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In X-ray observations of hard state black hole X-ray binaries (BHXRBs), rapid variations in accretion disc and coronal power-law emission are correlated and show Fourier-frequency-dependent time lags. On short (⁠|$\sim$| 0.1 s) time-scales, these lags are thought to be due to reverberation and therefore may depend strongly on the geometry of the corona. Low-frequency quasi-periodic oscillations (QPOs) are variations in X-ray flux that have been suggested to arise because of geometric changes in the corona, possibly due to general relativistic Lense–Thirring precession. Therefore, one might expect the short-term time lags to vary on the QPO time-scale. We performed novel spectral-timing analyses on Neutron Star Interior Composition ExploreR observations of the BHXRB MAXI J1820+070 during the hard state of its outburst in 2018 to investigate how the short-term time lags between a disc-dominated and a coronal power-law-dominated energy band vary on different time-scales. Our method can distinguish between variability due to the QPO and broad-band noise, and we find a linear correlation between the power-law flux and lag amplitude that is strongest at the QPO frequency. We also introduce a new method to resolve the QPO signal and determine the QPO phase dependence of the flux and lag variations, finding that both are very similar. Our results are consistent with a geometric origin of QPOs, but also provide evidence for a dynamic corona with a geometry varying in a similar way over a broad range of time-scales, not just the QPO time-scale. [ABSTRACT FROM AUTHOR]

We present a model-independent analysis of the short-time-scale energy dependence of lowfrequency quasi-periodic oscillations (QPOs) in the X-ray flux of GRS 1915+105. The QPO frequency in this source has previously been observed to depend on photon energy, with the frequency increasing with energy for observations with a high (≳2 Hz) QPO frequency, and decreasing with energy for observations with a low (≲2 Hz) QPO frequency. As this observed energy dependence is currently unexplained, we investigate if it is intrinsic to the QPO mechanism by tracking phase lags on (sub)second time-scales. We find that the phase lag between two broad energy bands systematically increases for 5-10 QPO cycles, after which the QPO becomes decoherent, the phase lag resets and the pattern repeats. This shows that the band with the higher QPO frequency is running away from the other band on short time-scales, providing strong evidence that the energy dependence of the QPO frequency is intrinsic. We also find that the faster the QPO decoheres, the faster the phase lag increases, suggesting that the intrinsic frequency difference contributes to the decoherence of the QPO.We interpret our results within a simple geometric QPO model, where different radii in the inner accretion flow experience Lense-Thirring precession at different frequencies, causing the decoherence of the oscillation. By varying the spectral shape of the inner accretion flow as a function of radius, we are able to qualitatively explain the energy-dependent behaviour of both QPO frequency and phase lag. [ABSTRACT FROM AUTHOR]