact Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 X-ray Binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Stationary Periodicities in X-ray Binaries . . . . . . . . . . . . . . . . . . . 5
1.3.1 Orbital Period { Eclipse and Dip . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Spin Period { Pulsar and Burst QPO . . . . . . . . . . . . . . . . . 7
1.4 Non-stationary Variability in X-ray Binaries . . . . . . . . . . . . . . . . . . 9
1.4.1 Quasi-Periodic Oscillation . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Superorbital Modulation . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Active Galactic Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.1 Unication Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5.2 Radio-Quiet AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5.3 Radio-Loud AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 Variability of AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6.1 QPO in AGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.7 Outline of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Time-Frequency Analysis Method 20
2.1 Lomb-Scargle Periodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 Dynamic Power Spectrum . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Hilbert-Huang Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Empirical Mode Decomposition . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Ensemble EMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Applying on Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 Pure Sinusoidal Function . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Sinusoidal Function with Increasing Frequency . . . . . . . . . . . . 30
2.3.3 Sinusoidal Function with Frequency and Amplitude Modulation . . . 30
2.3.4 Sinusoidal Function with Frequency Modulation and Noise . . . . . 33
3 Superorbital Modulation of SMC X-1 38
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Observation and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 RXTE ASM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 EEMD decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 Hilbert Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.2 Superorbital Modulation Prole . . . . . . . . . . . . . . . . . . . . . 46
3.3.3 Correlation between Period and Amplitude . . . . . . . . . . . . . . 49
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4 Superorbital Phase Resolved Analysis of SMC X-1 52
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Observation and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 RXTE PCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.2 RXTE ASM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 High and Low State X-ray Spectra . . . . . . . . . . . . . . . . . . . 55
4.3.2 Superorbital Phase-Resolved Variation in Spectral Parameters . . . 57
4.3.3 Superorbital Phase-Resolved Variation in Orbital Prole . . . . . . . 61
4.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 The QPO of RE J1034+396 67
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Time-Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3.1 HHT Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3.2 O { C Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.3 Phase Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3.4 Correlation between QPO Period and Flux . . . . . . . . . . . . . . 79
5.4 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.1 Fits to High- and Low-Intensity Phases . . . . . . . . . . . . . . . . 81
5.4.2 Phase-Resolved Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.1 The Spotted Disk Model . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.2 Diskoseismology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.5.3 Oscillation of Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 Summary and Outlook 90
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
A On the Complex Variability of the Superorbital Modulation Period of
LMC X-4 102
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.2 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.3.1 The Lomb-Scargle Periodograms . . . . . . . . . . . . . . . . . . . . 103
A.3.2 The Evolution of the Superorbital Modulation . . . . . . . . . . . . 104
A.4 Summary and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
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