|Abstract: ||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。|
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.