Timing in the Time Domain： Cygnus X—1

1 INTRODUCTIONStudying short time scale variability of the X-ray emission of blaCk-hole systems and lowmass X-ray binaries is an importal approach to understanding the emitting region and elinssionmechanism of high-energy photons. The time-averaged spectra of hard X-rays from Cyg X-1and other black-hole candidates are relatively well explained in terms of a simple model: hardX-rays result from the Comptonization of soft photons in a hot electron cloud of constattemperature and optical d…     

Spectral evolution of magnetic flares and time lags in accreting black hole sources

We present a model for the short time-scale spectral variability of accreting black holes. It describes the time-averaged spectra well, and also temporal characteristics such as the power-density spectrum, time/phase lags, and coherence function of Cygnus X-1. We assume that X/ γ -rays are produced in compact magnetic flares at radii ≲100 GM c ² from the central black hole. The tendency for magnetic loops to inflate and detach from the underlying accretion disc causes the spectrum of a flare to evolve from soft to hard because of the decrease of the feedback from the cold disc, so causing time delays between hard and soft photons. We identify the observed time lags with the evolution time-scales of the flares, which are of the order of the Keplerian time-scale. We model the overall temporal variability using a pulse avalanche model in which each flare has a certain probability of triggering a neighbouring flare, thus occasionally producing long avalanches. The duration of the avalanches determines the Fourier frequencies at which most of the power emerges.     

Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with Poissonian Fluctuations: A Case Study

Hilbert-Huang Transform (HHT) is a novel data analysis technique for nonlinear and non-stationary data. We present a time-frequency analysis of both simulated light curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform (WFFT) methods. Our results show that the HHT method has failed in all cases for light curves with Poissonian fluctuations which are typical for all photon counting instruments used in astronomy, whereas the WFFT method can sensitively detect the periodic signals in the presence of Poissonian fluctuations; the only drawback of the WFFT method is that it cannot detect sharp frequency variations accurately.     

The Temporal Phenomena of Black Hole Transient XTE J1650-500 in Its 2001-2002 Outburst

Using the data observed by Rossi X-ray Timing Explorer, a systematic study of temporal phenomena of the black-hole transient XTE J1650-500 in its 2001–2002 outburst is presented. By using the time lag in the Fourier frequency domain, three characteristic frequency ranges are analysed, namely the band limited noise, red noise, and QPOs (Quasi-Periodic Oscillations). The properties and evolution behaviours in these frequency ranges may be dominated by different accretion regions. It is commonly believed that the smaller timescale corresponds to the more inner region. The low-hard state and hard intermediate state are especially highlighted. The results of data analysis are discussed in the framework of Lense-Thirring precession. Results are in favor of the disturbance propagation model for explaining the observed time lags. Although the timing analysis in the frequency ranges of band-limited noise and red noise is carried out, and a possibly existed inflection point is found, the model to explain them is still not well established. More work is needed to understand the innermost accretion region.     

On the detection of high‐frequency oscillations in short gamma‐ray bursts

In this work we present the results of an investigation aimed at a search for an oscillatory phenomenon during short gamma‐ray bursts. The wavelet technique, used for this analysis, is applied to the data from the BATSE 3B catalogue. We have detected oscillations, which periods are found to be in the milliseconds range and their amplitudes up to dozens of percents. A possible scenario for such a phenomenon is the coalescence of stellar‐mass black holes and neutron stars. During the coalescence process the matter orbiting the black hole produces rapid, periodic phenomena. Such system will also emit gravitational waves which cause the orbital radius to decrease and leads to the emission of a chirp of radiation. Estimates lead to a timescale of milliseconds for the coalescence process and oscillation frequencies of hundreds of Hz. The gamma‐ray bursts considered in this paper, show both frequencies and survival times of oscillations close to the mentioned values. A chirp phenomenon is also present. We therefore argue in favor of the black hole – neutron star coalescence as a scenario for the production of short gamma‐ray bursts (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral lag of gamma‐ray bursts caused by the intrinsic spectral evolution and the curvature effect

Assuming an intrinsic ‘Band’ shape spectrum and an intrinsic energy‐independent emission profile we have investigated the connection between the evolution of the rest‐frame spectral parameters and the spectral lags measured in gamma‐ray burst (GRB) pulses by using a pulse model. We first focus our attention on the evolution of the peak energy, E_0,p, and neglect the effect of the curvature effect. It is found that the evolution of E_0,p alone can produce the observed lags. When E_0,p varies from hard to soft only the positive lags can be observed. The negative lags would occur in the case of E_0,p varying from soft to hard. When the evolution of E_0,p and the low‐energy spectral index α₀ varying from soft to hard then to soft we can find the aforesaid two sorts of lags. We then examine the combined case of the spectral evolution and the curvature effect of fireball and find the observed spectral lags would increase. A sample including 15 single pulses whose spectral evolution follows hard to soft has been investigated. All the lags of these pulses are positive, which is in good agreement with our theoretical predictions. Our analysis shows that only the intrinsic spectral evolution can produce the spectral lags and the observed lags should be contributed by the intrinsic spectral evolution and the curvature effect. But it is still unclear what cause the spectral evolution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral lags caused by the curvature effect of fireballs

Recently, Shen et al. have studied the contributions of the curvature effect of fireballs to the spectral lag and have shown that the observed lags can be accounted for by the effect. Here, we check their results by performing a more precise calculation with both formulae presented by Shen et al. and Qin et al. Several other aspects which were not considered by Shen et al. are investigated. We find that in the case of ultrarelativistic motions, both formulae are identical as long as the whole fireball surface is concerned. In our analysis, the previous conclusion that the detected spectral lags can be accounted for by the curvature effect is confirmed, while the conclusion that the lag has no dependence on the radius of fireballs is not true. We find that introducing extreme physical parameters is not the only outlet to explain these observed large lags. Even for the larger lags (∼5 s), a wider local pulse  (Δ t _θ,FWHM= 10⁷ s)  can account for it. Some conclusions not presented in Shen et al. or those modified in our analysis are listed below: (i)  lag ∝Γ^−ε  with  ε > 2  ; (ii) lag is proportional to the local pulse width and the full width at half-maximum of the observed light curves; (iii) a large lag requires a large α₀ and a small β₀ as well as a large   E _0,p  ; (iv) when the rest-frame spectrum varies with time, the lag would become larger; (v) lag decreases with the increase of   R_c   ; (vi) lag ∝ E within the certain energy range for a given Lorentz factor; (vii) lag is proportional to the opening angle of uniform jets when  θ_j < 0.6Γ⁻¹  .     

The continuum and line spectra of SGR 1806-20 bursts

The defining property of Soft Gamma Repeaters is the emission of short, bright bursts of X-rays and soft γ-rays. Here we present the continuum and line spectral properties of a large sample of bursts from SGR 1806-20, observed with the Proportional Counter Array (PCA) onboard the Rossi X-ray Timing Explorer (RXTE). Using 10 trail spectral models (5 single and 5 two component models), we find that the burst continua are best fitted by the single component models: cutoff power-law, optically thin bremsstrahlung, and simple power-law. Time resolved spectroscopy show that there are two absorption lines at ∼5 keV and 20 keV in some bursts. The lines are relatively narrow with 90% upper limit on the line widths of 0.5–1.5 keV for the 5 keV feature and 1–3 keV for the 20 keV feature. Both lines have considerable equivalent width of 330–850 eV for the 5 keV feature and 780–2590 eV for the 20 keV feature. We examined whether theses spectral lines are dependent upon the choice of a particular continuum model and find no such dependence. Besides, we find that the 5 keV feature is pronounced with high confidence in the cumulative joint spectrum of the entire burst sample, both in the individual detectors of the PCA and in the co-added detectors spectrum. We confront the features against possible instrumental effects and find that none can account for the observed line properties. The two features do not seem to be connected to the same physical mechanism because (1) they do not always occur simultaneously, (2) while the 5 keV feature occurs at about the same energy, the 20 keV line centroid varies significantly from burst to burst over the range 18–22 keV, and (3) the centroid of the lines shows anti-correlated red/blue shifts. The transient appearance of the features in the individual bursts and in portions of the same burst, together with the spectral evolution seen in some bursts point to a complex emission mechanism that requires further investigation.      

Relationship between pulse width and energy in GRB 060124: from X-ray to γ-ray bands

GRB 060124 is the first event that both prompt and afterglow emission were observed simultaneously by the three Swift instruments. Its main peak also triggered Konus-Wind and HETE-II. Therefore, investigation on both the temporal and spectral properties of the prompt emission can be extended to X-ray bands. We perform a detailed analysis on the two well identified pulses of this burst, and find that the pulses are narrower at higher energies, and both X-rays and γ-rays follow the same w–E relation for an individual pulse. However, there is no a universal power-law index of the w–E relation among pulses. We find also that the rise-to-decay ratio r/d seems not to evolve with E and the r/d values are well consistent with that observed in typical GRBs. The broadband spectral energy distribution also suggests that the X-rays are consistent with the spectral behavior of the γ-rays. These results indicate that the X-ray emission tracks the γ-ray emission and the emissions in the two energy bands are likely to be originated from the same physical mechanism.     

CygX—1硬态高能光子的时延

硬X射线和软射线光子的时延时研究主能辐射的一个重要方面，傅里叶交叉谱常常被用于教育处硬软光子之间的时延，但是交叉说示能在高于30Hz的傅里叶频率上从CygX-1测量到有统计意义的快速光变，由李惕培在时域上发展的交叉相关函方法能有效测量不同时间尺度上的时延，利用此交叉相关分析方法，讨论了不同观测时期CygX-1硬态高能光子时延 的性质，分析结果表明，CygX-1硬态在短的尺度（＜0．1秒）上存存在有意义的时间延迟，并将短时间尺度上的观测结果和各种CygX-1硬态模型进行了比较讨论。     

Relationships between Relative Spectral Lags and Relative Widths of Gamma-ray Bursts

The phenomenon of gamma-ray burst (GRB) spectral lags is very common, but a definitive explanation has not yet been given. From a sample of 82 GRB pulses we find that the spectral lags are correlated with the pulse widths, however, there is no correlation be- tween the relative spectral lags and the relative pulse widths. We suspect that the correlations between spectral lags and pulse widths might be caused by the Lorentz factor of the GRBs concerned. Our analysis on the relative quantities suggests that the intrinsic spectral lag might reflect other aspect of pulses than the aspect associated with the dynamical time of shocks or that associated with the time delay due to the curvature effect.     

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.     

Tail Emission from a Ring-like Jet: Its Application to Shallow Decays of Early Afterglows and GRB 050709

Similar to the case of pulsars the magnetic axis and the spin axis of gamma-ray burst sources may not lie on the same line. This may cause the formation of a ring-like jet due to collimation of the processing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with a temporal index of -1/2 if the Lorentz factor of the ejecta is not very high, which is consistent with the shallow decay phase of some early X-ray afterglow detected by Swift. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709.     

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.     

新近对耀变体(Blazar)的X射线观测

本文综述了ASCA ,RXTE ,BeppoSAX和XMM -NEWTON对TeV耀变体 (Blazar)X射线研究的最新进展。主要集中在X射线资料的时间和光谱分析的最重要的方面 ,包括功率谱密度 ,结构函数 ,带间时间延迟 ,同步峰值能量的漂移和谱演化。对这些新结果的物理意义也进行了简要讨论。     

Inferring the emission regions for different kinds of gamma‐ray bursts

Using a theoretical model describing pulse shapes, we have clarified the relations between the observed pulses and their corresponding timescales, such as the angular spreading time, the dynamic time as well as the cooling time. We find that the angular spreading timescale caused by curvature effect of fireball surface only contributes to the falling part of the observed pulses, while the dynamic one in the co‐moving frame of the shell merely contributes to the rising portion of pulses provided the radiative time is negligible. In addition, the pulses resulted from the pure radiative cooling time of relativistic electrons exhibit properties of fast rise and slow decay (a quasi‐FRED) profile together with smooth peaks. Besides, we interpret the phenomena of wider pulses tending to be more asymmetric to be a consequence of the difference in emission regions. Meanwhile, we find the intrinsic emission time is decided by the ratios of lorentz factors and radii of the shells between short and long bursts. Based on the analysis of asymmetry, our results suggest that the long GRB pulses may occur in the regions with larger radius, while the short bursts could locate at the smaller distance from central engine. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Supernovae in helium star–compact object binaries: a possible γ-ray burst mechanism

Helium star–compact object binaries, and helium star–neutron star binaries in particular, are widely believed to be the progenitors of the observed double-neutron-star systems. In these, the second neutron star is presumed to be the compact remnant of the helium star supernova. In this paper, the observational implications of such a supernova are discussed, and in particular are explored as a candidate γ-ray burst mechanism. In this scenario, the supernova results in a transient period of rapid accretion on to the compact object, extracting via magnetic torques its rotational energy at highly super-Eddington luminosities in the form of a narrowly beamed, strongly electromagnetically dominated jet. Compton scattering of supernova photons advected within the ejecta, and photons originating at shocks driven into the ejecta by the jet, will cool the jet and can produce the observed prompt emission characteristics, including the peak-inferred isotropic energy relation, X-ray flash characteristics, subpulse light curves, energy-dependent time lags and subpulse broadening, and late time spectral softening. The duration of the burst is limited by the rate of Compton cooling of the jet, eventually creating an optically thick, moderately relativistically expanding fireball that can produce the afterglow emission. If the black hole or neutron star stays bound to a compact remnant, late term light curve variability may be observed as in SN 2003dh.     

Afterglow light curves, viewing angle and the jet structure of γ-ray bursts

Gamma-ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets – some very narrow, and others with a similar power spread over a wider cone – the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.     

Time Lags of Z Source GX 5-1

We investigated the time lags and the evolution of the cross spectra of Z source GX 5-1, observed by the Rossi X-ray Timing Explorer (RXTE), when it is in the horizontal branch oscillations. We showed that the time lags of three horizontal branch oscillations are related to the position on the hardness intensity diagram. All of the three QPOs were shown to have hard time lags. However on the cross spectra, one is in a ‘dip’, one in a ‘bump’, the other has not so obvious characteristic. The time lags of two of the QPOs decrease with QPO's frequency, while the other has a trend increasing with its frequency. Moreover, in the normal branch, we found no significant time lags in the present observational data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Proper motions and variability of the H2 knots in the HH 111 and 121 protostellar outflows

We discuss the formation of spectral features in the decelerating ejecta of gamma-ray bursts, including the possible effect of inhomogeneities. These should lead to blueshifted and broadened absorption edges and resonant features, especially from H and He. An external neutral ISM could produce detectable H and He, as well as Fe X-ray absorption edges and lines. Hypernova scenarios may be diagnosed by Fe Kα and H Lyα emission lines.