Recovery of High-energy Low-frequency Quasiperiodic Oscillations from Black Hole X-Ray Binary MAXI J1535-571 with a Hilbert-Huang Transform Method

We propose a method based on the Hilbert-Huang transform (HHT) to recover the high-energy waveform of low-frequency quasiperiodic oscillations (QPOs). Based on the method, we successfully obtain the modulation of the phase-folded light curve above 170 keV using the QPO phase reconstructed at lower energies in MAXI J1535-571 with Insight-HXMT observations. A comprehensive simulation study is conducted to demonstrate that such modulation indeed originates from the QPO. Thus, the highest energies turn out to significantly exceed the upper limit of similar to 100 keV for QPOs reported previously using the Fourier method, marking the first opportunity to study QPO properties above 100 keV in this source. Detailed analyses of these high-energy QPO profiles reveal different QPO properties between the 30-100 and 100-200 keV energy ranges: the phase lag remains relatively stable, and the amplitude slightly increases below similar to 100 keV, whereas above this threshold, soft phase lags and a decrease in amplitude are observed. Given the reports of a hard-tail detection in broad spectroscopy, we propose that the newly discovered QPO properties above 100 keV are dominated by the hard-tail component, possibly stemming from a relativistic jet. Our findings also indicate a strong correlation between the QPOs originating from the jet and corona, supporting the scenario of jet-corona coupling precession. We emphasize that our proposed HHT-based method can serve as an efficient manner in expanding the high-energy band for studying QPOs, thereby enhancing our understanding of their origin.