Impact of reverberation in flared accretion discs on temporal characteristics of X-ray binaries

Observations suggest that accretion discs in many X-ray binaries are likely flared. An outer edge of the disc intercepts radiation from the central X-ray source. Part of that radiation is absorbed and re-emitted in the optical/UV spectral ranges. However, a large fraction of that radiation is reflected and appears in the broad-band X-ray spectrum as a Compton reflection bump. This radiation is delayed and variability is somewhat smeared compared with the intrinsic X-ray radiation. We compute response functions for flat and flared accretion discs and for isotropic and anisotropic X-ray sources. A simple approximation for the response function which is valid in the broad range of the disc shapes and inclinations, inner and outer radii, and the plasma bulk velocity is proposed. We also study the impact of the X-ray reprocessing on temporal characteristics of X-ray binaries such as the power spectral density, auto- and cross-correlation functions, and time/phase lags. We propose a reprocessing model which explains the secondary peaks in the phase lag Fourier spectra observed in Cyg X-1 and other Galactic black hole sources. The position of the peaks could be used to determine the size of the accretion disc.     

Superorbital variability in hard X-rays

We present the results of a study with the Swift Burst Alert Telescope in the 14–195 keV range of the long-term variability of five low-mass X-ray binaries with reported or suspected superorbital periods – 4U 1636−536, 4U 1820−303, 4U 1916−053, Cyg X-2 and Sco X-1. No significant persistent periodic modulation was detected around the previously reported periods in the 4U 1916−053, Cyg X-2 or Sco X-1 light curves. The ∼170-d period of 4U 1820−303 was detected up to 24 keV, consistent with variable accretion due to the previously proposed triple system model. The ∼46-d period in 4U 1636−536 was detected up to 100 keV, with the modulation in the low- and high-energy bands found to be phase shifted by ∼180° with respect to each other. This phase shift, when taken together with the near-coincident onset of the ∼46-d modulation and the low/hard X-ray state, leads us to speculate that the modulation could herald transient jet formation.     

Spectral fit of Cygnus X-1 in high energy— a self-consistent study

We fit the spectra of Cyg X-1 using two component advective flows with Keplerian accretion disks on the equatorial plane surrounded by sub-Keplerian disks when standing shocks are present. The soft photons generated by the bremsstrahlung and synchrotron processes in the sub-Keplerian flow, as well as the multi-colour black body emission from the Keplerian disk are Comptonized by the thermal and non-thermal electrons. By varying Keplerian and sub-Keplerian rates we are able to reproduce the observed soft and hard states as far as X-ray region is concerned and ‘low γ-ray intensity’ and ‘high γ-ray intensity’ states as far as the soft γ-ray region is concerned. We also find two pivotal points where the spectra intersect as is observed in Cyg X-1.      

On the X-ray time-lags in the black hole candidates

It is shown that the energy dependence of the time-lags in Cygnus X-1 excludes any significant contribution of the standard reflected component to the observed lags. The conclusion is valid in the     frequency range where time-lags have been detected with sufficient significance. In fact, the data hint that the reflected component is working in the opposite direction, reducing the lags at energies where the contribution of the reflected component is significant.
We argue that the observed logarithmic dependence of time-lags on energy could be due to the small variations of the spectral index in the frame of a very simple phenomenological model. We assume that an optically thin flow/corona, emitting a power law like spectrum, is present at a range of distances from the compact object. The slope of the locally emitted spectrum is a function of distance, with the hardest spectrum emitted in the innermost region. If perturbations with different time-scales are introduced to the accretion flow at different radii, then X-ray lags naturally appear, caused by the inward propagation of perturbations on the diffusion time-scales.     

Properties of X-ray shots of Cyg X-1 in high state

Temporal variations in the high-energy radiation of Cyg X-1 can be represented by the properties of its X-ray short bursts (shots). The properties of the X-ray shots of Cyg X-1 have been studied extensively, especially for the Cyg X-1 in its typical low/hard state. In this paper, we study the shot properties when Cyg X-1 is in its high/soft state, using direct superposition of shots and the autocorrelation function. Our result shows that when Cyg X-1 is in the high state, the shot structure is qualitatively similar to that of the low state, and that the full-width at half-maximum (FWHM) of the shot decreases with increasing energy, which is inconsistent with the prediction of the Comptonization model. In addition, the evolution of the shot energy spectrum and the asymmetry of the shot structure can explain the observed time lag in Cyg X-1.     

A classification of the X-ray and radio states of Cyg X-3 and their long-term correlations

We present a detailed classification of the X-ray states of Cyg X-3 based on the spectral shape and a new classification of the radio states based on the long-term correlated behaviour of the radio and soft X-ray light curves. We find a sequence of correlations, starting with a positive correlation between the radio and soft X-ray fluxes in the hard spectral state, changing to a negative one at the transition to soft spectral states. The temporal evolution can be in either direction on that sequence, unless the source goes into a very weak radio state, from which it can return only following a major radio flare. The flare decline is via relatively bright radio states, which results in a hysteresis loop on the flux–flux diagram. We also study the hard X-ray light curve, and find its overall anticorrelation with the soft X-rays. During major radio flares, the radio flux responds exponentially to the level of a hard X-ray high-energy tail. We also specify the detailed correspondence between the radio states and the X-ray spectral states. We compare our results to those of black hole and neutron star binaries. Except for the effect of strong absorption and the energy of the high-energy break in the hard state, the X-ray spectral states of Cyg X-3 closely correspond to the canonical X-ray states of black hole binaries. Also, the radio/X-ray correlation closely corresponds to that found in black hole binaries, but it significantly differs from that in neutron star binaries. Overall, our results strongly support the presence of a black hole in Cyg X-3.     

On the precession of accretion discs in X-ray binaries

In this Letter, recent results on the nodal precession of accretion discs in close binaries are applied to the discs in some X-ray binary systems. The ratio between the tidally forced precession period and the binary orbital period is given, as well as the condition required for the rigid precession of gaseous Keplerian discs. Hence the minimum precessional period that may be supported by a fluid Keplerian disc is determined. It is concluded that near-rigid body precession of tilted accretion discs can occur and generally reproduce observationally inferred precession periods, for reasonable system parameters. In particular, long periods in SS 433, Her X-1, LMC X-4 and SMC X-1 can be fitted by the tidal model. It is also found that the precession period that has been tentatively put forward for Cyg X-2 cannot be accommodated by a tidally precessing disc model for any realistic choice of system parameters.     

A comparative analysis of standard accretion discs spectra: an application to ultraluminous X-ray sources

We compare standard models of accretion discs around black holes (BHs) that include the appropriate zero-torque inner boundary condition and relativistic effects on the emission and propagation of radiation. The comparison is performed adopting the multicolour disc blackbody model (MCD) as reference and looking for the parameter space in which it is in statistical agreement with 'more physical' accretion disc models. We find simple 'recipes' that can be used for adjusting the estimates of the physical inner radius of the disc, the BH mass and the accretion rate inferred using the parameters of the MCD fits. We applied these results to four ultraluminous X-ray sources for which MCD spectral fits of their X-ray soft spectral components have been published and find that, in three cases (NGC 1313 X-1, X-2 and M 81 X-9), the BH masses inferred for a standard disc around a Schwarzschild BH are in the interval  ∼100–200 M_⊙  . Only if the BH is maximally rotating are the masses comparable to the much larger values previously derived in the literature.     

Cyg X-1高态中短暴性质的研究

CygX-1高能辐射的时变特征可以通过短暴(shot)的性质反映．因此CygX-1的短暴性质，特别是处于低态时的性质曾被广泛研究,利用直接叠加短暴和自相关函数，对CygX-1高态时短暴的性质进行了研究．结果表明，当CygX-1处于高态时，其短暴的结构类似于低态时所具有的性质，短暴的半高宽随能量的增加按指数下降．此结果和康普顿化模型不一致．另外，短暴的能谱演化及结构的非对称性可以解释CygX-1中的时延现象．     

Iron Kα line profiles and the inner boundary condition of accretion flows

Recent X-ray observations have shown evidence for exceptionally broad and skewed iron Kα emission lines from several accreting black hole systems. The lines are assumed to be due to fluorescence of the accretion disc illuminated by a surrounding corona and require a steep emissivity profile increasing into the innermost radius. This appears to question both standard accretion disc theory and the zero-torque assumption for the inner boundary condition, both of which predict a much less extreme profile. Instead it argues that a torque may be present due to magnetic coupling with matter in the plunging region or even to the spinning black hole itself. Discussion so far has centred on the torque acting on the disc. However, the crucial determinant of the iron line profile is the radial variation of the power radiated in the corona. Here we study the effects of different inner boundary conditions on the coronal emissivity and on the profiles of the observable Fe Kα lines. We argue that in the extreme case where a prominent highly redshifted component of the iron line is detected, requiring a steep emissivity profile in the innermost part and a flatter one outside, energy from the gas plunging into the black hole is being fed directly to the corona.     

Radiation mechanisms and geometry of Cygnus X-1 in the soft state

We present X-ray/ γ -ray spectra of Cyg X-1 observed during the transition from the hard to the soft state and in the soft state by ASCA , RXTE and CGRO /OSSE in 1996 May and June. The spectra consist of a dominant soft component below ∼2 keV and a power-law-like continuum extending to at least ∼800 keV. We interpret them as emission from an optically thick, cold accretion disc and from an optically thin, non-thermal corona above the disc. A fraction f ≳0.5 of total available power is dissipated in the corona.
We model the soft component by multicolour blackbody disc emission taking into account the torque-free inner-boundary condition. If the disc extends down to the minimum stable orbit, the ASCA RXTE data yield the most probable black hole mass of M _X≈10 M_⊙ and an accretion rate,     , locating Cyg X-1 in the soft state in the upper part of the stable, gas-pressure-dominated, accretion-disc solution branch.
The spectrum of the corona is well modelled by repeated Compton scattering of seed photons from the disc off electrons with a hybrid, thermal/non-thermal distribution. The electron distribution can be characterized by a Maxwellian with an equilibrium temperature of kT _e∼30–50 keV, a Thomson optical depth of τ ∼0.3 and a quasi-power-law tail. The compactness of the corona is 2≲ℓ_h≲7, and a presence of a significant population of electron–positron pairs is ruled out.
We find strong signatures of Compton reflection from a cold and ionized medium, presumably an accretion disc, with an apparent reflector solid angle, Ω/2π∼0.5–0.7. The reflected continuum is accompanied by a broad iron K α line.     

X-ray reverberation around accreting black holes

Luminous accreting stellar mass and supermassive black holes produce power–law continuum X-ray emission from a compact central corona. Reverberation time lags occur due to light travel time delays between changes in the direct coronal emission and corresponding variations in its reflection from the accretion flow. Reverberation is detectable using light curves made in different X-ray energy bands, since the direct and reflected components have different spectral shapes. Larger, lower frequency, lags are also seen and are identified with propagation of fluctuations through the accretion flow and associated corona. We review the evidence for X-ray reverberation in active galactic nuclei and black hole X-ray binaries, showing how it can be best measured and how it may be modelled. The timescales and energy dependence of the high-frequency reverberation lags show that much of the signal is originating from very close to the black hole in some objects, within a few gravitational radii of the event horizon. We consider how these signals can be studied in the future to carry out X-ray reverberation mapping of the regions closest to black holes.     

X-ray spectra of accretion discs with dynamic coronae

We compute the X-ray spectra produced by non-static coronae atop accretion discs around black holes and neutron stars. The hot corona is radiatively coupled to the underlying disc (the reflector) and generates an X-ray spectrum which is sensitive to the bulk velocity of the coronal plasma, β = v / c . We show that an outflowing corona reproduces the hard-state spectrum of Cyg X-1 and similar objects. The dynamic model predicts a correlation between the observed amplitude of reflection R and the X-ray spectrum slope Γ since both strongly depend on β . A similar correlation was observed and its shape was well fitted by the dynamic model. The scattering of soft radiation in an outflowing corona can also account for the observed optical–UV polarization pattern in active galactic nuclei.     

Echoes from the companion star in Sco X-1

We present simultaneous X-ray ( RXTE ) and optical (ULTRACAM) narrow-band (Bowen blend/He  ii and nearby continuum) observations of Sco X-1 at 2–10 Hz time resolution. We find that the Bowen/He  ii emission lags the X-ray light curves with a light traveltime of     s which is consistent with reprocessing in the companion star. The echo from the donor is detected at orbital phase ∼0.5 when Sco X-1 is at the top of the flaring branch (FB). Evidence of echoes is also seen at the bottom of the FB but with time-lags of 5–10 s which are consistent with reprocessing in an accretion disc with a radial temperature profile. We discuss the implication of our results for the orbital parameters of Sco X-1.     

Precessing warped accretion discs in X-ray binaries

We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing.
We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well-resolved solution.
We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable 'superorbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed recently by Wijers and Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.     

X-ray variability of the Seyfert 1 Markarian 335: power spectrum and time lags

To investigate further the comparison between active galactic nuclei (AGN) and black hole X-ray binaries, we have studied the main X-ray variability properties of the Seyfert 1 galaxy Mrk 335. We put particular emphasis on the X-ray time lags, which is a potentially important diagnostic of physical models. From a 100 ks observation by XMM–Newton , we show that the power spectrum of this source is well fitted by a bending power-law model, and the bend time-scale T _b is precisely at the value predicted by the T _b versus Hβ linewidth relation of McHardy et al. Variations in different energy bands show time-scale-dependent time lags, where higher energy bands lag lower ones. The lag, τ, varies as a function of the Fourier frequency, f , of the variability component in the light curves as  τ∝ f ⁻¹  at low frequencies, but there is a sharp cut-off in the lags at a frequency close to the bend frequency in the power spectrum. Similar behaviour is seen in black hole X-ray binary systems. The length of the time lags increases continuously with energy separation, in an almost loglinear relation. We show that the lag spectra can be produced by fluctuations propagating through the accretion flow as long as the energy spectrum of the X-ray emitting region hardens towards the centre.     

A complete relativistic ionized accretion disc in Cygnus X-1

The galactic black hole candidate Cygnus X-1 is observed to be in one of two X-ray spectral states: either the low/hard (low soft X-ray flux and a flat power-law tail) or high/soft (high blackbody-like soft X-ray flux and a steep power-law tail) state. The physical origin of these two states is unclear. We present here a model of an ionized accretion disc, the spectrum of which is blurred by relativistic effects, and fit it to the ASCA , Ginga and EXOSAT data of Cygnus X-1 in both spectral states. We confirm that relativistic blurring provides a much better fit to the low/hard state data and, contrary to some previous results, find the data of both states to be consistent with an ionized thin accretion disc with a reflected fraction of unity extending to the innermost stable circular orbit around the black hole. Our model is an alternative to those that, in the low/hard state, require the accretion disc to be truncated at a few tens of Schwarzschild radii, within which there is a Thomson-thin, hot accretion flow. We suggest a mechanism that may cause the changes in spectral state.     

星风吸积下的有盘X射线脉冲星

近年来对吸积流的数值模拟工作证实了在星风吸积中吸积盘的存在。本文在此基础上，讨论具有早型伴星的Ｘ射线脉冲星吸积过程中吸积盘与球吸积流的相互作用。我们发现，盘吸积率和球吸积率的相对变化可以导致吸积盘和吸积矩的改变，从而解释了这类脉冲星脉冲周期的复杂变化，我们以典型星ＶｅｌａＸ－１和Ａ０５３５＋２６为例分别作了讨论。     

The nature of the hard state of Cygnus X-3

The X-ray binary Cygnus X-3 (Cyg X-3) is a highly variable X-ray source that displays a wide range of observed spectral states. One of the main states is significantly harder than the others, peaking at ∼20 keV, with only a weak low-energy component. Due to the enigmatic nature of this object, hidden inside the strong stellar wind of its Wolf–Rayet companion, it has remained unclear whether this state represents an intrinsic hard state, with truncation of the inner disc, or whether it is just a result of increased local absorption. We study the X-ray light curves from RXTE /ASM and CGRO /BATSE in terms of distributions and correlations of flux and hardness and find several signs of a bimodal behaviour of the accretion flow that are not likely to be the result of increased absorption in a surrounding medium. Using INTEGRAL observations, we model the broad-band spectrum of Cyg X-3 in its apparent hard state. We find that it can be well described by a model of a hard state with a truncated disc, despite the low cut-off energy, provided the accreted power is supplied to the electrons in the inner flow in the form of acceleration rather than thermal heating, resulting in a hybrid electron distribution and a spectrum with a significant contribution from non-thermal Comptonization, usually observed only in soft states. The high luminosity of this non-thermal hard state implies that either the transition takes place at significantly higher   L / L _E  than in the usual advection models, or the mass of the compact object is  ≳20 M_⊙  , possibly making it the most-massive black hole observed in an X-ray binary in our Galaxy so far. We find that an absorption model as well as a model of almost pure Compton reflection also fit the data well, but both have difficulties explaining other results, in particular the radio/X-ray correlation.     

Are there three peaks in the power spectra of GX 339−4 and Cyg X-1?

Among the variability behaviours exhibited by neutron star systems are the so-called 'horizontal branch oscillations' (HBO, with frequencies ≈50 Hz), the 'lower-frequency kHz quasi-periodic oscillation' (QPO) and the 'upper-frequency kHz QPO', with the latter two features being separated in frequency by an amount comparable to, but varying slightly from, the suspected spin-frequency of the neutron star. Recently, Psaltis, Belloni & van der Klis have suggested that there exists a correlation between these three frequencies that, when certain identifications of variability features are made, even encompasses black hole sources. We consider this hypothesis by reanalysing a set of GX 339−4 observations. The power spectral density (PSD) constructed from a composite of seven separate, but very similar, observations shows evidence for three broad peaks in the PSD. If the peak frequencies of these features are identified with QPO, then their frequencies approximately fit the correlations suggested by Psaltis, Belloni, & van der Klis. We also reanalyse a Cyg X-1 observation and show that the suggested QPO correlation may also hold, but that complications arise when the QPOs (which, in reality, are fairly broad features) are considered as a function of energy band. These fits suggest the existence of at least three separate, independent physical processes in the accretion flow, a hypothesis that is also supported by consideration of the Fourier frequency-dependent time lags and coherence function between variability in different energy bands. If these variability features have a common origin in neutron star and black hole systems, then 'beat frequency models' of kHz QPO in neutron star systems are called into question.