MAXI J1820 Research Articles

Crust Cooling of Soft X-Ray Transients—the Uncertainties of Shallow Heating

Crust cooling of soft X-ray transients has been observed after outbursts, but an additional shallow heating during accretion in outburst is needed to explain the quiescent light curve. However, shallow heating is significantly different between sources and even within one source between different outbursts, and the source of shallow heat is as yet unknown. Using the open source code “dStar” which solves the fully general relativistic heat diffusion equation for the crust, we investigate the effect of magnitude and depth of shallow heating on crust cooling and find that some exceptional sources (Swift J174805.3-244637, MAXI J0556-332 during outburst II and GRO J1750-27) in which shallow heating may be inactive could be explained by a deeper shallow heating mechanism. We compare our results with those from previous works and find that the shallow heating is model dependent. In addition, the effects of mass and radius of a neutron star on shallow heating are studied, and it is shown that the more compact the star, the less shallow heating will be needed to fit the crust cooling light curves.

The Donor of the Black Hole X-Ray Binary MAXI J1820+070

We estimate the parameters of the donor of the accreting black hole binary MAXI J1820+070. The measured values of the binary period, rotational and radial velocities, and constraints on the orbital inclination imply the donor is a subgiant with the mass of and the radius of . We reanalyze the previously obtained optical spectrum from the Gran Telescopio Canarias and found it yields a strict lower limit on the effective temperature of T > 4200 K. We compile optical and infrared fluxes observed during the quiescence of this system. From the minima r- and i-band fluxes found in Pan-STARSS1 Data Release 2 prediscovery imaging and for a distance of D ≈ 3 kpc, reddening of E(B – V) = 0.23, and R 2 ≈ 1.11R ⊙, we find T ≲ 4230 K, very close to the above lower limit. For a larger distance, the temperature can be higher, up to about 4500 K (corresponding to a K5 spectral type, preferred by previous studies) at D = 3.5 kpc, allowed by the Gaia parallax. We perform evolutionary calculations for the binary system and compare them to the observational constraints. Our model fitting the above temperature and radius constraints at D ≈ 3 kpc has a mass of 0.4M ⊙, T ≈ 4200 K, and solar metallicity. Two alternative models require D ≳ 3.3–3.4 kpc at 0.4M ⊙, T ≈ 4500 K and half-solar metallicity, and 0.5M ⊙, T ≈ 4300 K, and solar metallicity. These models yield mass-transfer rates of ∼10−10 M ⊙ yr−1, compatible with those based on the estimated accreted mass of ≈2 × 1025 g and the time between the 2018 discovery and the 1934 historical outburst.

Optical and X-Ray Observations of MAXI J1820+070 During the Early Outburst Phase in 2018: Zooming in the Low Frequency QPOs* *Supported by the National Natural Science Foundation of China.

We report a further investigation of the optical low frequency quasi periodic oscillations (LF QPOs) detected in the black hole transient MAXI J1820+070 in the 2018 observations with the YFOSC mounted on Lijiang 2.4 m telescope (LJT). In addition, we make use of the Insight-HXMT/HE observations to measure the properties of the quasi-simultaneous X-ray LF QPOs of MAXI J1820+070 on the same day. We compared the centroid frequency, the full width at half maximum (FWHM) and the fractional rms of the LF QPOs in both wavelength ranges. We found that the centroid frequency of the optical QPO is at a frequency of 51.58 mHz, which is consistent with that of the X-ray LF QPO detected on the same day within 1 mHz. We also found that the FWHM of the optical LF QPO is significantly smaller than that of the X-ray LF QPO, indicating that the optical QPO has a higher coherence. The quasi-simultaneous optical and the X-ray LF QPO at a centroid frequency of about 52 mHz suggests that the actual mechanisms of these LF QPOs as the Lense–Thirring precession should work in the vicinity of a radius of about 80–117 gravitational radii (R g = GM/c 2, M is the mass of the black hole) from the black hole if the QPO frequency is related to a proxy of the orbital frequency in the accretion flow as the Lense–Thirring precession model suggests. Furthermore, the apparent higher coherence of the optical QPO favors that it is a more original signal as compared with the X-ray QPO.

The evolution of the corona in MAXI J1535−571 through type-C quasi-periodic oscillations with Insight-HXMT

ABSTRACT 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. For the first time, we show 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 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. Compared 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.

The spins of the Galactic black holes in MAXI J1535–571 and 4U 1630–472 from Insight-HXMT

ABSTRACT Insight-HXMT is the first Chinese X-ray astronomical mission. With a 1–250 keV bandpass, an energy resolution of 150 eV at 6 keV, and without being subject to pile-up distortions, it is suitable to study bright X-ray sources like Galactic black holes. In this paper, we study Insight-HXMT observations of the X-ray binaries MAXI J1535–571 and 4U 1630–472 during their outbursts in 2017 and 2020, respectively. From the analysis of the reflection features, we are able to infer the black hole spin parameter in the two sources. For MAXI J1535–571, we find a spin parameter very close to 1, a* = 0.9916 ± 0.0012 (90 per cent C.L., statistical error), which is consistent with the previous NuSTAR measurement. For 4U 1630–472, we find a moderately high value of the black hole spin parameter, a* = 0.817 ± 0.014 (90 per cent C.L., statistical error), which is lower than the almost extremal value found with NuSTAR data.

Insight-HXMT, NuSTAR, and INTEGRAL Data Show Disk Truncation in the Hard State of the Black Hole X-Ray Binary MAXI J1820+070

Abstract We study X-ray and soft gamma-ray spectra from the hard state of the accreting black hole binary MAXI J1820+070. We perform an analysis of joint spectra from HXMT, NuSTAR, and INTEGRAL. We find an overall agreement between the spectra from all three satellites. Satisfactory fits to the data require substantial spectral complexity, with our models including two Comptonization regions and their associated disk reflection, a disk blackbody, and a narrow Fe Kα line. Our fits confirm the presence of the truncation of the reflecting optically thick disk at least at >10 gravitational radii. However, we find that the HXMT data alone cannot significantly constrain the disk inner radii.

Black hole spin-orbit misalignment in the x-ray binary MAXIJ1820+070.

The observational signatures of black holes in x-ray binary systems depend on their masses, spins, accretion rate, and the misalignment angle between the black hole spin and the orbital angular momentum. We present optical polarimetric observations of the black hole x-ray binary MAXIJ1820+070, from which we constrain the position angle of the binary orbital. Combining this with previous determinations of the relativistic jet orientation, which traces the black hole spin, and the inclination of the orbit, we determine a lower limit of 40° on the spin-orbit misalignment angle. The misalignment must originate from either the binary evolution or black hole formation stages. If other x-ray binaries have similarly large misalignments, these would bias measurements of black hole masses and spins from x-ray observations.

Estimating the Spin of the Black Hole Candidate MAXI J1659-152 with the X-Ray Continuum-fitting Method

Abstract As a transient X-ray binary, MAXI J1659-152 contains a black hole candidate as its compact star. MAXI J1659-152 was discovered on 2010 September 25 during its only known outburst. Previously published studies of this outburst indicate that MAXI J1659-152 may have an extreme retrograde spin, which, if confirmed, would provide an important clue as to the origin of black hole spin. In this paper, utilizing updated dynamical binary system parameters (i.e., the black hole mass, the orbital inclination, and the source distance) provided by Torres et al., we analyze 65 spectra of MAXI J1659-152 from RXTE/PCA, in order to assess the spin parameter. With a final selection of nine spectra matching our f sc ≲ 25%, soft state criteria, we apply a relativistic thin disk spectroscopic model kerrbb2 over 3.0–45.0 keV. We find that inclination angle correlates inversely with spin, and, considering the possible values for inclination angle, we constrain spin to be −1 < a * ≲ 0.44 at a 90% confidence interval via X-ray continuum fitting. We can only rule out an extreme prograde (positive) spin. We confirm that an extreme retrograde solution is possible and is not ruled out by considering accretion torques given the young age of the system.

Jet Parameters in the Black Hole X-Ray Binary MAXI J1820+070

Abstract We study the jet in the hard state of the accreting black hole (BH) binary MAXI J1820+070. From the available radio-to-optical spectral and variability data, we put strong constraints on the jet parameters. We find while it is not possible to uniquely determine the jet Lorentz factor from the spectral and variability properties alone, we can estimate the jet opening angle (≈1.°5 ± 1°), the distance at which the jet starts emitting synchrotron radiation (∼3 × 1010 cm), and the magnetic field strength there (∼104 G), with relatively low uncertainty, as they depend weakly on the bulk Lorentz factor. We find the breaks in the variability power spectra from radio to submillimeter wavelength are consistent with variability damping over the timescale equal to the travel time along the jet at any Lorentz factor. This factor can still be constrained by the electron–positron pair-production rate within the jet base, which we calculate based on the observed X-ray/soft-gamma-ray spectrum, and the jet power, required to be less than the accretion power. The minimum (∼1.5) and maximum (∼4.5) Lorentz factors correspond to the dominance of pairs and ions, and the minimum and maximum jet power, respectively. We estimate the magnetic flux threading the BH and find the jet can be powered by the Blandford–Znajek mechanism in a magnetically arrested flow accretion flow. We point out the similarity of our derived formalism to that of core shifts, observed in extragalactic radio sources.

A full spectral-timing model to map the accretion flow in black hole binaries: the low/hard state of MAXI J1820+070

ABSTRACT The nature and geometry of the accretion flow in the low/hard state of black hole binaries is currently controversial. While most properties are generally explained in the truncated disc/hot inner flow model, the detection of a broad residual around the iron line argues for strong relativistic effects from an untruncated disc. Since spectral fitting alone is somewhat degenerate, we combine it with the additional information in the fast X-ray variability and perform a full spectral-timing analysis for NICER and NuSTAR data on a bright low/hard state of MAXI J1820+070. We model the variability with propagating mass accretion rate fluctuations by combining two separate current insights: that the hot flow is spectrally inhomogeneous, and that there is a discontinuous jump in viscous time-scale between the hot flow and variable disc. Our model naturally gives the double-humped shape of the power spectra, and the increasing high-frequency variability with energy in the second hump. Including reflection and reprocessing from a disc truncated at a few tens of gravitational radii quantitatively reproduces the switch in the lag-frequency spectra, from hard lagging soft at low frequencies (propagation through the variable flow) to the soft lagging hard at the high frequencies (reverberation from the hard X-ray continuum illuminating the disc). The viscous time-scale of the hot flow is derived from the model, and we show how this can be used to observationally test ideas about the origin of the jet.

Synchronous X-ray/optical quasi-periodic oscillations from the black hole LMXB MAXI J1820+070

ABSTRACT We present high-speed optical photometry from SAAO and SALT on the black hole LMXB MAXI J1820+070 (ASSASN-18ey), some of it simultaneous with NICER, Swift, and Insight-HXMT X-ray coverage. We detect optical quasi-periodic oscillations (QPOs) that move to higher frequencies as the outburst progresses, tracking both the frequency and evolution of similar X-ray QPOs previously reported. Correlated X-ray/optical data reveal a complex pattern of lags, including an anticorrelation and a sub-second lag that evolve over the first few weeks of outburst. They also show correlated components separated by a lag equal to the QPO period roughly centered on zero lag, implying that the inter-band variability is strongly and consistently affected by these QPOs at a constant phase lag of roughly ±π. The synchronization of X-ray and optical QPOs indicates that they must be produced in regions physically very close to each other; we, thus, propose that they can be explained by a precessing jet model, based on analogies with V404 Cyg and MAXI J1348−630.

Tracking the evolution of the accretion flow in MAXI J1820+070 during its hard state with the JED-SAD model

Context. X-ray binaries in outburst typically show two canonical X-ray spectral states (i.e., hard and soft states), as well as different intermediate states, in which the physical properties of the accretion flow are known to change. However, the truncation of the optically thick disk and the geometry of the optically thin accretion flow (corona) in the hard state are still debated. Recently, the JED-SAD paradigm has been proposed for black hole X-ray binaries, aimed at addressing the topic of accretion and ejection and their interplay in these systems. According to this model, the accretion flow is composed of an outer standard Shakura-Sunyaev disk (SAD) and an inner hot jet emitting disk (JED). The JED produces both hard X-ray emission, effectively playing the role of the hot corona, and radio jets. The disruption of the JED at the transition to the soft state coincides with the quenching of the jet. Aims. In this paper we use the JED-SAD model to describe the evolution of the accretion flow in the black hole transient MAXI J1820+070 during its hard and hard-intermediate states. Unlike the previous applications of this model, the Compton reflection component has been taken into account. Methods. We use eight broadband X-ray spectra, including NuSTAR, NICER, and the Neil Gehrels Swift Observatory data, providing a total spectral coverage of 0.8–190 keV. The data were directly fitted with the JED-SAD model. We performed the procedure twice, considering two different values for the innermost stable circular orbit (ISCO): 4 RG (a* = 0.55) and 2 RG (a* = 0.95). Results. Our results suggest that the optically thick disk (the SAD) does not extend down to the ISCO in any of the considered epochs. In particular, assuming RISCO = 4 RG, as the system evolves toward the transitional hard-intermediate state, we find an inner radius within a range of ∼60 RG in the first observation down to ∼30 RG in the last one. The decrease of the inner edge of the SAD is accompanied by an increase in the mass-accretion rate. However, when we assume RISCO = 2 we find that the mass accretion rate remains constant and the evolution of the accretion flow is driven by the decrease in the sonic Mach number mS, which is unexpected. In all hard–intermediate state observations, two reflection components, characterized by different values of ionization, are required to adequately explain the data. These components likely originate from different regions of the SAD. Conclusions. The analysis performed provides a coherent physical evolution of the accretion flow in the hard and hard-intermediate states and supports a truncated disk scenario. We show that a flared outer disk could, in principle, explain the double reflection component. The odd results obtained for RISCO = 2 RG can also be considered as further evidence that MAXI J1820+070 harbors a moderately spinning black hole, as suggested in other works.

A temporal scale to track the spectral transitions in low-mass X-ray binaries

ABSTRACT The results of a temporal analysis of observations for a sample of nine low-mass X-ray binaries (LMXBs) are presented. Of these sources, five host a neutron star (NS) primary (4U1608−52, Aql X-1, 4U1705−44, GX17+2-, and Cyg X-2), and four host a black hole (BH) (GX339-4, XTE J1859+226, H1743−322, and MAXI J1659−152). The NS group includes three Atolls and two Z-type sources. We utilized archival Proportional Counter Array (PCA)/RXTE data to construct high-resolution light-curves. A wavelet transform of the light curves is deployed to extract a minimal time-scale (MTS) associated with the spectral state of the sources. The MTS, together with the fractional root-mean-square (rms) and hardness ratios, is used to construct RMS–MTS and hardness–MTS diagrams that enable a direct comparison of the evolution of spectral transitions in the target sources. Observations with high fractional rms and high hardness cluster in a broad region occupied jointly by BH and NS sources. For low fractional rms observations, the Atolls exhibit large MTS whereas Z-type sources exhibit small MTS. This new feature raises the possibility of discriminating between these two types of sources. Moreover, in the hardness–MTS plane, BH sources are the sole occupiers of the low-hardness and small-MTS domain thus potentially signalling a unique property for distinguishing BH and NS hosts in LMXBs.

Evidence for an expanding corona based on spectral-timing modelling of multiple black hole X-ray binaries

Abstract Galactic black hole X-ray binaries (BHXBs) provide excellent laboratories to study accretion, as their relatively quick evolution allows us to monitor large changes in the in-flowing and/or out-flowing material over human timescales. However, the details of how the inflow-outflow coupling evolves during a BHXB outburst remain an area of active debate. In this work we attempt to probe the physical changes underlying the system evolution, by performing a systematic analysis of the multi-wavelength data of three BHXB sources: XTE J1752-223, MAXI J1659-152, and XTE J1650-500, during hard and hard-intermediate states. Using the power spectral hue which characterises the X-ray variability properties, we identify several clusters of BHXB epochs and perform the joint multi-wavelength spectral modelling to test their commonality with a physical jet model. Under the assumption that the corona is related to the base of the jet, we find that the power spectral hue traces the variation of the coronal radius (from ∼10Rg − ∼ 40Rg) in multiple BHXBs at hard and hard-intermediate states, and that the data are consistent with moderately truncated accretion discs (<25Rg) during hard-intermediate states. We also find that all epochs of low disc reflection have high hue located near the hard-intermediate to soft-intermediate state transition, indicating that in these states the vertical extent of the corona and/or its bulk speed are increasing. Our results link the geometrical similarity in the corona among multiple BHXB sources to their timing characteristics, and probe the corona responding to the disc-jet interactions at hard and intermediate states during outbursts.

Large optical modulations during 2018 outburst of MAXI J1820 + 070 reveal evolution of warped accretion disc through X-ray state change

ABSTRACT The black hole X-ray transient MAXI J1820 + 070 (= ASSASN-18ey) discovered in 2018 March was one of the optically brightest ever seen, which has resulted in very detailed optical outburst light curves being obtained. We combine them here with X-ray and radio light curves to show the major geometric changes the source undergoes. We present a detailed temporal analysis that reveals the presence of remarkably high amplitude (>0.5 mag) modulations, which evolve from the superhump (16.87 h) period towards the presumed orbital (16.45 h) period. These modulations appear ∼87 d after the outburst began, and follow the Swift/BAT hard X-ray light curve, which peaks 4 d before the radio flare and jet ejection, when the source undergoes a rapid hard to soft state transition. The optical modulation then moves closer to the orbital period, with a light-curve peak that drifts slowly in orbital phase from ∼0.8 to ∼0.3 during the soft state. We propose that the unprecedentedly large amplitude modulation requires a warp in the disc in order to provide a large enough radiating area, and for the warp to be irradiation driven. Its sudden turn-on implies a change in the inner disc geometry that raises the hard X-ray-emitting component to a height where it can illuminate the warped outer disc regions.

A timing-based estimate of the spin of the black hole in MAXI J1820+070

ABSTRACT MAXI J1820+070 (ASSASN-18ey) is a black hole (BH) X-ray binary discovered in 2018. The brightness of the source triggered multi-wavelength campaigns of this source from different observatories. We analyse the power density spectra (PDS) obtained from NICER high cadence observations of the source in the hard state. We obtain the evolution of the characteristic frequencies by modelling the PDS. We interpret the characteristic frequencies of various PDS components (both QPOs and broad-band noise components) as variability occurring at a particular radius, and explain them in the context of the Relativistic Precession Model (RPM). We estimate the dimensionless spin of the BH at $0.799^{+0.016}_{-0.015}$ by fitting the RPM.

The inner flow geometry in MAXI J1820+070 during hard and hard-intermediate states

Context. We present a systematic X-ray spectral-timing study of the recently discovered, exceptionally bright black hole X-ray binary system MAXI J1820+070. Our analysis focuses on the first part of the 2018 outburst, covering the rise throughout the hard state, the bright hard and hard-intermediate states, and the transition to the soft-intermediate state. Aims. We address the issue of constraining the geometry of the innermost accretion flow and its evolution throughout an outburst. Methods. We employed two independent X-ray spectral-timing methods applied to archival NICER data of MAXI J1820+070. We first identified and tracked the evolution of a characteristic frequency of soft X-ray thermal reverberation lags (lags of the thermally reprocessed disc emission after the irradiation of variable hard X-ray photons). This frequency is sensitive to intrinsic changes in the relative distance between the X-ray source and the disc. Then, we studied the spectral evolution of the quasi-thermal component responsible for the observed thermal reverberation lags. We did so by analysing high-frequency covariance spectra, which single out spectral components that vary in a linearly correlated way on the shortest sampled timescales and are thus produced in the innermost regions of the accretion flow. Results. The frequency of thermal reverberation lags steadily increases throughout most of the outburst, implying that the relative distance between the X-ray source and the disc decreases as the source softens. However, near transition this evolution breaks, showing a sudden increase (decrease) in lag amplitude (frequency). On the other hand, the temperature of the quasi-thermal component in covariance spectra, due to disc irradiation and responsible for the observed soft reverberation lags, consistently increases throughout all the analysed observations. Conclusions. This study proposes an alternative interpretation to the recently proposed contracting corona scenario. Assuming a constant height for the X-ray source, the steady increase in the reverberation lag frequency and in the irradiated disc temperature in high-frequency covariance spectra can be explained in terms of a decrease in the disc inner radius as the source softens. The behaviour of thermal reverberation lags near transition might be related to the relativistic plasma ejections detected at radio wavelengths, suggesting a causal connection between the two phenomena. Throughout most of the hard and hard-intermediate state, the disc is consistent with being truncated (with an inner radius Rin ≳ 10 Rg), reaching close to the innermost stable circular orbit only near transition.

Accretion geometry of the black hole binary MAXI J1820+070 probed by frequency-resolved spectroscopy

ABSTRACT The geometry of the inner accretion flow in the hard and hard-intermediate states of X-ray binaries remains controversial. Using Neutron star Interior Composition Explorer observations of the black hole X-ray binary MAXI J1820+070 during the rising phase of its 2018 outburst, we study the evolution of the timing properties, in particular the characteristic variability frequencies of the prominent iron K α line. Using frequency-resolved spectroscopy, which is robust against uncertainties in the line profile modelling, we find that reflection occurs at large distances from the Comptonizing region in the bright hard state. During the hard-to-soft transition, the variability properties suggest that the reflector moves closer to the X-ray source. In parallel, the peak of the iron line shifts from 6.5 to ∼7 keV, becoming consistent with that expected of from a highly inclined disc extending close to the black hole. We additionally find significant changes in the dependence of the root-mean-square (rms) variability on both energy and Fourier frequency as the source softens. The evolution of the rms-energy dependence, the line profile, and the timing properties of the iron line as traced by the frequency-resolved spectroscopy all support the picture of a truncated disc/inner flow geometry.

AstroSat observation of non-resonant type-C QPOs in MAXI J1535-571

Galactic transient black hole candidate (BHC) MAXI J1535-571 was discovered on 2017 September 02 simultaneously by {\it MAXI}/GSC and {\it Swift}/BAT instruments. It has also been observed by India's first multi-wavelength astronomy-mission satellite {\it AstroSat}, during the rising phase of its 2017-18 outburst. We make both the spectral and the temporal analysis of the source during 2017 September 12-17 using data of {\it AstroSat}'s Large Area X-ray Proportional Counter (LAXPC) in the energy range of $3-40$~keV to infer the accretion flow properties of the source. Spectral analysis is done with the physical two-component advective flow (TCAF) solution-based {\it fits} file. From the nature of the variation of the TCAF model fitted physical flow parameters, we conclude and confirm that the source was in the intermediate spectral state during our analysis period. We observe sharp type-C quasi-periodic oscillations (QPOs) in the frequency range of $\sim 1.75-2.81$~Hz. For a better understanding of the nature and evolution of these type-C QPOs, a dynamic study of the power density spectra is done. We also investigate the origin of these QPOs from the shock oscillation model. We find that non-satisfaction of Rankine-Hugoniot conditions for non-dissipative shocks and not their resonance oscillations is the cause of the observed type-C QPOs.

Modelling correlated variability in accreting black holes: the effect of high density and variable ionization on reverberation lags

ABSTRACT We present a new release of the reltrans model to fit the complex cross-spectrum of accreting black holes as a function of energy. The model accounts for continuum lags and reverberation lags self-consistently in order to consider the widest possible range of X-ray variability time-scales. We introduce a more self-consistent treatment of the reverberation lags, accounting for how the time variations of the illuminating flux change the ionization level of the accretion disc. This process varies the shape of the reflection spectrum in time causing an additional source of lags besides the light crossing delay. We also consider electron densities in the accretion disc up to 1020 cm−3, which are found in most of the stellar mass black holes and in some active galactic nuclei. These high densities increase the amplitude of the reverberation lags below 1 keV since the reflection flux enhances in the same energy range. In addition, we investigate the properties of hard lags produced by variations in the power-law index of the continuum spectrum, which can be interpreted as due to roughly $3{{\ \rm per\ cent}}$ variability in the corona’s optical depth and temperature. As a test case, we simultaneously fit the lag-energy spectra in a wide range of Fourier frequency for the black hole candidate MAXI J1820+0701820 observed with NICER. The best fit shows how the reverberation lags contribute even at the longer time-scales where the hard lags are important. This proves the importance of modelling these two lags together and self-consistently in order to constrain the parameters of the system.