type-C Quasi-periodic Oscillations Research Articles

Timing and spectral analysis of the black hole X-ray binary MAXI J1803–298 with Insight-HXMT data

Abstract We present a comprehensive analysis of the 2021 outburst of MAXI J1803–298 utilizing observations of the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) spanning from the low hard state to the high soft state. Within the Insight-HXMT dataset, compared to the previous work, we identify a more prolonged presence of type-C quasi-periodic oscillations (QPOs) with centroid frequencies ranging from ∼0.16 to 6.3 Hz, which present correlations with the hardness ratio and the photon index of the Comptonized component. For QPO frequencies less than ∼2 Hz, the QPO phase lags are hard (photons of 10–19 keV arrive later than those of 1–4 keV), while at higher frequencies, lags transition to soft lags after reaching ∼4 Hz. Furthermore, the spectra in all Insight-HXMT observations consist of a multi-color blackbody component and a Comptonized component, as commonly observed in classical black-hole X-ray binaries. We analyze state transitions and the evolution of accretion geometry in this work. The fitted inner disk radius increases abnormally during the low hard state, hypothesized to result from the corona condensing onto the inner disk. Additionally, two significant drops in flux are observed during the soft intermediate state, maybe implying changes in the corona/jet and the disk, respectively.

The bicoherence study of quasi-periodic oscillations in MAXI J1535−571

ABSTRACT Bicoherence is a way to measure the phase coupling of triplets of Fourier frequencies. We use this method to analyse quasi-periodic oscillations (QPOs) in the black hole X-ray binary MAXI J1535−571 during its 2017 September–October outburst. The bicoherence provides an interesting new diagnostic to uncover QPO behaviour and the relationships between QPO harmonics and broad-band noise. The bicoherence pattern of type-C QPOs starts as a ‘web’ pattern and changes to a ‘hypotenuse’ pattern after the presence of type-B QPOs, indicating that MAXI J1535−571 is a low-inclination source. The intensity of bicoherence also exhibits variations across different energy bands. We try to explain the bicoherence results in the scenario of a dual-corona geometry.

Different behaviors of wavelet results for type-B and type-C QPOs of MAXI J1535-571 based on NICER data

Wavelet analysis, in addition to power density spectra, is another method to study the quasi-periodic signals in the light curves, but has been rarely used in black hole X-ray transients. We performed wavelet analysis of X-ray timing features and quasi-periodic oscillations (QPOs) based on NICER observations of the black hole candidate MAXI J1535-571 in this paper. Separating the light curves by the confidence level of wavelet results, we find significant differences exist in the PDS, hardness ratio and mean count between light curve segments above and below the confidence level. The S-factor, which is defined as the ratio of the effective oscillation time and the total time, demonstrates distinct values between type-C and type-B QPOs. Based on our results, the S-factor for type-B QPO is very close or equal to 0, no matter the confidence level is set as 95% or 68%, while the S-factor of type-C QPO is significantly higher, especially in the 68% confidence level case. We discuss the implications of the wavelet results on resolving type-B and type-C QPOs in black hole X-ray binaries.

Truncated, tilted discs as a possible source of Quasi-Periodic Oscillations

ABSTRACT Many accreting black holes and neutron stars exhibit rapid variability in their X-ray light curves, termed quasi-periodic oscillations (QPOs). The most commonly observed type is the low-frequency (≲10 Hz), type-C QPO, while only a handful of sources exhibit high-frequency QPOs (≳60 Hz). The leading model for the type-C QPO is Lense-Thirring precession of a hot, geometrically thick accretion flow that is misaligned with the black hole’s spin axis. However, existing versions of this model have not taken into account the effects of a surrounding, geometrically thin disc on the precessing, inner, geometrically thick flow. In Bollimpalli et. al 2023, using a set of GRMHD simulations of tilted, truncated accretion discs, we confirmed that the outer thin disc slows down the precession rate of the precessing torus, which has direct observational implications for type-C QPOs. In this paper, we provide a detailed analysis of those simulations and compare them with an aligned truncated disc simulation. We find that the misalignment of the disc excites additional variability in the inner hot flow, which is absent in the comparable aligned-disc simulations. This suggests that the misalignment may be a crucial requirement for producing QPOs. We attribute this variability to global vertical oscillations of the inner torus at epicyclic frequencies corresponding to the transition radius. This explanation is consistent with current observations of higher frequency QPOs in black hole X-ray binary systems.

Accretion Flow Properties of EXO 1846-031 during Its Multi-peaked Outburst after Long Quiescence

We study the recent outburst of the black hole candidate EXO 1846-031, which went into an outburst in 2019 after almost 34 yr in quiescence. We use archival data from the Swift/XRT, MAXI/GSC, NICER/XTI, and NuSTAR/FPM satellites/instruments to study the evolution of the spectral and temporal properties of the source during the outburst. The low-energy (2–10 keV) X-ray flux of the outburst shows multiple peaks, making it a multipeak outburst. Evolving type-C quasi-periodic oscillations are observed in the NICER data in the hard, hard-intermediate, and soft-intermediate states. We use the physical two-component advective flow (TCAF) model to analyze the combined spectra of multiple satellite instruments. According to the TCAF model, the accreting matter is divided into Keplerian and sub-Keplerian parts, and the variation in the observed spectra in different spectral states arises out of the variable contributions of these two types of accreting matter in the total accretion rate. Studying the evolution of the accretion rates and other properties of the accretion flow obtained from the spectral analysis, we show that the multiple peaks in the outburst flux arise out of the variable supply of accreting matter from the pile-up radius. We determine the probable mass of the black hole to be from the spectral analysis with the TCAF model. We also estimate the viscous timescale of the source in this outburst to be ∼8 days from the peak difference of the Keplerian and sub-Keplerian mass-accretion rates.

Unveiling hidden variability components in accreting X-ray binaries using both the Fourier power and cross-spectra

ABSTRACT We present a novel method for measuring the lags of (weak) variability components in neutron-star and black-hole low-mass X-ray binaries (LMXBs). For this we assume that the power and cross-spectra of these sources consists of a number of components that are coherent in different energy bands, but are incoherent with one another. The technique is based on fitting simultaneously the power spectrum (PS) and the Real and Imaginary parts of the cross-spectrum (CS) with a combination of Lorentzian functions. We show that, because the PS of LMXBs is insensitive to signals with a large Imaginary part and a small Real part in the CS, this approach allows us to uncover new variability components that are only detected in the CS. We also demonstrate that, contrary to earlier claims, the frequency of the type-C quasi-periodic oscillation (QPO) in the black-hole binary GRS 1915+105 does not depend on energy. Rather, the apparent energy dependence of the QPO frequency can be explained by the presence of a separate QPO component with a slightly higher frequency than that of the QPO, whose rms amplitude increases faster with energy than the rms amplitude of the QPO. From all the above we conclude that, as in the case of the PS, the CS of black-hole and neutron-star binaries can be fitted by a combination of Lorentzian components. Our findings provide evidence that the frequency-dependent part of the transfer function of these systems can be described by a combination of responses, each of them acting over relatively well-defined time-scales. This conclusion challenges models that assume that the main contribution to the lags comes from a global, broadband, transfer function of the accreting system.

A systematic study of the high-frequency bump in the black-hole low-mass X-ray binary GX 339 − 4

ABSTRACT The high-frequency bump, characterized by a frequency exceeding ∼30 Hz, represents a seldom-explored time-variability feature in the power density spectrum (PDS) of black-hole X-ray binaries. In the 2002, 2004, 2007, and 2010 outbursts of GX 339 − 4, the bump has been occasionally observed in conjunction with type-C quasi-periodic oscillations (QPOs). We systematically study the properties of the bump during these four outbursts observed by Rossi X-ray Timing Explorer (RXTE) in the 2–60 keV bands and detect the bump in 39 observations. While the frequencies of the type-C QPOs are in the range of ∼0.1–9 Hz, the root-mean-square (rms) amplitude of the bump shows an evolution in the hardness ratio versus the type-C QPO frequency plot. By comparing the rms amplitude of the bump with the corona temperature and simultaneous radio jet flux of the source, as previously studied in GRS 1915 + 105, we establish that in the hard state of GX 339 − 4, the bump is always strong, with the measurements of the rms amplitude in the range of 4–10 per cent. At the same time, the corona temperature is high and the radio flux is low. These findings indicate that, using the bump as a proxy, the majority of the accretion energy is directed towards the hot corona rather than being channeled into the radio jet. We discuss this phenomenon in terms of an inefficient energy transfer mechanism between the corona and jet in GX 339 − 4.

Investigating the energy-dependent temporal nature of black hole binary system H 1743-322

ABSTRACT Black hole X-ray binaries routinely exhibit quasi-periodic oscillations (QPOs) in their power density spectrum. Studies of QPOs have demonstrated immense ability to understand these dynamical systems although their unambiguous origin still remains a challenge. We investigate the energy-dependent properties of the Type-C QPOs detected for H 1743-322 as observed with AstroSat in its two X-ray outbursts of 2016 and 2017. The combined broad-band LAXPC and SXT spectrum is well modelled with a soft thermal and a hard Comptonization component. The QPO exhibits soft/negative lags i.e. variation in soft-band lags the variation in hard band, although the upper harmonic shows opposite behaviour i.e. hard/positive lags. Here, we model energy-dependent properties (fractional root mean square and time-lag variation with energy) of the QPO and its upper harmonic individually with a general scheme that fits these properties by utilizing the spectral information and consequently allows to identify the radiative component responsible for producing the variability. Considering the truncated disc picture of accretion flow, a simple model with variation in inner disc temperature, heating rate, and fractional scattering with time delays is able to describe the fractional rms and time-lag spectra. In this work, we show that this technique can successfully describe the energy-dependent features and identify the spectral parameters generating the variability.

A variable corona during the transition from type-C to type-B quasi-periodic oscillations in the black hole X-ray binary MAXI J1820+070

ABSTRACT We analyse a Neutron Star Interior Composition Explorer observation of the black hole X-ray binary MAXI J1820+070 during a transition from type-C to type-B quasi-periodic oscillations (QPOs). We find that below ∼2 keV, for the type-B QPOs the rms amplitude is lower and the magnitude of the phase lags is larger than for the type-C QPOs. Above that energy, the rms and phase-lag spectra of the type-B and type-C QPOs are consistent with being the same. We perform a joint fit of the time-averaged spectra of the source, and the rms and phase-lag spectra of the QPOs with the time-dependent Comptonization model vkompth to study the geometry of the corona during the transition. We find that the data can be well fitted with a model consisting of a small and a large corona that are physically connected. The sizes of the small and large coronae increase gradually during the type-C QPO phase whereas they decrease abruptly at the transition to type-B QPO. At the same time, the inner radius of the disc moves inward at the QPO transition. Combined with simultaneous radio observations showing that discrete jet ejections happen around the time of the QPO transition, we propose that a corona that expands horizontally during the type-C QPO phase, from ∼104 km ($\sim 800\, R_{\rm g}$) to 105 km ($\sim 8000\, R_{\rm g}$) overlying the accretion disc, transforms into a vertical jet-like corona extending over ∼104 km ($\sim 800\, R_{\rm g}$) during the type-B QPO phase.

The X-ray corona in the black hole binary GRO J1655−40 from the properties of non-harmonically related quasi-periodic oscillations

ABSTRACT The study of quasi-periodic oscillations (QPOs) plays a vital role in understanding the nature and geometry of the Comptonizing medium around black hole X-ray binaries. The spectral-state dependence of various types of QPOs (namely A, B, and C) suggests that they could have different origins. The simultaneous presence of different types of QPOs would therefore imply the simultaneous occurrence of different mechanisms. In this work, we study the radiative properties of two non-harmonically related QPOs in the black hole binary GRO J1655−40 detected at the peak of the ultraluminous state during the 2005 outburst of the source. The two QPOs have been previously identified as types B and C, respectively. We jointly fit the phase-lag and rms spectra of the QPOs and the time-averaged spectrum of the source with the time-dependent Comptonization model vkompth to infer the geometry of the media producing the QPOs. The time-averaged spectrum required a hot disc of 2.3 keV and a steep power law with index 2.7, revealing that the source was in an ultraluminous state. The corona that drives the variability of the type-B QPO is smaller in size and has a lower feedback fraction than the one that drives the variability of the type-C QPO. This suggests the simultaneous presence of a horizontally extended corona covering the accretion disc and a vertically elongated jet-like corona that are responsible for the type-C and B QPOs, respectively.

A Spectral-timing Study of the Inner Flow Geometry in MAXI J1535-571 with Insight-HXMT and NICER

We have performed a spectral-timing analysis of the black hole X-ray binary MAXI J1535-571 during its 2017 outburst, with the aim of exploring the evolution of the inner accretion flow geometry. X-ray reverberation lags are observed in the hard-intermediate state (HIMS) and soft-intermediate state of the outburst. During the HIMS, the characteristic frequency of the reverberation lags ν 0 (the frequency at which the soft lag turns to zero in lag–frequency spectra) increases when the spectrum softens. This reflects a reduction of the spatial distance between the corona and accretion disk, when assuming the measured time lags are associated with the light travel time. We also find a strong correlation between ν 0 and the type-C quasi-periodic oscillation (QPO) centroid frequency ν QPO, which can be well explained by the Lense–Thirring precession model under a truncated disk geometry. Despite the degeneracy in the spectral modeling, our results suggest that the accretion disk is largely truncated in the low hard state, and moves inward as the spectrum softens. Combine the spectral modeling results with the ν 0 – ν QPO evolution, we are inclined to believe that this source probably has a truncated disk geometry in the hard state.

Testing the dynamic origin of Quasi-periodic Oscillations in MAXI J1535−571 and H 1743−322

ABSTRACT We investigate spectro-temporal properties for two black hole X-ray binary sources, MAXI J1535−571 and H 1743−322, during their hard and hard-intermediate states. For MAXI J1535−571, we analyse swift/XRT, NuSTAR, and nicer observations, specifically focusing on the occurrence of type-C Quasi-periodic Oscillations (QPOs). Regarding H 1743−322, we analyse multi-epoch observations of nicer and AstroSat, identifying a type-C QPO with centroid frequency ranging from 0.1–0.6 Hz. In both sources, we fit the spectra with a relativistic truncated disc and a power-law component. In MAXI J1535−571, we also observe an additional relativistically smeared iron-line. Through temporal and spectral analysis, we estimate the QPO centroid frequency and spectral parameters, such as the accretion rate and inner disc radii. We test the origin of type-C QPOs as relativistic precession frequency, and dynamic frequency (i.e. the inverse of the sound crossing time $\frac{r}{c_\mathrm{ s}(r)}$). The dependence of QPO frequency on both the accretion rate and inner disc radii favours the QPO origin as dynamic frequency. We discuss the implications of these results.

The luminous, hard state can’t be MAD

ABSTRACT We present a straightforward argument for why the luminous, hard state of black hole X-ray binaries (BHXRBs) cannot always be associated with a magnetically arrested accretion disc (MAD). It relies on three core premises: (1) that the type-C quasi-periodic oscillation (QPO) is best explained by Lense–Thirring (LT) precession of a tilted, inner, hot flow; (2) that observed optical and infrared (IR) QPOs with the same or lower frequency as the type-C QPO suggest the jet, too, must precess in these systems; and (3) that numerical simulations of MADs show that their strong magnetic fields promote alignment of the disc with the black hole and, thereby, suppress LT precession. If all three premises hold true, then, at least whenever the optical and IR QPOs are observed alongside the type-C QPO, these systems cannot be in the MAD state. Extending the argument further, if the type-C QPO is always associated with LT precession, then it would rule out MADs anytime this timing feature is seen, which covers nearly all BHXRBs when they are in the luminous, hard and hard-intermediate states.

Timing analysis of the new black hole candidate MAXI J1803−298 with Insight–HXMT and NICER

ABSTRACT We present the timing analysis results of MAXI J1803−298, a black hole candidate, during its 2021 outburst using data obtained from the Insight–Hard X-ray Modulation Telescope (Insight–HXMT) and the Neutron star Interior Composition Explorer (NICER). Our analysis reveals that the source undergoes a state transition from the low hard state to the hard intermediate state, followed by the soft intermediate state, ultimately reaching the high soft state. We searched for the quasi-periodic oscillations (QPOs) and studied the characteristics of the outburst. At the beginning of the outburst, the source was in the hard state, many type-C QPOs were seen in the Insight–HXMT data, and the frequency of these QPOs increased from ∼0.16 to 2.6 Hz. Our analysis of the rms–frequency relationship of the type-C QPOs indicates a turning point in the frequency. We also analysed the phase lag versus frequency and energy relationship and deduced that the source likely has a high inclination angle, consistent with previous research. The observed rms and phase-lag features in type-C QPOs could be explained by the Lense–Thirring precession model, although alternatives would be still viable. The lag spectrum of type-B QPOs exhibits a U-shaped pattern similar to that of many other sources, and the type-B QPOs’ rms increases as the energy increases. This phenomenon can be explained by the dual-corona model.

A journey from the hard to the soft state: How do QPOs evolve in the 2021 outburst of GX 339–4?

ABSTRACT We investigated the snapshots of five NICER observations of the black hole transient GX 339–4 when the source transited from the hard state into the soft state during its outburst in 2021. In this paper, we focused our study on the evolution of quasi-periodic oscillations (QPOs) and noise components using power-density spectra. In addition, we derived hardness ratios by comparing count rates above and below 2 keV. The evolution from the hard to the soft state was a somewhat erratic process, showing several transitions between states that are dominated by top-flat noise and can show type-C QPOs; those that are dominated by red noise and can show type-B QPOs. From the parameters that we studied, we only found a strong correlation between the hardness ratio and the type of QPO observed. This implies that the appearance of type-B QPOs is related to a change in the accretion geometry of the system that also reflects in altered spectral properties. We also observed that the type-B QPO forms from or disintegrates into a broad peaked feature when the source comes out of or goes to the hard intermediate state, respectively. This implies some strong decoherence in the process that creates this feature.

The comptonizing medium of the black hole X-ray binary MAXI J1535−571 through type-C quasi-periodic oscillations

ABSTRACT We present a detailed spectral and temporal analysis of the black hole candidate MAXI J1535−571 using NICER observations in 2017 September and October. 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 ∼104–3× 10 3 km as the QPO frequency increases from ∼ 1.8–9.0 Hz. The fits suggest that the system would consist 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 between 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 ν c ≈ 3.0 Hz. Interestingly, the QPO reaches this critical frequency simultaneously as the radio emission from the jet in this source is quenched.

Effect of geometrically thin discs on precessing, thick flows: relevance to type-C QPOs

ABSTRACT Type-C quasi-periodic oscillations (QPOs) are the low-frequency QPOs most commonly observed during the hard spectral state of X-ray binary systems. The leading model for these QPOs is the Lense-Thirring precession of a hot geometrically thick accretion flow that is misaligned with respect to the black hole spin axis. However, none of the work done to date has accounted for the effects of a surrounding geometrically thin disc on this precession, as would be the case in the truncated disc picture of the hard state. To address this, we perform a set of general relativistic magnetohydrodynamics simulations of truncated discs misaligned with the spin axes of their central black holes. Our results confirm that the inner-hot flow still undergoes precession, though at a rate that is only 5 per cent of what is predicted for an isolated precessing torus. We find that the exchange of angular momentum between the outer thin and the inner thick disc causes this slow-down in the precession rate and discuss its relevance to type-C QPOs.

Spectral and Timing Analysis of the Black Hole Transient MAXI J1631–479 During its 2019 Outburst Observed with Insight-HXMT

We report spectral and timing analysis of the black hole transient MAXI J1631–479 during the hard intermediate state of its 2019 outburst from the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) observations. We find that the energy dependence of the type-C quasi-periodic oscillation (QPO) frequency evolves with time: during the initial rise of a small flare (∼MJD 58526.0-58527.1), the QPO frequency increases with increasing energy from ∼1 to ∼100 keV, and then the frequency remains constant after MJD 58527.1. We discover a possible new phenomenon of Fe line’s QPO frequency jump that has never been observed for other black hole transients: during the small flare, the QPO frequency around the Fe line energy is higher than any other energy band, with the frequency difference Δf = 0.25 ± 0.08 Hz between 5.5–7.5 keV and other energy bands. The spectral analysis shows that the evolution of QPOs is related to the equivalent width of the narrow Fe line, and its equivalent width increases during this small flare. We propose that the QPO frequency difference results from the differential precession of a vertically extended jet, and the higher QPO frequency of Fe line could be caused by the layered jet when the jet scale increases. At the same time, the evolution of QPOs is related to the accretion rate, while the energy dependence of QPOs supports the existence of deceleration in the vertically distributed jet.

Transitions and Origin of the Type-B Quasi-periodic Oscillations in the Black Hole X-Ray Binary MAXI J1348–630

The fast transitions between different types of quasi-periodic oscillations (QPOs) are generally observed in black hole transient sources (BHTs). We present a detailed study of the timing and spectral properties of the transitions of type-B QPOs in MAXI J1348–630, observed by Insight-HXMT. The fractional rms variability–energy relationship and energy spectra reveal that type-B QPOs probably originate from jet precession. Compared to a weak power-law dominated power spectrum, when type-B QPOs are present, the corresponding energy spectrum shows an increase in the Comptonization component and the need for the xillverCp component, and a slight increase in the height of the corona when using the relxilllp model. Therefore, we suggest that a coupled inner disk-jet region is responsible for the observed type-B QPO transitions. The timescale for the appearance/disappearance of type-B QPOs is either long or short (seconds), which may indicate instability of the disk-jet structure. For these phenomena, we hypothesize that the Bardeen–Petterson effect causes the disk-jet structure to align with the BH spin axis or that the disappearance of small-scale jets bound by the magnetic flux tubes leads to the disappearance of type-B QPOs. We observed three events regarding the B/C transitions, one of which occurred over a short time period from ∼9.2 Hz (C) to ∼4.8 Hz (B). The energy spectral analysis for the other two transitions shows that when type-C QPO is present, the Comptonization flux is higher, the spectrum is harder, and the inner radius of the disk changes insignificantly. We suggest that type-C QPOs probably originate from relatively stronger jets or the corona.

Wavelet analysis of the transient QPOs in MAXI J1535−571 with Insight-HXMT

ABSTRACT Using wavelet analysis and power density spectrum, we investigate two transient quasi-periodic oscillations (QPOs) observed in MAXI J1535−571 observed with Insight-HXMT. The transient QPOs have a centroid frequency of ∼10 Hz with an FWHM ∼0.6 Hz, and an rms amplitude $\sim 14{{\ \rm per\ cent}}$. Energy spectra of QPO and non-QPO regimes are also separated and analysed, and the spectra become softer with higher Ecut in the non-QPO regime compared to the QPO regime. Our results suggest that the transient QPOs detected in MJD 58016 and 58017 are still the type-C QPO, and the source remains in its HIMS. The duration of all type-C QPO signals based on wavelet is positively correlated with the mean count rate above ∼10 keV, implying appearance of QPOs in different time-scales should be coupled with the corona. The transient QPO properties could be related to the jet or flares, perhaps the partial ejection of the corona is responsible for the disappearance of the type-C QPO.