Applications of the Hilbert-Huang Transform on Millihertz Quasi-periodic Oscillations in 4U1636-53

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謝弘恩(Hung-En Hsieh) 查詢紙本館藏

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天文研究所

論文名稱

(Applications of the Hilbert-Huang Transform on Millihertz Quasi-periodic Oscillations in 4U1636-53)

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摘要(中)

在某一些低質量X光雙星中，發現有約100 秒時間尺度的準週期震盪現象，稱之為毫赫茲準週期震盪（millisecond Hertz quasi-periodic oscillation, mHz QPO）。這些頻率約8 mHz QPO出現在以中子星為主星的X光雙星中於第一型X射線爆發前幾數千秒。這個現象目前認為是由中子星表面特定區域（熱點）內熱核反應微小變化導致熱輻射發生震盪所致。但先前的研究顯示二個非常不同的結論，一個研究結果支持理論預測展現出溫度的變化而熱輻射面積不變，而另一個研究結果卻顯示面積的變化而溫度不變。目前主要造成這種差異的原因尚不清楚。在前人的研究中曾試圖利用相位解析光譜探討造成mHz QPO的特性。然而，傳統的分析方法在定義QPO準確的瞬時相位時有所限制。利用近年來新發展的希爾伯特-黃轉換，我們能定出瞬間頻率與相位，可以克服傳統定義瞬時相位不夠精準的問題。因此，由希爾伯特-黃轉換定義出的精準相位有利於研究造成mHz QPO的成因。
此研究中，我利用希爾伯特-黃轉換針對XMM-Newton觀測X射線雙星4U 1636-53中的mHz QPO進行分析。希爾伯特-黃轉換是個強大的工具，使我能夠得到具有非平穩定週期性的mHz QPO的瞬時頻率、震幅以及相位。由定義準確的相位可以展現在4U 1636-53中mHz QPO的精準震盪曲線 (oscillation profile)。除此之外，還可構建了完整週期的相位解析光譜。分析後發現了與前人的研究不同的結果，在四筆觀測到mHz QPO的資料中，有三筆資料顯示熱點的面積在變化，但溫度幾乎不變，另一筆資料卻是溫度在做準週期震盪，而熱點面積不變。雖然對於造成此差異的原因目前尚不清楚，但後者之高能波段的顏色(hard color)與其他三筆明顯不同，因此差異是或許與當時之光譜狀態有關。
最後,我將我的研究工作做個總結,並且針對 HHT 在mHz QPO的應用, 提出其他可行的未來研究方向。

摘要(英)

Millihertz quasi-periodic oscillation (mHz QPO), a kind of QPO with a time scale of 100 seconds was observed in some of low mass X-ray binaries with neutron stars as accretors. The ~8 mHz QPO can be detected about several thousand seconds right before a type-I X-ray burst. This QPO was interpreted as oscillation of thermal emission due to marginally stable nuclear burning on the neutron star surface. However, the previous studies show two distinct results. Strohmayer et al. (2018) found that the temperature variation with the constant area in the mHz QPO of GS 1826-238, whereas Stiele et al. (2016) detected the area variation with the constant temperature in mHz QPO of 4U 1636-53. Which factor is the main reason for flux variation of mHz QPOs was controversial. In their study, phase-resolved spectra are a useful method to investigate the natural of mHz QPOs. However, traditional analysis methods have their limitations to determine the phase precisely for the QPOs. Recently, a method called Hilbert-Huang transform (HHT) was developed. This method can evaluate the instantaneous phase as a function of time precisely. HHT can overcome the limitations from the traditional analysis methods which contains ambiguity in evaluating the oscillation phase. Therefore, precise phases constructed by HHT benefit investigation for the reason of mHz oscillation.
In this research, I adopted the HHT to analyze the mHz QPOs in 4U 1636-53 by using the data collected by XMM-Newton. The HHT is a powerful tool that enables me to obtain the mHz QPOs’ instantaneous frequency, amplitude, and phase. With well-defined phases, the oscillation profile of the ∼8 mHz QPO for 4U 1636-53 can be precisely revealed even if the oscillation is nonstationary. In addition, phase-resolved spectra for the complete cycle can be constructed. From the correlation between spectral parameters and fluxes, I found that the oscillation is mainly attributed to variations in the area emitting blackbody radiation in three out of four observations with mHz QPO detections, whereas the other one shows a concurrent variation of temperature and flux with a constant emitting area. Although the cause of the difference is not clear, it might be related to the spectral state of the source that can be observed from a hard color difference in the color-color diagram.
Finally, I summarized my research works and pointed out possible future applications of the HHT on mHz QPOs.

關鍵字(中)

★ X射線雙星
★ X射線爆發
★ 吸積
★ 中子星

關鍵字(英)

★ X-ray binary stars
★ X-ray bursts
★ Accretion
★ Neutron stars

論文目次

摘要 ii
Abstract iii
List of figures vi
List of tables viii
1 Introduction 1
1.1 X-ray Binary ................................. 1
1.2 Millihertz Quasi-periodic Oscillations ....................3
1.2.1 X-ray Burst.............................. 3
1.2.2 Millihertz Quasi-periodic Oscillations . . . . . . . . . . . . . . . . 8
1.3 Outline of this Thesis............................. 12
2 Time-Frequency Analysis Method 13
2.1 Lomb-Scargle periodogram.......................... 13
2.1.1 Dynamic Power Spectrum ...................... 14
2.2 Hilbert-Huang Transform........................... 15
2.2.1 Empirical Mode Decomposition................... 16
2.2.2 Hilbert Spectral Analysis....................... 18
2.2.3 Scientific and Engineering Applications . . . . . . . . . . . . . . . 19
3 Phase-Resolved Spectra Analysis Method 20
3.1 Oscillation Profile............................... 20
3.2 Phase-Resolved Spectra............................ 22
4 Millihertz Quasi-periodic Oscillations in 4U 1636-53 28
4.1 Introduction.................................. 28
4.2 Observation.................................. 30
4.3 Data Analysis and Results .......................... 31
4.3.1 Hilbert-Huang Transform ...................... 31
4.3.2 Oscillation profile and Phase-Resolved Spectra . . . . . . . . . . . 32
4.4 Discussion................................... 36
5 Summary and Outlook 42
5.1 Summary ................................... 42
5.2 Outlook.................................... 42
References 44
Appendix A Publication List 49

參考文獻

Altamirano, D., van der Klis, M., Wijnands, R., and Cumming, A. (2008). Millihertz Oscil- lation Frequency Drift Predicts the Occurrence of Type I X-Ray Bursts. ApJ, 673(1):L35.
Arnaud, K. A. (1996). XSPEC: The First Ten Years. In Jacoby, G. H. and Barnes, J., editors, Astronomical Data Analysis Software and Systems V, volume 101 of Astronomical Society of the Pacific Conference Series, page 17.
Bedrosian, E. (1963). A product theorem for Hilbert transforms. Proceedings of the IEEE, 51:868–869.
Bildsten, L. (1998). Thermonuclear Burning on Rapidly Accreting Neutron Stars. In Buc- cheri, R., van Paradijs, J., and Alpar, A., editors, The Many Faces of Neutron Stars., vol- ume 515 of NATO Advanced Study Institute (ASI) Series C, page 419.
Chakrabarty, D., Morgan, E. H., Muno, M. P., Galloway, D. K., Wijnands, R., van der Klis, M., and Markwardt, C. B. (2003). Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars. Nature, 424(6944):42–44.
Chou, Y., Hsieh, H.-E., Hu, C.-P., Yang, T.-C., and Su, Y.-H. (2016). Orbital and Spin Parameter Variations of Partial Eclipsing Low Mass X-Ray Binary X 1822-371. ApJ, 831(1):29.
Clarkson, W. I., Charles, P. A., Coe, M. J., and Laycock, S. (2003). Long-term properties of accretion discs in X-ray binaries - II. Stability of radiation-driven warping. MNRAS, 343(4):1213–1223.
Cooper, R. L. and Narayan, R. (2007). The Latitude of Type I X-Ray Burst Ignition on Rapidly Rotating Neutron Stars. ApJ, 657(1):L29–L32.
Fujimoto, M. Y., Hanawa, T., and Miyaji, S. (1981). Shell flashes on accreting neutron stars and X-ray bursts. ApJ, 247:267–278.
Galloway, D. K. and Keek, L. (2021). Thermonuclear X-ray Bursts. Astrophysics and Space Science Library, 461:209–262.
Galloway, D. K., Psaltis, D., Chakrabarty, D., and Muno, M. P. (2003). Eddington-limited X-Ray Bursts as Distance Indicators. I. Systematic Trends and Spherical Symmetry in Bursts from 4U 1728-34. ApJ, 590(2):999–1007.
Galloway, D. K., Psaltis, D., Muno, M. P., and Chakrabarty, D. (2006). Eddington-limited X-Ray Bursts as Distance Indicators. II. Possible Compositional Effects in Bursts from 4U 1636-536. ApJ, 639(2):1033–1038.
Gao, P. X. (2016). Long-term Trend of Sunspot Numbers. ApJ, 830(2):140.
Grindlay, J., Gursky, H., Schnopper, H., Parsignault, D. R., Heise, J., Brinkman, A. C., and Schrijver, J. (1976). Discovery of intense X-ray bursts from the globular cluster NGC 6624. ApJ, 205:L127–L130.
Heger, A., Cumming, A., and Woosley, S. E. (2007). Millihertz Quasi-periodic Oscillations from Marginally Stable Nuclear Burning on an Accreting Neutron Star. ApJ, 665(2):1311– 1320.
Hiemstra, B., Méndez, M., Done, C., Díaz Trigo, M., Altamirano, D., and Casella, P. (2011). A strong and broad Fe line in the XMM-Newton spectrum of the new X-ray transient and black hole candidate XTE J1652-453. MNRAS, 411(1):137–150.
Hsieh, H.-E. and Chou, Y. (2020). Phase-resolved Analyses of Millihertz Quasi-periodic Oscillations in 4U 1636-53 using the Hilbert-Huang Transform. ApJ, 900(2):116.
Hu, C.-P., Chou, Y., Yang, T.-C., and Su, Y.-H. (2014). Tracking the Evolution of Quasi-periodic Oscillation in RE J1034+396 Using the Hilbert-Huang Transform. ApJ, 788(1):31.
Huang, N., Wu, Z., Long, S., Arnold, K., Chen, X., and Blank, K. (2009). On instantaneous frequency. Advances in Adaptive Data Analysis, 1:177–229.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London Series A, 454(1971):903–998.
Huang, N. E. and Wu, Z. (2008). A review on Hilbert-Huang transform: Method and its applications to geophysical studies. Reviews of Geophysics, 46:RG2006.
Keek, L., Cyburt, R. H., and Heger, A. (2014). Reaction Rate and Composition Dependence of the Stability of Thermonuclear Burning on Accreting Neutron Stars. ApJ, 787(2):101.
Keek, L., Langer, N., and in’t Zand, J. J. M. (2009). The effect of rotation on the stability of nuclear burning in accreting neutron stars. A&A, 502(3):871–881.
Kolotkov, D. Y., Smirnova, V. V., Strekalova, P. V., Riehokainen, A., and Nakariakov, V. M. (2017). Long-period quasi-periodic oscillations of a small-scale magnetic structure on the Sun. A&A, 598:L2.
Kunwar, A., Jha, R., Whelan, M., and Janoyan, K. (2013). Damage detection in an exper- imental bridge model using hilbert–huang transform of transient vibrations. Structural Control and Health Monitoring, 20(1):1–15.
Lewin, W. H. G., Doty, J., Clark, G. W., Rappaport, S. A., Bradt, H. V. D., Doxsey, R., Hearn, D. R., Hoffman, J. A., Jernigan, J. G., Li, F. K., Mayer, W., McClintock, J., Primini, F., and Richardson, J. (1976). The discovery of rapidly repetitive X-ray bursts from a new source in Scorpius. ApJ, 207:L95–L99.
Linares, M., Altamirano, D., Chakrabarty, D., Cumming, A., and Keek, L. (2012). Millihertz Quasi-periodic Oscillations and Thermonuclear Bursts from Terzan 5: A Showcase of Burning Regimes. ApJ, 748(2):82.
Lomb, N. R. (1976). Least-Squares Frequency Analysis of Unequally Spaced Data. Ap&SS, 39(2):447–462.
Lyu, M., Méndez, M., and Altamirano, D. (2014). Discovery of a correlation between the frequency of the mHz quasi-periodic oscillations and the neutron-star temperature in the low-mass X-ray binary 4U 1636-53. MNRAS, 445(4):3659–3668.
Lyu, M., Méndez, M., Altamirano, D., and Zhang, G. (2016). Millihertz quasi-periodic oscillations in 4U 1636-53 associated with bursts with positive convexity only. MNRAS, 463(3):2358–2362.
Lyu, M., Méndez, M., Zhang, G., and Keek, L. (2015). Spectral and timing analysis of the mHz QPOs in the neutron-star low-mass X-ray binary 4U 1636-53. MNRAS, 454(1):541– 549.
Makishima, K., Maejima, Y., Mitsuda, K., Bradt, H. V., Remillard, R. A., Tuohy, I. R., Hoshi, R., and Nakagawa, M. (1986). Simultaneous X-Ray and Optical Observations of GX 339-4 in an X-Ray High State. ApJ, 308:635.
Maurer, I. and Watts, A. L. (2008). Ignition latitude and the shape of Type I X-ray bursts. MNRAS, 383(1):387–398.
Mitsuda, K., Inoue, H., Koyama, K., Makishima, K., Matsuoka, M., Ogawara, Y., Shibazaki, N., Suzuki, K., Tanaka, Y., and Hirano, T. (1984). Energy spectra of low-mass binary X- ray sources observed from Tenma. PASJ, 36:741–759.
Nakano, H., Narikawa, T., Oohara, K.-i., Sakai, K., Shinkai, H.-a., Takahashi, H., Tanaka, T., Uchikata, N., Yamamoto, S., and Yamamoto, T. S. (2019). Comparison of vari- ous methods to extract ringdown frequency from gravitational wave data. Phys. Rev. D, 99(12):124032.
Nath, N. R., Strohmayer, T. E., and Swank, J. H. (2002). Bounds on Compactness for Low- Mass X-Ray Binary Neutron Stars from X-Ray Burst Oscillations. ApJ, 564(1):353–360.
Orlandini, M., Doroshenko, V., Zampieri, L., Bozzo, E., Baykal, A., Blay, P., Chernyakova, M., Corbet, R., D’Aì, A., Enoto, T., Ferrigno, C., Finger, M., Klochkov, D., Kreykenbohm, I., Inam, S. C., Jenke, P., Leyder, J. C., Masetti, N., Manousakis, A., Mihara, T., Paul, B., Postnov, K., Reig, P., Romano, P., Santangelo, A., Shakura, N., Staubert, R., Torrejón, J. M., Walter, R., Wilms, J., and Wilson-Hodge, C. (2015). Probing stellar winds and ac- cretion physics in high-mass X-ray binaries and ultra-luminous X-ray sources with LOFT. arXiv e-prints, page arXiv:1501.02777.
Paczynski, B. (1983). A one-zone model for shell flashes on accreting compact stars. ApJ, 264:282–295.
Pan, H.-J., Chen, M.-T., Kong, D., Lin, X., Wong, K.-T., Tsai, H.-L., Liu, S., Shi, X., and Yokoyama, Y. (2020). Surface Ocean Hydrographic Changes in the Western Pacific Marginal Seas since the Early Holocene. Frontiers in Earth Science, 8:200.
Patruno, A. (2012). Evidence of Fast Magnetic Field Evolution in an Accreting Millisecond Pulsar. ApJ, 753(1):L12.
Pigorini, A., Casali, A., Casarotto, S., Ferrarelli, F., Baselli, G., Mariotti, M., Massimini, M., and Rosanova, M. (2011). Time–frequency spectral analysis of TMS-evoked EEG oscillations by means of Hilbert–Huang transform. Journal of Neuroscience Methods, 198:236–245.
Press, W. H. and Rybicki, G. B. (1989). Fast Algorithm for Spectral Analysis of Unevenly Sampled Data. ApJ, 338:277.
Revnivtsev, M., Churazov, E., Gilfanov, M., and Sunyaev, R. (2001). New class of low frequency QPOs: Signature of nuclear burning or accretion disk instabilities? A&A, 372:138–144.
Sanna, A., Hiemstra, B., Méndez, M., Altamirano, D., Belloni, T., and Linares, M. (2013). Broad iron line in the fast spinning neutron-star system 4U 1636-53. MNRAS, 432(2):1144–1161.
Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. ApJ, 263:835–853.
Schatz, H., Bildsten, L., Cumming, A., and Wiescher, M. (1999). The Rapid Proton Process Ashes from Stable Nuclear Burning on an Accreting Neutron Star. ApJ, 524(2):1014– 1029.
Stiele, H., Yu, W., and Kong, A. K. H. (2016). Millihertz Quasi-periodic Oscillations in 4U 1636-536: Putting Possible Constraints on the Neutron Star Size. ApJ, 831(1):34.
Strohmayer, T. E. and Altamirano, D. (2012). Marginally Stable Nuclear Burning. In Ameri- can Astronomical Society Meeting Abstracts #219, volume 219 of American Astronomical Society Meeting Abstracts, page 249.03.
Strohmayer, T. E., Gendreau, K. C., Altamirano, D., Arzoumanian, Z., Bult, P. M., Chakrabarty, D., Chenevez, J., Guillot, S., Guver, T., Homan, J., Jaisawal, G. K., Keek, L., Mahmoodifar, S., Miller, J. M., and Ozel, F. (2018). NICER Discovers mHz Oscillations in the “Clocked” Burster GS 1826-238. ApJ, 865(1):63.
Strohmayer, T. E., Zhang, W., Swank, J. H., Smale, A., Titarchuk, L., Day, C., and Lee, U. (1996). Millisecond X-Ray Variability from an Accreting Neutron Star System. ApJ, 469:L9.
Su, S. Y., Tsai, L. C., Liu, C. H., Nayak, C., Caton, R., and Groves, K. (2019). Ionospheric Es layer scintillation characteristics studied with Hilbert-Huang transform. Advances in Space Research, 64(10):2137–2144.
Su, Y.-H., Chou, Y., Hu, C.-P., and Yang, T.-C. (2015). Characterizing Intermittency of 4- Hz Quasi-periodic Oscillation in XTE J1550-564 Using Hilbert-Huang Transform. ApJ, 815(1):74.
Sztajno, M., van Paradijs, J., Lewin, W. H. G., Trumper, J., Stollman, G., Pietsch, W., and van der Klis, M. (1985). Unusual X-ray burst profiles from 4U/MXB 1636-53. ApJ, 299:487–495.
Tse, K., Galloway, D. K., Chou, Y., Heger, A., and Hsieh, H.-E. (2021). Detection of milli- hertz quasi-periodic oscillations in the X-Ray binary 1RXS J180408.9-342058. MNRAS, 500(1):34–39.
Ulmer, M. P., Lewin, W. H. G., Hoffman, J. A., Doty, J., and Marshall, H. (1977). Some further information on the rapid burster MXB 1730-335. ApJ, 214:L11–L15.
van der Klis, M. (2006). Rapid X-ray Variability, pages 39–112.
Verner, D. A., Ferland, G. J., Korista, K. T., and Yakovlev, D. G. (1996). Atomic Data for Astrophysics. II. New Analytic FITS for Photoionization Cross Sections of Atoms and Ions. ApJ, 465:487.
Wang, Y.-H., Yeh, C.-H., Young, H.-W. V., Hu, K., and Lo, M.-T. (2014). On the computa- tional complexity of the empirical mode decomposition algorithm. Physica A Statistical Mechanics and its Applications, 400:159–167.
Wilms, J., Allen, A., and McCray, R. (2000). On the Absorption of X-Rays in the Interstellar Medium. ApJ, 542(2):914–924.
Wolszczak, P., Łygas, K., and Litak, G. (2018). Dynamics identification of a piezoelectric vibrational energy harvester by image analysis with a high speed camera. Mechanical Systems and Signal Processing, 107:43–52.
Woosley, S. E. and Taam, R. E. (1976). ?-ray bursts from thermonuclear explosions on neutron stars. Nature, 263(5573):101–103.
Yeh, J.-R., Shieh, J.-S., and Huang, N. (2010). Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method. Advances in Adaptive Data Analysis, 2:135–156.
Yu, W. and van der Klis, M. (2002). Kilohertz Quasi-periodic Oscillation Frequency Anticorrelated with Millihertz Quasi-periodic Oscillation Flux in 4U 1608-52. ApJ, 567(1):L67–L70.
Zdziarski, A. A., Johnson, W. N., and Magdziarz, P. (1996). Broad-band ?-ray and X-ray spectra of NGC 4151 and their implications for physical processes and geometry. MNRAS, 283(1):193–206.
Zechmeister, M. and Kürster, M. (2009). The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms. A&A, 496(2):577– 584.
Życki, P. T., Done, C., and Smith, D. A. (1999). The 1989 May outburst of the soft X-ray transient GS 2023+338 (V404 Cyg). MNRAS, 309(3):561–575.

指導教授

周翊(Yi Chou)

審核日期

2021-10-26

推文