Important Property of GRB Pulse: Power-Law Indices of Time Properties on Energy

The dependence of pulse temporal properties (pulse width, pulse rise width and pulse decay width) on energy is power-law function. Some correlated relationships between the power-law indices of the pulse time properties on energy and the spectral lags, relative spectral lags, spectral parameters of band function, and photon flux using a well-separated long-duration γ-ray burst (GRB) pulse sample is demonstrated here. We argue that the curvature effect can explain the correlated properties.     

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)     

同步辐射和费米伽马暴光谱的一致性检验

定义了一个新的量,曲率宽度,去检查同步模型与伽玛射线暴(GRB)光谱的一致性.此量用于测量GRB中辐射能谱(νFν,ν和Fν分别是频率和随频率变化的能量流量)峰值处的光谱拐折锐度.然后使用它检查了理论同步模型与观测到的GRB光谱之间的一致性.首先计算几种典型的同步模型的曲率宽度,包括单能、单幂律和拐折幂律电子同步模型.其次从Fermi/GBM (Gamma-ray Burst Monitor)长GRB时间分辨光谱目录中选择包含1198个光谱的GRB样本,将光谱与常用的经验模型拟合,并计算最佳拟合模型的光谱曲率宽度.通过比较两个曲率宽度,发现大多数样本与同步模型不一致,因为同步模型的光谱拐折比数据的光谱拐折更加平滑.结果表明同步模型很难适合大多数观测到的GRB光谱.此外,在暴脉冲中发现光子流量和曲率宽度之间存在强的反相关性,这表明流量越高,光谱拐折越尖锐,或者与同步模型的偏差就越大.     

On the Maximum Mass of Differentially Rotating Neutron Stars

The analysis of spectral lag between energy bands, which combines temporal and spectral analyses, can add strict constraints to gamma-ray burst (GRB) models. In previous studies, the lag analysis focused on the lags between channel 1 (25-57 keV) and channel 3 (115-320 keV) from the Burst and Transient Source Experiment (BATSE). In this Letter, we analyzed the cross-correlation average lags (including approximate uncertainties) between energy bands for two GRB samples: 19 events detected by Ginga and 109 events detected by BATSE. We paid special attention to the BATSE GRBs with known redshifts because there has been a reported connection between lag and luminosity. This extends our knowledge of spectral lags to lower energy ( approximately 2 keV). We found that lags between energy bands are small. The lag between the peak of approximately 50 keV photons and that of approximately 200 keV photons is approximately 0.08 s. The upper limit in the lag between approximately 9 and approximately 90 keV photons is approximately 0.5 s. Thus, there are not large shifts at low energy. We found that about 20% of GRBs have detectable lags between energy bands in the Ginga and BATSE samples. From the internal shock model, we found that there are three sources of time structure in GRB pulses: cooling, hydrodynamics, and angular effects. We argue that cooling is much too fast to account for our observed lags and that angular effects are independent of energy. Thus, only hydrodynamics can produce these lags. Perhaps the radiation process varies as the reverse shock moves through the shell.     

GRB 090618: different pulse temporal and spectral characteristics within a burst

GRB 090618 was simultaneously detected by Swift-BAT and Fermi-GBM. Its light curve shows two emission episodes consisting of four prominent pulses. The pulse in the first episode (episode A) has a smoother morphology than the three pulses in the second episode (episode B). Using the pulse peak-fit method, we have performed a detailed analysis of the temporal and spectral characteristics of these four pulses and found out that the first pulse (pulse A) exhibits distinctly different properties than the others in episode B (pulses B1, B2 and B3) in the following aspects. (i) Both the pulse width (w) and the rise-to-decay ratio of pulse (r/d, pulse asymmetry) in GRB 090618 are found to be energy-dependent. The indices of the power-law correlation between w and E for the pulses in episode B however are larger than that in episode A. Moreover the pulses B1, B2 and B3 tend to be more symmetric at the higher energy bands while the pulse A displays a reverse trend. (ii) Pulse A shows a hard-to-soft spectral evolution pattern, while the three pulses in the episode B follow the light curve trend. (iii) Pulse A has a longer lag than the pulses B1, B2 and B3. The mechanism which causes the different pulse characteristics within one single GRB is unclear.     

Statistical Properties of the Highest Pulses in Gamma-Ray Bursts

We study the statistical properties of the highest pulses within individual gamma-ray bursts (GRBs). A wavelet package analysis technique and a developed pulse-finding algorithm have been applied to identify the highest pulses from burst profiles observed by BATSE on board CGRO from 1991 April 21 to 1999 January 26. The statistical light curves of the highest pulses in four energy channels have been derived by an aligning method, which illustrate the temporal evolution of the pulse emission. Our result that narrower pulses go with higher energies is consistent with previous findings. By normalizing both the pulse durations and counts to unity, “characteristic” profiles of the highest pulses in the four channels are also derived. The four characteristic profiles are turned out to be almost the same, thus strongly support the previous conclusion that the temporal profiles in different energy channels are self-similar and the previous conjecture on GRB pulses, implying that the emission process is similar at different energies. The cosmological time dilation effect is examined by investigating the relationship between the pulse flux and pulse duration. An anti-correlation between the two was found, which agrees with the expectation of the cosmological time dilation effect. Also, the evolution of the pulse duration with the observational epoch is studied. The result shows that the pulse duration tends to be shorter in later epochs. This trend cannot be explained by the present theoretical models, and may represent a great challenge to current theories.     

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.     

Catalog of short gamma-ray transients detected in the SPI/INTEGRAL experiment

We analyzed the data obtained by the SPI telescope onboard the INTEGRAL observatory to search for short transient events with a duration from 1 ms to a few tens of seconds. An algorithm for identifying gamma-ray events against the background of a large number of charged particle interactions with the detector has been developed. The classification of events was made. Apart from the events associated with cosmic gamma-ray bursts (GRBs) confirmed by other space experiments and the activity of known soft gamma repeaters (for example, SGR 1806-20), previously unreported GRBs have been found. GRB candidates and short gamma-ray events probably associated with the activity of known SGRs and AXPs have been selected. The spectral evolution of 28 bright GRBs from the catalog has been studied extensively. A new method for investigating the spectral evolution is proposed. The energy dependence of the spectral lag for bursts with a simple structure of their light curves and for individual pulses of multipulse events is shown to be described by a logarithmic function, lag ～ Alog(E). It has been established that the parameter A depends on the pulse duration, with the dependence being universal for all of the investigated GRBs. No negative spectral lags have been detected for bursts with a simple structure of their light curves.     

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)     

Timescale Analysis of Spectral Lags

A technique for timescale analysis of spectral lags performed directly in the time domain is developed. Simulation studies are made to compare the time domain technique with the Fourier frequency analysis for spectral time lags. The time domain technique is applied to studying rapid variabilities of X-ray binaries and γ-ray bursts. The results indicate that in comparison with the Fourier analysis the timescale analysis technique is more powerful for the study of spectral lags in rapid variabilities on short time scales and short duration flaring phenomena.     

Time-scales in long gamma-ray bursts

We analyse a sample of bright long bursts and find that the pulse durations have a lognormal distribution while the intervals between pulses have an excess of long intervals (relative to lognormal distribution). This excess can be explained by the existence of quiescent times , long periods with no signal above the background level. The lognormal distribution of the intervals (excluding the quiescent times ) is similar to the distribution of the pulse widths. This result suggests that the quiescent times are made by a different mechanism than the rest of the intervals. It also suggests that the intervals (excluding the quiescent times ) and the pulse width are connected to the same parameters of the source. We find that there is a correlation between a pulse width and the duration of the interval preceding it. There is a weaker, but still a significant, correlation between a pulse width and the interval following it. The significance of the correlation drops substantially when the intervals considered are not adjacent to the pulse.     

A unified picture for the γ-ray and prompt optical emissions of GRB 990123

The prompt optical emission of GRB 990123 was uncorrelated to the γ-ray light curve and exhibited temporal properties similar to those of the steeply decaying, early X-ray emission observed by Swift at the end of many bursts. These facts suggest that the optical counterpart of GRB 990123 was the large-angle emission released during (the second pulse of) the burst. If the optical and γ-ray emissions of GRB 990123 have, indeed, the same origin then their properties require that (i) the optical counterpart was synchrotron emission and γ-rays arose from inverse-Compton scatterings (the 'synchrotron self-Compton model'), (ii) the peak energy of the optical-synchrotron component was at ∼20 eV and (iii) the burst emission was produced by a relativistic outflow moving at Lorentz factor  ≳450  and at a radius  ≳10¹⁵  cm, which is comparable to the outflow deceleration radius. Because the spectrum of GRB 990123 was optically thin above 2 keV, the magnetic field behind the shock must have decayed on a length-scale of  ≲1  per cent  of the thickness of the shocked gas, which corresponds to  10⁶–10⁷  plasma skin depths. Consistency of the optical counterpart decay rate and its spectral slope (or that of the burst, if they represent different spectral components) with the expectations for the large-angle burst emission represents the most direct test of the unifying picture proposed here for GRB 990123.     

Spectral lags and the energy dependence of pulse width in gamma-ray bursts: contributions from the relativistic curvature effect

We compute the temporal profiles of the gamma-ray burst pulse in the four Burst and Transient Source Experiment (BATSE) Large Area Detector (LAD) discriminator energy channels, with the relativistic curvature effect of an expanding fireball being explicitly investigated. Assuming an intrinsic 'Band' shape spectrum and an intrinsic energy-independent emission profile, we show that merely the curvature effect can produce detectable spectral lags if the intrinsic pulse profile has a gradually decaying phase. We examine the spectral lag's dependences on some physical parameters, such as the Lorentz factor Γ, the low-energy spectral index, α, of the intrinsic spectrum, the duration of the intrinsic radiation   t '_d  and the fireball radius R . It is shown that approximately the lag  ∝Γ⁻¹  and  ∝ t '_d  , and a spectrum with a more extruded shape (a larger α) causes a larger lag. We find no dependence of the lag on R . Quantitatively, the lags produced from the curvature effect are marginally close to the observed ones, while larger lags require extreme physical parameter values, e.g.  Γ < 50  , or  α > −0.5  . The curvature effect causes an energy-dependent pulse width distribution but the energy dependence of the pulse width we obtained is much weaker than the observed   W ∝ E ^−0.4  one. This indicates that some intrinsic mechanism(s), other than the curvature effect, dominates the pulse narrowing of gamma-ray bursts.     

A Test on Different Types of the Time Curve of Hardness Ratio of Gamma-Ray Bursts based on the Curvature Effect

We analyzed a sample of 66 gamma-ray bursts (GRBs) and statistically confirmed the prediction on the time curve of the hardness ratio of GRBs made by Qin et al. based on the curvature effect. In their analysis, GRB pulses are divided into three types according to the shape of their raw hardness ratio (RHR) time curves, defined as to include the background counts to the signal counts, so as to make use of counts within small time intervals. Of the three types, very hard sources exhibit a perfect pulse-like profile (type 1), hard bursts possess a pulse-like profile with a dip in the decay phase (type 2), and soft bursts show no pulse-like profile but have only a dipped profile (type 3). In terms of the conventional hardness ratio, type 3 sources are indeed generally softer than those of type 1 and type 2, in agreement with the prediction. We found that the minimum value of RHR is sensitive in distinguishing the different types. We propose that GRB pulses can be classified according to the minimum value of RHR and that the different type sources may be connected with different strengths of the shock or/and the magnetic field.     

A Close Correlation between the Spectral Lags and Redshifts of Gamma-Ray Bursts

Based on nine BATSE GRBs with known redshifts, we found that the maximum spectral lag of all the pulses in a gamma-ray burst (GRB) appears to be anti-correlated with the redshift of the burst. In order to confirm this finding, we analyzed 10 GRBs detected by HETE-2 with known redshifts and found a similar relation. Using the relation, we estimated the redshifts of 878 long GRBs in the BATSE catalog, then we investigated the distributions of the redshifts and 869 Eiso of these GRBs. The distribution of the estimated redshifts is concentrated at z = 1.4 and the distribution of Eiso peaks at 1052.5 erg. The underlying physics of the correlation is unclear at present.     

Millisecond pulsar radiation properties

Two investigations of millisecond pulsar radiation are discussed: average total intensity pulse morphology and individual pulse to pulse fluctuations. The average emission profiles of millisecond pulsars are compared with those of slower pulsars in the context of polar cap models. In general the full widths of pulsar emission regions continue to widen inversely with periodP as P^-(0.30-0.5) as expected for dipole polar cap models. Many pulse components are very narrow. The period scaling of pulsar profiles -separations and widths -can tell us about the angular distribution of radiating currents. An investigation of individual pulses from two millisecond pulsars at 430 MHz shows erratic pulse to pulse variations similar to that seen in slow pulsars. PSR B1937+21 displays occasional strong pulses that are located in the trailing edge of the average profile with relative flux densities in the range of 100 to 400. These are similar to the giant pulses seen in the Crab pulsar.     

Comparison between Swift and pre-Swift gamma-ray bursts

The gamma-ray burst (GRB) mission Swift has made a much deeper GRBsurvey than any previous one. I present a systematical comparison between GRB samples detected with pre-Swift missions and those from Swift, in order to investigate whether they show any statistical difference. Our Swift GRB sample includes the bursts detected by Swift/BAT before 2007 September. With both flux-limited surveys and redshift-known GRB samples, I show that, apparently, the observed distributions of the redshifts, T90, and log N-log P are significantly different, but not for the spectral hardness ratio, fluence and Eiso. The redshifts of the Swift GRB sample are statistically larger than those of pre-Swift GRBs, with a mean of 1.95±0.17 compared to ～ 1 for pre-Swift GRBs. The cosmological effect on the observables is thus considerable. This effect on the spectral hardness ratio, fluence and Eiso is cancelled out, and the distributions of these quantities indeed do not show significant differences between the Swift and pre-Swift GRBs. Taking this effect into account, I found that the corrected distributions of T90 for long GRBs and log N - log P observed with Swift/BAT are also consistent with those observed with CGRO/BATSE. These results indicate that the Swift and pre-Swift GRBs are from the same population.     

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  .     

Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n _ext ∝  R ^{− k} , we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t _⊕ =  R /4(4− k ) γ²c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t _co = 2 R /(5− k ) γc. We next study the evolution of the fireball by using the analytic solution of Blandford &38; McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p  = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k  = 2.     

Studying the SN‐GRB connection with X‐shooter: The GRB 100316D / SN 2010bh case

During the last ten years, observations of long‐duration gamma‐ray bursts brought to the conclusion that at least a fraction of them is associated with bright supernovae of type Ib/c. In this talk, after a short review on the previously observed GRB‐SN connection cases, we present the recent case of GRB 100316/SN 2010bh. In particular, during the observational campaign of SN 2010bh, a pivotal role was played by VLT/X‐shooter, sampling with unique high quality data the spectral energy distribution of the early evolution phases from the UV to the K band (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)