Timing Analysis of Black Hole X-Ray Binaries with Insight-HXMT

The Hard X-ray Modulation Telescope (HXMT), China’s first X-ray astronomy satellite, has significantly contributed to the study of fast variability in black hole X-ray binaries through its broad energy coverage (1–250 keV), high timing resolution, and sensitivity to hard X-rays. This review presents a comprehensive overview of timing analysis techniques applied to black hole X-ray binaries using Insight-HXMT data. We introduce the application and comparative strengths of several time-frequency analysis methods, including traditional Fourier analysis, wavelet transform, bicoherence analysis, and Hilbert-Huang transform. These methods offer complementary insights into the non-stationary and nonlinear variability patterns observed in black hole X-ray binaries, particularly during spectral state transitions and quasi-periodic oscillations. We discuss how each technique has been employed in recent Insight-HXMT studies to characterize timing features such as low-frequency QPOs, phase lags, and power spectrum evolution across different energy bands. Moreover, we present novel phenomena revealed by Insight-HXMT observations, including the detection of high-energy QPOs, spectral parameter modulation with QPO phase, and a new classification scheme for QPO types. The integration of multiple analysis methods enables a more nuanced understanding of the accretion dynamics and the geometry of the inner accretion flow, shedding light on fundamental physical processes in relativistic environments.