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。

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.

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