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研究生:蘇羿豪
研究生(外文):Yi-Hao Su
論文名稱(外文):Applications of the Hilbert-Huang Transform on Low-Frequency Quasi-periodic Oscillations in Black Hole X-ray Binaries
指導教授:周翊周翊引用關係
指導教授(外文):Yi Chou
學位類別:博士
校院名稱:國立中央大學
系所名稱:天文研究所
學門:自然科學學門
學類:天文及太空科學學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:68
中文關鍵詞:黑洞吸積時頻分析準週期振盪希爾伯特-黃轉換
外文關鍵詞:black holeaccretiontime-frequency analysisquasi-periodic oscillationHilbert-Huang transform
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低頻準週期振盪是在黑洞X光雙星中常見的非穩態天文物理現象。其振盪頻率範圍在數毫赫茲與30赫茲間,且根據其傅立葉功率密度頻譜的特性,低頻準週期振盪可細分為A、B及C三種型態。先前的時頻分析研究顯示,低頻準週期振盪是由頻率會變化且斷斷續續的訊號所構成。然而,基於傅立葉或小波分析所發展的時頻分析方法,因為其時頻解析度的限制,且因預先假設訊號符合某種波型或其頻率為常數,使得這類時頻分析方法難以解析超出其限制外的資訊,而它們的假設也可能太過嚴格以致於與低頻準週期振盪的性質不符。因此,我在本論文中將近年新發展的時頻分析方法「希爾伯特-黃轉換」(Hilbert-Huang transform, HHT),應用在低頻準週期振盪的分析上,以克服先前時頻分析方法的解析度限制。HHT能追蹤低頻準週期振盪這類非穩態訊號的相位、頻率及振幅的瞬時變化,且不預先對訊號做太嚴格的數學假設。

為了追蹤低頻準週期振盪的頻率及振幅詳細變化,我們首先將HHT應用在黑洞X光雙星XTE J1550-564中一個4赫茲的C型低頻準週期振盪。我們用HHT把X射線光變曲線拆解出一個約4赫茲的振盪項,並計算出它的瞬時頻率,發現該低頻準週期振盪是由頻率在3到5赫茲間的斷斷續續的訊號所構成。我們進一步利用HHT的信賴區間來統計該低頻準週期振盪的斷斷續續特徵,其結果顯示每次振盪維持的平均時間約為1.45秒,而回復振盪所需的平均時間為0.42秒。我們總結該低頻準週期振盪是由於頻率會變化且斷斷續續的訊號所造成,該結果能由Lense-Thirring進動模型解釋。

有了成功運用HHT的經驗,我們更進一步用它來追蹤黑洞X光雙星GX 339-4中14個B型低頻準週期振盪的X射線光譜變化。我們先利用HHT檢視這些B型低頻準週期振盪的頻率、相位和振幅等變化,發現這些低頻準週期振盪是由斷斷續續的訊號所構成(每次維持振盪的時間約為1秒)。為了追蹤光譜物理參數的變化,我們進一步分析來自不同相位的X射線光譜,其結果顯示黑洞附近產生逆康普頓散射(硬X射線)的熱冕有很明顯的準週期振盪變化,而吸積盤內緣溫度也有些微的準週期振盪。我們並提出光譜變化的可能解釋。

最後,我將我的研究工作做個總結,並且針對HHT在低頻準週期振盪的應用,提出其他可行的未來研究方向。
Low-frequency quasi-periodic oscillations (LFQPOs) with frequencies ranging from a few millihertz to 30 Hz are non-stationary astrophysical phenomena observed in most of black hole X-ray binaries (BHXBs). According to their Fourier power spectral shapes and fitting parameters, LFQPOs are further classified into A, B and C types. Previous time-frequency analysis research showed that LFQPOs are composed of frequency varying oscillations appearing occasionally. However, due to the time-frequency limitation and prior mathematical assumptions (a constant frequency or a waveform), the time-frequency analysis methods based on Fourier or wavelet transforms are difficult to resolve further information beyond the limitation and their assumptions may be too strict to be consistent with the properties of LFQPOs. Therefore, I adopted a recently developed time-frequency analysis method, the Hilbert-Huang transform (HHT), to cross the limitations for analyzing LFQPOs. HHT can instantaneously track phase, frequency, and amplitude variations of non-stationary signals such as LFQPOs, without strictly mathematical assumptions regarding the oscillatory components.

To track detailed frequency and amplitude variations of LFQPOs, we first apply HHT on a 4-Hz type-C LFQPO from the BHXB XTE J1550-564. By adaptively decomposing the ∼ 4-Hz oscillatory component from the X-ray light curve and acquiring its instantaneous frequency, the Hilbert spectrum illustrates that the LFQPO is composed of a series of intermittent oscillations appearing occasionally between 3 Hz and 5 Hz. We further characterized this intermittency by computing the confidence limits of the instantaneous amplitudes of the intermittent oscillations, and constructed both the distributions of the QPO’s high and low amplitude durations, which are the time intervals with and without significant ∼ 4-Hz oscillations, respectively. The mean high amplitude duration is 1.45 s and 90% of the oscillation segments have lifetimes below 3.1 s. The mean low amplitude duration is 0.42 s and 90% of these segments are shorter than 0.73 s. In addition, these intermittent oscillations exhibit a correlation between the oscillation’s rms amplitude and mean count rate. This correlation could be analogous to the linear rms-flux relation found in the 4-Hz LFQPO through Fourier analysis. We conclude that the LFQPO peak in the power spectrum is broadened owing to intermittent oscillations with varying frequencies, which could be explained by using the Lense-Thirring precession model.

Based on the successful application to the 4-Hz type-C LFQPO around XTE J1550-564, we further utilized HHT to track X-ray spectral modulations of 14 type-B LFQPOs in the BHXB GX 339-4. It has been shown that type-B QPO frequencies have strong correlation with the hard X-ray flux, but the detailed variations of hard X-ray spectral components during the oscillation are still not clear. To track modulations of spectral parameters, we utilized the HHT to characterize the HHT-based timing properties, extract the QPO instantaneous phases, and then construct its phase-resolved spectra. We found that these QPOs are composed of a series of intermittent oscillations with coherence times less than ∼ 1 s. Furthermore, the phase-resolved spectra illustrate significant modulations of Comptonization parameters with much smaller but also significant modulation of thermal disk component. We discussed possible interpretations of the spectral modulations.

Finally, I summarized my research works and pointed out possible future applications of the HHT on LFQPOs.
摘要ii
Abstract iii
List of figures vii
List of tables x
1 Introduction 1
1.1 Black Hole X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 X-ray Timing and Spectral Properties of Black Hole X-ray Binaries 2
1.1.2 States and Transitions in Black Hole X-ray Binaries . . . . . . . . . 5
1.2 Quasi-periodic oscillations in Black Hole X-ray Binaries . . . . . . . . . . 8
1.2.1 High-frequency Quasi-periodic Oscillations . . . . . . . . . . . . . 8
1.2.2 Low-frequency Quasi-periodic Oscillations and their subtypes . . . 9
1.2.3 Time-frequency Variations of Low-frequency Quasi-periodic Oscillations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Outline of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Hilbert-Huang Transform Analysis 13
2.1 Empirical Mode Decomposition . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Hilbert Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Scientific and Engineering Applications . . . . . . . . . . . . . . . . . . . 17
3 Intermittency of a 4-Hz Quasi-periodic Oscillation in XTE J1550-564 18
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Hilbert-Huang Transform Analysis . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Adaptive Decomposition of the X-ray Light Curve . . . . . . . . . 21
3.3.2 Instantaneous Frequency and Amplitude of the 4-Hz Oscillation . . 24
3.3.3 Confidence Limits of the Instantaneous Frequency and Amplitude . 25
3.3.4 Characterization of the Intermittent Oscillations . . . . . . . . . . . 26
3.4 Interpretation of the Intermittent Oscillations . . . . . . . . . . . . . . . . 28
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 X-ray Spectral Modulations of Type-B Quasi-periodic Oscillations in GX 339-4 31
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 QPO selection and data reduction . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Hilbert-Huang Transform Analysis . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Adaptive Decomposition of a Quasi-periodic Oscillation Light Curve 35
4.3.2 Extraction of Instantaneous Phase, Frequency and Amplitude . . . 36
4.3.3 Confidence Limits and Intermittency Characterization . . . . . . . 38
4.4 Phase-resolved Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . 41
4.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 Summary and Outlook 46
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
References 48
Appendix A Publication List 53
Appendix B Table of Acronyms 54
Appendix C HHTpywrapper and QPOpytracker 55
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