Low mass X-ray binaries (LMXBs) show strong variability over a broad range of time scales. The analysis of this variability, in particular of the quasi-periodic oscillations (QPO), is key to understanding the properties of the innermost regions of the accretion flow in these systems. We present a time-dependent Comptonisation model that fits the energy-dependent rms-amplitude and phase-lag spectra of low-frequency QPOs in black hole (BH) LMXBs. We model the accretion disc as a multi-temperature blackbody source emitting soft photons which are then Compton up-scattered in a spherical corona, including feedback of Comptonised photons that return to the disc. We compare our results with those obtained with a model in which the seed-photons source is a spherical blackbody: at low energies the time-averaged, rms and phase-lag spectra are smoother for the disk-blackbody than for a blackbody, while at high energies both models give similar spectra. In general, we find that the rms increases with energy, the slope of the phase-lag spectrum depends strongly on the feedback, while the minimum-lag energy is correlated with the disc temperature. We fit the model to a 4.45-Hz type-B QPO in the BH LMXB MAXI J1438–630 and find statistically-better fits and more compatible parameters with the steady-state spectrum than those obtained with a blackbody seed-photons source. Furthermore, we successfully apply the model to the type-C QPO in the BH LMXB GRS 1915+105, and thus conclude that this variable-Comptonisation model reproduces the rms and phase-lags of both type B and C low-frequency QPOs in BH LMXBs.

Type-C quasi-periodic oscillations (QPOs) in black hole X-ray transients can appear when the source is in the low-hard and hard-intermediate states. The spectral-timing evolution of the type-C QPO in MAXI J1535−571 has been recently studied with Insight-HXMT. Here we fit simultaneously the time-averaged energy spectrum, using a relativistic reflection model, and the fractional rms and phase-lag spectra of the type-C QPOs, using a recently developed time-dependent Comptonization model when the source was in the intermediate state. We show, for the first time, that the time-dependent Comptonization model can successfully explain the X-ray data up to 100 keV. We find that in the hard-intermediate state the frequency of the type-C QPO decreases from 2.6 Hz to 2.1 Hz, then increases to 3.3 Hz, and finally increases to ∼ 9 Hz. Simultaneously with this, the evolution of corona size and the feedback fraction (the fraction of photons up-scattered in the corona that return to the disc) indicates the change of the morphology of the corona. Comparing with contemporaneous radio observations, this evolution suggests a possible connection between the corona and the jet when the system is in the hard-intermediate state and about to transit into the soft-intermediate state.

MAXI J1535−571 is a black-hole X-ray binary that in 2017 exhibited a very bright outburst which reached a peak flux of up to 5 Crab in the 2–20 keV band. Given the high flux, several X-ray space observatories obtained unprecedented high signal-to-noise data of key parts of the outburst. In our previous paper we studied the corona of MAXI J1535−571 in the hard-intermediate state (HIMS) with Insight-HXMT. In this paper we focus on the study of the corona in the soft-intermediate state (SIMS) through the spectral-timing analysis of 26 NICER detections of the type-B quasi-periodic oscillations (QPOs). From simultaneous fits of the energy, rms and lag spectra of these QPOs with our time-dependent Comptonization model, we find that in the SIMS the corona size is ∼ 6500 km and vertically extended. We detect a narrow iron line in the energy spectra, which we interpret to be due to the illumination of the outer part of the accretion disk by this large corona. We follow the evolution of the corona and the radio jet during the HIMS-SIMS transition, and find that the jet flux peaks after the time when the corona extends to its maximum vertical size. The jet flux starts to decay after the corona contracts vertically towards the black hole. This behavior points to a connection between the X-ray corona and the radio jet similar to that seen in other sources.

We present a detailed spectral and temporal analysis of the black-hole candidate MAXI J1535−571 using NICER observations in September and October 2017. We focus specifically on observations in the hard-intermediate state when the source shows type-C quasi-periodic oscillations (QPOs). We fitted the time-averaged spectrum of the source and the rms and phase-lag spectra of the QPO with a one-component time-dependent Comptonization model. We found that the corona contracts from ∼104 to ∼3 × 103 km as the QPO frequency increases from ∼1.8 Hz to ∼9.0 Hz. The fits suggest that the system would consists of two coronas, a small one that dominates the time-averaged spectrum and a larger one, possibly the jet, that dominates the rms and lag spectra of the QPO. We found a significant break in the relation of the spectral parameters of the source and the properties of the QPO, including its lag spectra, with QPO frequency. The change in the relations happens when the QPO frequency crosses a critical frequency νc ≈ 3.0 Hz. Interestingly, the QPO reaches this critical frequency simultaneously as the radio emission from the jet in this source is quenched.