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Low mass X-ray binaries (LMXBs) show strong variability over a broad range oftime scales. The analysis of this variability, in particular of thequasi-periodic oscillations (QPO), is key to understanding the properties ofthe innermost regions of the accretion flow in these systems. We present atime-dependent Comptonisation model that fits the energy-dependentrms-amplitude and phase-lag spectra of low-frequency QPOs in black-hole (BH)LMXBs. We model the accretion disc as a multi-temperature blackbody sourceemitting soft photons which are then Compton up-scattered in a sphericalcorona, including feedback of Comptonised photons that return to the disc. Wecompare our results with those obtained with a model in which the seed-photonssource is a spherical blackbody: at low energies the time-averaged, rms andphase-lag spectra are smoother for the disk-blackbody than for a blackbody,while at high energies both models give similar spectra. In general, we findthat the rms increases with energy, the slope of the phase-lag spectrum dependsstrongly on the feedback, while the minimum-lag energy is correlated with thedisc temperature. We fit the model to a 4.45-Hz type-B QPO in the BH LMXB MAXIJ1438-630 and find statistically-better fits and more compatible parameterswith the steady-state spectrum than those obtained with a blackbodyseed-photons source. Furthermore, we successfully apply the model to the type-CQPO in the BH LMXB GRS 1915+105, and thus conclude that thisvariable-Comptonisation model reproduces the rms and phase-lags of both type Band C low-frequency QPOs in BH LMXBs.

vKompth: A variable Comptonisation model for low-frequency quasi-periodic oscillations in black-hole X-ray binaries