Time-lag Spectra Research Articles

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.

Long-term Evolution of the Short-term X-Ray Variability of the Jetted TDE Swift J1644+57

Abstract The short-term X-ray variability of tidal disruption events (TDEs) and its similarities with that of active galactic nuclei are poorly understood. In this work, we show the diversity of TDEs’ short-term X-ray variability, and take Swift J1644+57 as an example to study the evolution of various properties related to the short-term X-ray variability, such as the X-ray flux distribution, power spectral density (PSD), rms variability, time lag, and coherence spectra. We find that the flux distribution of Swift J1644+57 has a lognormal form in the normal state, but deviates from it significantly in the dipping state, thereby implying different physical mechanisms in the two states. We also find that during the first two XMM-Newton observations in the dipping state, Swift J1644+57 exhibited different variability patterns, which are characterized by steeper PSDs and larger rms than the normal state. A significant soft X-ray lag is detected in these two observations, which is ∼50 s between 0.3–1 keV and 2–10 keV with a high coherence. Using the 2–10 keV rms of 0.10–0.50, the black hole mass of Swift J1644+57 is estimated to be ( 0.6 – 7.9 ) × 10 6 M ⊙ , but the variation of rms as the TDE evolves introduces a large uncertainty. Finally, we discuss the value of conducting similar studies on other TDEs, especially in the coming era of time-domain astronomy when a lot more TDEs will be discovered in X-rays promptly. This also heralds a significant increase in the demand for deep follow-up observations of X-ray selected TDEs with X-ray telescopes of large effective areas and long orbital periods.

X-ray reverberation models of the disc wind in ultraluminous X-ray source NGC 5408 X−1

ABSTRACT Majority of ultraluminous X-ray sources (ULXs) are believed to be super-Eddington objects, providing a nearby prototype for studying an accretion in supercritical regime. In this work, we present the study of time-lag spectra of the ULX NGC 5408 X−1 using a reverberation mapping technique. The time-lag data were binned using two different methods: time-averaged-based and luminosity-based spectral bins. These spectra were fitted using two proposed geometric models: single and multiple photon scattering models. While both models similarly assume that a fraction of hard photons emitted from inner accretion disc could be downscattered with the super-Eddington outflowing wind becoming lagged, soft photons, they are different by the number that the hard photons scattering with the wind, i.e. single versus multiple times. In case of an averaged spectrum, both models consistently constrained the mass of ULX in the range of ∼80–500 M⊙. However, for the modelling results from the luminosity-based spectra, the confidence interval of the BH mass is significantly improved and is constrained to the range of ∼75–90 M⊙. In addition, the models suggest that the wind geometry is extended in which the photons could downscatter with the wind at the distance of ∼104–10$^{6}\, r_{\rm g}$. The results also suggest the variability of the lag spectra as a function of ULX luminosity, but the clear trend of changing accretion disc geometry with the spectral variability is not observed.

UV/Optical Disk Thermal Reverberation in Active Galactic Nuclei: An In-depth Study with an Analytic Prescription for Time-lag Spectra

Abstract Several active galactic nuclei show correlated variations in the UV/optical range, with time delays increasing at longer wavelengths. Thermal reprocessing of the X-rays illuminating the accretion disk has been proposed as a viable explanation. In this scenario, the variable X-ray flux irradiating the accretion disk is partially reflected in X-rays and partially absorbed, thermalized, and reemitted with some delay by the accretion disk at longer wavelengths. We investigate this scenario assuming an X-ray pointlike source illuminating a standard Novikov–Thorne accretion disk around a rotating black hole. We consider all special and general relativistic effects to determine the incident X-ray flux on the disk and in propagating light from the source to the disk and to the observer. We also compute the disk reflection flux, taking into consideration the disk ionization. We investigate the dependence of the disk response function and time lags on various physical parameters, such as the black hole mass and spin; X-ray corona height, luminosity, and photon index; accretion rate; inclination; and inner/outer disk radii. We find it is important to consider relativistic effects and the disk ionization in estimating the disk response. We also find a strong nonlinearity between the X-ray luminosity and the disk response. We present an analytic function for the time-lag dependence on wavelength, which can be used to fit observed time-lag spectra. We also estimate the fraction of the reverberation signal with respect to the total flux, and we suggest possible explanations for the lack of X-ray–UV/optical correlated variations in a few sources.

Testing the X-ray reverberation model KYNREFREV in a sample of Seyfert 1 Active Galactic Nuclei

We present the first results obtained by the application of the KYNREFREV-reverberation model, which is ready for its use in XSPEC. This model computes the time dependent reflection spectra of the disc as a response to a flash of primary power-law radiation from a point source corona located on the axis of the black hole accretion disc (lamp-post geometry). Full relativistic effects are taken into account. The ionisation of the disc is set for each radius according to the amount of the incident primary flux and the density of the accretion disc. We tested the model by fitting model predictions to the observed time-lag spectra of three Narrow-Line Seyfert 1 galaxies (ARK 564, MCG-6-30-15 and 1H 0707-495), assuming either a rapidly or zero spinning black hole (BH). The time-lags strongly suggest a compact X-ray source, located close to the BH, at a height of approx. 4 gravitational radii. This result does not depend either on the BH spin or the disc ionization. There is no significant statistical difference between the quality of the best-fits in the rapidly and zero spinning BH scenarios in Ark 564 and MCG-6-30-15. But there is an indication that the hypothesis of a non-rotating BH in 1H 0707-495 is not consistent with its time-lag spectrum. Finally, the best-fits to the Ark 564 and 1H 0707-495 data are of rather low quality. We detect wavy-residuals around the best-fit reverberation model time-lags at high frequencies. This result suggests that the simple lamp-post geometry does not fully explain the X-ray source/disc configuration in Active Galactic Nuclei.

X-Ray Timing Analysis of Cyg X-3 Using AstroSat/LAXPC: Detection of Milli-hertz Quasi-periodic Oscillations during the Flaring Hard X-Ray State

Abstract We present here results from the X-ray timing and spectral analysis of the X-ray binary Cyg X-3 using observations from the Large Area X-ray proportional Counter on board AstroSat. Consecutive light curves observed over a period of one year show the binary orbital period of 17253.56 ± 0.19 s. Another low-amplitude, slow periodicity of the order of 35.8 ± 1.4 days is observed, which may be due to the orbital precession as suggested earlier by Molteni et al. During the rising binary phase, power density spectra from different observations during the flaring hard X-ray state show quasi-periodic oscillations (QPOs) at ∼5–8 mHz, ∼12–14 mHz, and ∼18–24 mHz frequencies at the minimum confidence of 99%. However, during the consecutive binary decay phase, no QPO is detected up to 2σ significance. Energy-dependent time-lag spectra show soft lag (soft photons lag hard photons) at the mHz QPO frequency and the fractional rms of the QPO increases with the photon energy. During the binary motion, the observation of mHz QPOs during the rising phase of the flaring hard state may be linked to the increase in the supply of the accreting material in the disk and corona via stellar wind from the companion star. During the decay phase, the compact source moves in the outer wind region causing the decrease in supply of material for accretion. This may cause weakening of the mHz QPOs below the detection limit. This is also consistent with the preliminary analysis of the orbital phase-resolved energy spectra presented in this paper.

Statistical properties of Fourier-based time-lag estimates

The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost region (i.e. close to the putative super-massive black hole) in these objects. To obtain reliable information from these studies, the statistical properties of time-lags estimated from data must be known as accurately as possible. Aims: We investigated the statistical properties of Fourier-based time-lag estimates (i.e. based on the cross-periodogram), using evenly sampled time series with no missing points. Our aim is to provide practical `guidelines' on estimating time-lags that are minimally biased (i.e. whose mean is close to their intrinsic value) and have known errors.} Methods: Our investigation is based on both analytical work and extensive numerical simulations. The latter consisted of generating artificial time series with various signal-to-noise ratios and sampling patterns/durations similar to those offered by AGN observations with present and past X-ray satellites. We also considered a range of different model time-lag spectra commonly assumed in X-ray analyses of compact accreting systems. Results: Discrete sampling, binning and finite light curve duration cause the mean of the time-lag estimates to have a smaller magnitude than their intrinsic values. Smoothing (i.e. binning over consecutive frequencies) of the cross-periodogram can add extra bias at low frequencies. The use of light curves with low signal-to-noise ratio reduces the intrinsic coherence, and can introduce a bias to the sample coherence, time-lag estimates, and their predicted error.

A model for the energy-dependent time-lag and rms of the heartbeat oscillations in GRS 1915+105

Energy dependent phase lags reveal crucial information about the causal relation between various spectral components and about the nature of the accretion geometry around the compact objects. The time-lag and the fractional root mean square (rms) spectra of GRS 1915+105 in its heartbeat oscillation class/$\rho$ state show peculiar behaviour at the fundamental and harmonic frequencies where the lags at the fundamental show a turn around at $\sim$ 10 keV while the lags at the harmonic do not show any turn around at least till $\sim$ 20 keV. The magnitude of lags are of the order of few seconds and hence cannot be attributed to the light travel time effects or Comptonization delays. The continuum X-ray spectra can roughly be described by a disk blackbody and a hard X-ray power-law component and from phase resolved spectroscopy it has been shown that the inner disk radius varies during the oscillation. Here, we propose that there is a delayed response of the inner disk radius (DROID) to the accretion rate such that $r_{in}(t)\propto \dot{m}^\beta (t-\tau_d)$. The fluctuating accretion rate drives the oscillations of the inner radius after a time delay $\tau_d$ while the power-law component responds immediately. We show that in such a scenario a pure sinusoidal oscillation of the accretion rate can explain not only the shape and magnitude of energy dependent rms and time-lag spectra at the fundamental but also the next harmonic with just four free parameters.

General relativistic modelling of the negative reverberation X-ray time delays in AGN★

We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above $10^{-4}$ Hz) i.e. soft band variations lag the hard band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral iron line (Fe k$\alpha$) at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly-used, but erroneous, top-hat models. Additionally we parametrize the positive part of the time-lag spectra (typically seen below $10^{-4}$ Hz) by a power-law. We find that the best-fitting BH masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, $\alpha$, the viewing angle, $\theta$, or the height of the X-ray source above the disc, $h$. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and the viewing angles are distributed uniformly between 20 and 60 degrees. Finally, there is a tentative indication that the distribution of spin parameters may be bimodal above and below 0.62.

Negative X-ray reverberation time delays from MCG–6-30-15 and Mrk 766

Abstract We present an X-ray time lag analysis, as a function of Fourier frequency, for MCG–6-30-15 and Mrk 766 using long-term XMM–Newton light curves in the 0.5–1.5 and the 2–4 keV energy bands, together with some physical modelling of the corresponding time lag spectra. Both the time lag spectra of MCG–6-30-15 and Mrk 766 show negative values (i.e. soft band variations lag behind the corresponding hard band variations) at high frequencies, around 10−3 Hz, similar to those previously observed from 1H 0707−495. The remarkable morphological resemblance between the time lag spectra of MCG–6-30-15 and Mrk 766 indicate that the physical processes responsible for the observed soft time delays are very similar in the two sources, favouring a reflection scenario from material situated very nearby to the central black hole.

Hard X-ray lags of Cygnus X-1 on short timescales

Calculating the time lags over different timescales using the cross-correlation technique may lead to a biased estimate of small timescales. Given a timescale for lightcurve binning, we propose to subtract the local average instead of the global average during the cross-correlation, in order to filter variations on timescales larger than the bin size. The new method allows us to make an unbiased estimate of the time lags using RXTE/PCA data on timescales as small as ∼5 ms, where the Fourier technique becomes invalid. We calculate the time lag spectra of Cygnus X-1 at different spectral states with the new method, and find that the source appears to have similar X-ray lags on small timescales independent of its spectral states.

Spectra and time variability of black-hole binaries in the low/hard state

We propose a jet model for the low/hard state of galactic black-hole X-ray sources which explains the energy spectra from radio to X-rays and a number of timing properties in the X-ray domain such as the time lag spectra, the hardening of the power density spectra and the narrowing of the autocorrelation function with increasing photon energy. The model assumes that (i) there is a magnetic field along the axis of the jet, (ii) the electron density in the jet drops inversely proportional to distance, (iii) the jet is “hotter” near its center than at its periphery, and (iv) the electrons in the jet follow a power-law distribution function. We have performed Monte Carlo simulations of Compton upscattering of soft photons from the accretion disk and have found power-law high-energy spectra with photon-number index in the range 1.5–2 and cutoff at a few hundred keV, power-law time lags versus Fourier frequency with index ∼0.8, and an increase of the rms amplitude of variability and a narrowing of the autocorrelation function with increasing photon energy as they have been observed in Cygnus X-1. The spectrum at long wavelengths (radio, infrared, optical) is modeled to come from synchrotron radiation of the energetic electrons in the jet. We find flat to inverted radio spectra that extend from the radio up to about the optical band. For magnetic field strengths of the order 10 5–10 6 G at the base of the jet, the calculated spectra agree well in slope and flux with the observations.

Spectra of black-hole binaries in the low/hard state: From radio to X-rays

We propose a jet model for the low/hard state of Galactic black-hole X-ray sources that can explain the energy spectra from radio to X-rays. The model assumes that i) there is a magnetic field along the axis of the jet; ii) the electron density in the jet drops inversely proportional to distance; and iii) the electrons in the jet follow a power law distribution function. We have performed Monte Carlo simulations of Compton upscattering of soft photons from the accretion disk and have found power-law high-energy spectra with photon-number index in the range 1.5 - 2 and cutoff at a few hundred keV. The spectrum at long wavelengths (radio, infrared, optical) is modeled to come from synchrotron radiation of the energetic electrons in the jet. We find flat to inverted radio spectra that extend from the radio up to about the optical band. For magnetic field strengths of the order of 10^5-10^6G at the base of the jet, the calculated spectra agree well in slope and flux with the observations. Our model has the advantage over other existing models that it also explains many of the existing timing data such as the time lag spectra, the hardening of the power density spectra and the narrowing of the autocorrelation function with increasing photon energy.

Spectra and time variability of Galactic black-hole X-ray sources in the low/hard state

We propose a jet model for the low/hard state of galactic black-hole X-ray sources which explains a) the X-ray spectra; b) the time-lag spectra; c) the increase of the variability amplitude (QPO and high frequency) with increasing photon energy; and d) the narrowing of the autocorrelation function with increasing photon energy. The model (in its simplest form) assumes that i) there is a uniform magnetic field along the axis of the jet; ii) the electron density in the jet is inversely proportional to distance; and iii) the jet is “hotter” near its center than at its periphery. We have performed Monte Carlo simulations of Compton upscattering of soft photons from the accretion disk and have found power-law high-energy spectra with photon-number index in the range 1.5–2, power-law time lags versus Fourier frequency with index ~0.8, and an increase of the rms amplitude of variability and a narrowing of the autocorrelation function with photon energy as has been observed in Cygnus X-1. Similar energy spectra and time variability have been observed in neutron-star systems in the island state. It is therefore quite likely that a similar model holds for these sources as well.

Energy and time-lag spectra of galactic black-hole X-ray sources in the low/hard state

Most, probably all, accreting binaries that are believed to contain a black-hole emit radio waves when they are in the low/hard state. Whenever this radio emission has been resolved, a jet-like structure has become apparent. We propose that Compton upscattering of low-energy photons in the jet can explain both the energy spectra and the time lags versus Fourier frequency observed in the low/hard state of black-hole systems. The soft photons originate in the inner part of the accretion disk. We have performed Monte Carlo simulations of Compton upscattering in a jet and have found that for a rather wide range of values of the parameters we can obtain power-law high-energy X-ray spectra with photon-number index in the range 1.5 - 2 and power-law time lags versus Fourier frequency with index ~ 0.7. The black-hole source Cyg X-1 in the low/hard state is well described by our model.

Two‐dimensional Monte Carlo/Fokker‐Planck Simulations of Flares in Accretion Disk Corona Models

We present and discuss first results of space- and time-dependent Monte Carlo/Fokker-Planck radiation transport/electron dynamics simulations of flares in accretion disk corona systems in two-dimensional, cylindrical geometry. Following a brief, general description of the code, two fundamentally different flaring mechanisms will be considered: (1) flares originating in the optically thick, geometrically thin accretion disk, whose radiation is subsequently processed through a hot, optically thin corona sandwiching the accretion disk; and (2) flares originating in the corona (e.g., magnetic flares), leading to enhanced energy release in a small portion of the corona over a short period of time. We present energy- and angle-dependent light curves, angle- and time-dependent photon spectra, and time and phase lag spectra for both classes of flaring scenarios. We also illustrate the detailed, time-dependent effect of both types of flares on the electron temperature distribution in the corona, which is calculated self-consistently, including both thermal and nonthermal heating and cooling mechanisms. Whereas for the disk-flaring scenario, the flaring is mostly restricted to X-rays below ~10 keV, accompanied by spectral softening during the flare, the coronal flaring scenario produces predominantly hard X-ray flares (restricted to E 10 keV) with spectral hardening during the flare. Both hard and soft lags may result in the disk-flaring scenario, which predicts a slight hardening of the high-frequency power spectra with increasing photon energy. In the coronal-flaring scenario, the variability around ~10 keV leads variations at other photon energies, and no dependence of the power spectra on photon energy is found.

Cygnus X-1 from RXTE: monitoring the short term variability

We present temporal and spectral results from monitoring Cygnus X-1 with the Rossi X-ray Timing Explorer (RXTE) in 1998 and 1999. We concentrate on the long term evolution of the hard state timing properties, comparing it to the 1996 soft state evolution. This leads to the following results: 1. the hard and soft state time lag spectra are very similar, 2. during state transitions, the lags in the 1–10 Hz range increase by more than an order of magnitude, 3. in the hard state itself, flaring events can be seen — the temporal and spectral evolution during the flare of 1998 July identifies it as a “failed state transition”. During (failed) state transitions, the time lag spectra and the power spectra change predominantly in the 1–10 Hz range. We suggest that this additional variability is produced in ejected coronal material disrupting the synchrotron radiation emitting outflows present in the hard state.