On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature at about t − t ₀=3.8 d. This event was interpreted as gravitational microlensing by Garnavich, Loeb & Stanek and subsequently used to derive constraints on the structure of the GRB optical afterglow. In this paper, we use these structural parameters to calculate the probability of such a microlensing event in a realistic scenario, where all compact objects in the universe are associated with observable galaxies. For GRB000301C at a redshift of z =2.04, the a posteriori probability for a microlensing event with an amplitude of Δ m 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat Λ-dominated Friedmann–Robertson–Walker (FRW) universe with Ω_m=0.3 and a fraction f ∗=0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Δ m 0.10 mag, the probabilities for microlensing events of GRB afterglows increase to 17 per cent (57 per cent). We emphasize that this low probability for a microlensing signature of almost 1 mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especially in light of the fact that a galaxy was found within 2 arcsec from the GRB. In that case, however, a more robust upper limit on the a posteriori probability of ≈5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow microlensing events for statistical studies of their physical conditions on microarcsec scales.     

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.     

Star formation history up to z= 7.4: implications for gamma-ray bursts and cosmic metallicity evolution

The current Swift sample of gamma-ray bursts (GRBs) with measured redshifts allows us to test the assumption that GRBs trace star formation in the Universe. Some authors have claimed that the rate of GRBs increases with cosmic redshift faster than the star formation rate, whose cause is not yet known. In this paper, I investigate the possibility of interpreting the observed discrepancy between the GRB rate history and the star formation rate history using cosmic metallicity evolution. I am motivated by the observation that cosmic metallicity evolves with redshift and GRBs tend to occur in low-metallicity galaxies. First, I derive a star formation history up to redshift   z = 7.4  from an updated sample of star formation rate densities. This is obtained by adding the new ultraviolet measurements of Bouwens et al. and the new ultraviolet and infrared measurements of Reddy et al. to the existing sample compiled by Hopkins & Beacom. Then, adopting a simple model for the relation between GRB production and the cosmic metallicity history as proposed by Langer & Norman, I show that the observed redshift distribution of the Swift GRBs can be reproduced with good accuracy. Although the results are limited by the small size of the GRB sample and the poorly understood selection biases in detection and localization of GRBs and in redshift determination, they suggest that GRBs trace both star formation and metallicity evolution. If the star formation history can be accurately measured with other approaches, which is presumably achievable in the near future, it will be possible to determine the cosmic metallicity evolution using the study of the redshift distribution of GRBs.     

Testing the gamma-ray burst variability/peak luminosity correlation on a Swift homogeneous sample

We test the gamma-ray burst (GRB) correlation between temporal variability and peak luminosity of the γ-ray profile on a homogeneous sample of 36 Swift /Burst Alert Telescope (BAT) GRBs with firm redshift determination. This is the first time that this correlation can be tested on a homogeneous data sample. The correlation is confirmed, as long as the six GRBs with low luminosity (  <5 × 10⁵⁰   erg s⁻¹  in the rest-frame 100–1000 keV energy band) are ignored. We confirm that the considerable scatter of the correlation already known is not due to the combination of data from different instruments with different energy bands, but it is intrinsic to the correlation itself. Thanks to the unprecedented sensitivity of Swift /BAT, the variability/peak luminosity correlation is tested on low-luminosity GRBs. Our results show that these GRBs are definite outliers.     

Precursor activity in bright, long BATSE gamma-ray bursts

We study a sample of bright, long Burst and Transient Source Experiment (BATSE) gamma-ray burst (GRB) light curves in the 200 s before the detection of the GRB prompt emission. We find that in a sizable fraction of cases (∼20 per cent) there is evidence of emission above the background coming from the same direction as the GRB. This emission is characterized by a softer spectrum with respect to the main spectrum and contains a small fraction (0.1–1 per cent) of the total event counts. The precursors have typical delays of several tens of seconds extending (in few cases) up to 200 s (the limit of the investigated period). Their spectra are typically non-thermal power-law spectra, aside from a few cases. Such long delays and the non-thermal origin of their spectra are hard to reconcile with any model for the progenitor.     

Millimetric properties of gamma-ray burst host galaxies

We present millimetre (mm) and submillimetre (submm) photometry of a sample of five host galaxies of gamma-ray bursts (GRBs), obtained using the Max Planck Millimetre Bolometer (MAMBO2) array and Submillimetre Common-User Bolometer Array (SCUBA). These observations were obtained as part of an ongoing project to investigate the status of GRBs as indicators of star formation. Our targets include two of the most unusual GRB host galaxies, selected as likely candidate submm galaxies: the extremely red  ( R − K ≈ 5)  host of GRB 030115, and the extremely faint  ( R > 29.5)  host of GRB 020124. Neither of these galaxies is detected, but the deep upper limits for GRB 030115 impose constraints on its spectral energy distribution, requiring a warmer dust temperature than is commonly adopted for submillimetre galaxies (SMGs).
As a framework for interpreting these data, and for predicting the results of forthcoming submm surveys of Swift -derived host samples, we model the expected flux and redshift distributions based on luminosity functions of both submm galaxies and GRBs, assuming a direct proportionality between the GRB rate density and the global star formation rate density. We derive the effects of possible sources of uncertainty in these assumptions, including (1) introducing an anticorrelation between GRB rate and the global average metallicity, and (2) varying the dust temperature.     

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.     

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.     

Gamma-ray bursts from stellar remnants: probing the Universe at high redshift

A gamma-ray burst (GRB) releases an amount of energy similar to that of a supernova explosion, which combined with its rapid variability suggests an origin related to neutron stars or black holes. Since these compact stellar remnants form from the most massive stars not long after their birth, GRBs should trace the star formation rate in the Universe; we show that the GRB flux distribution is consistent with this. Because of the strong evolution of the star formation rate with redshift, it follows that the dimmest known bursts have z  ∼ 6, much above the value usually quoted and beyond the most distant quasars. This explains the absence of bright galaxies in well-studied GRB error boxes. The increased distances imply a peak luminosity of 8.3 × 10⁵¹ erg s⁻¹ and a rate density of 0.025 per million years per galaxy. These values are 20 times higher and 150 times lower, respectively, than are implied by fits with non-evolving GRB rates. This means either that GRBs are caused by a much rarer phenomenon than mergers of binary neutron stars, or that their gamma-ray emission is often invisible to us due to beaming. Precise burst locations from optical transients will discriminate between the various models for GRBs from stellar deaths, because the distance between progenitor birth place and burst varies greatly among them. The dimmest GRBs are then the most distant known objects, and may probe the Universe at an age when the first stars were forming.     

Testing the Ep,i–Lp,iso–T0.45 correlation on a BeppoSAX and Swift sample of gamma-ray bursts

Using a sample of 14 BeppoSAX and 74 Swift GRBs with measured redshift we tested the correlation between the intrinsic peak energy of the time-integrated spectrum,   E _{p, i}   , the isotropic-equivalent peak luminosity,   L _p,iso  , and the duration of the most intense parts of the GRB computed as T _0.45 ('Firmani correlation'). For 41 out of 88 GRBs we could estimate all of the three required properties. Apart from 980425, which appears to be a definite outlier and notoriously peculiar in many respects, we used 40 GRBs to fit the correlation with the maximum likelihood method discussed by D'Agostini, suitable to account for the extrinsic scatter in addition to the intrinsic uncertainties affecting every single GRB. We confirm the correlation. However, unlike the results by Firmani et al., we found that the correlation does have a logarithmic scatter comparable with that of the   E _{p, i} – E _iso  ('Amati') correlation. We also find that the slope of the product   L _p,iso  T _0.45  is equal to ∼0.5, which is consistent with the hypothesis that the   E _{p, i} – L _p,iso– T _0.45  correlation is equivalent to the   E _{p, i} – E _iso  correlation (slope ∼0.5). We conclude that, based on presently available data, there is no clear evidence that the   E _{p, i} – L _p,iso– T _0.45  correlation is different (both in terms of slope and dispersion) from the   E _{p, i} – E _iso  correlation.     

Strong correlation between the peak power density in the time domain and the luminosity of long γ-ray bursts

This work presents a possible luminosity estimator for long γ-ray bursts (GRBs) based on their light curves. We use the method of variability analysis in the time domain to calculate the power density spectrum (PDS) for each of the 12 GRBs with known redshifts observed by CGRO/BATSE. The peak of the power density spectrum P is a measure of the intensity of variability of the given light curve and a strong correlation is found between P and the isotropic peak luminosity L of the GRB. It is a successor to the lag-luminosity relation of Norris et al. (2000) and the variability-luminosity relation of Reichart et al. (2001).     

Energetics–spectral correlations versus the BATSE gamma-ray bursts population

The proposed correlations between the energetics of gamma-ray bursts (GRBs) and their spectral properties, namely the peak energy of their prompt emission, can broadly account for the observed fluence distribution of all 'bright' BATSE GRBs, under the hypothesis that the GRB rate is proportional to the star formation rate and that the observed distribution in peak energy is independent of redshift. The correlations can also be broadly consistent with the properties of the whole BATSE long GRB population for a peak energy distribution smoothly extending towards lower energies, and in agreement with the properties of a sample at 'intermediate' fluences and with the luminosity functions inferred from the GRB number counts. We discuss the constraints that this analysis imposes on the shape of such peak energy distribution, the opening angle distribution and the tightness of the proposed correlations.     

Searching for multifractal scaling in gamma ray burst time series

We present a multifractal analysis of GRB time series used to quantify the variability of the light curve. We discuss the advantages and disadvantages of multifractal analysis, including sensitivity to noise, and burst intensity, and present results for a few sample bursts.     

A mini-supernova model for optical afterglows of gamma-ray bursts

An energy deposition of ∼10⁵⁰ erg into the exterior 10⁻³ M⊙ layers of a red giant is calculated to produce an optical phenomenon similar to afterglows of gamma-ray bursts (GRB) recently observed. This mechanism can be realized if a GRB is generated by some mechanism in a close binary system. In contrast to a 'hypernova' scenario for GRB recently proposed by Paczyński, this model does not require huge kinetic energy in the expanding shell to explain optical afterglows of GRB.     

Time-dependent photoionization opacities in dense gamma-ray burst environments

The recent detection of a transient absorption feature in the X-ray prompt emission of GRB 990705 showed the importance of such observations in the understanding of gamma-ray bursts and their progenitors. We investigate the time dependence of photoionization edges during the prompt emission of bursts in different environments. We show that their variability can be used to infer the density and geometry of the surrounding medium, giving important clues to unveil the nature of the burst progenitor.     

Can all breaks in gamma-ray burst afterglows be explained by jet effects?

Whether gamma-ray bursts are highly beamed or not is a very important question, as it has been pointed out that the beaming will lead to a sharp break in the afterglow light curves during the ultrarelativistic phase, with the breaking point determined by  Γ∼1/ θ ₀  , where Γ is the bulk Lorentz factor and θ ₀ is the initial half opening angle of the ejecta, and such a break is claimed to be present in the light curves of some GRBs. In this paper we will examine whether all the observed breaks in GRB afterglow light curves can be explained by jet effects. Here we present a detailed calculation of the jet evolution and emission, and have obtained a simple formula of bulk Lorentz factor evolution. We show that the light curves are very smoothly steepened by jet effect, and the shape of the light curve is determined by only one parameter –     , where E and n are the fireball energy and surrounding medium density, respectively. We find that for GRB 990123 and GRB 991216, the jet model can approximately fit their light curves, and the values of     are about 0.17 and 0.22, respectively. On the other hand, the light curves of GRB 990510, GRB 000301c, GRB 000926 and GRB 010222 cannot be fitted by the jet model, which suggests that the breaks may be caused by some other reasons, and the jet effect should be not the unique reason.     

Confidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightness

A strong correlation between the gamma-ray burster peak energy and the peak luminosity of the associated supernova was discovered by Li for four GRBs. Despite the fact that the formal significance level of the correlation is 0.3 per cent, the smallness of the data set requires careful further evaluation of the result. Subject to the assumption that the data are bivariate Gaussian, a 95 per cent confidence interval of  (−0.9972, 0.02)  for the correlation is derived. Using data from the literature, it is shown that the distribution of known peak GRB energies is not Gaussian if X-ray flashes are included in the sample. This leads to a proposed alternative to the bivariate Gaussian model, which entails describing the dependence between the two variables by a Gaussian copula. The copula is still characterized by a correlation coefficient. The Bayesian posterior distribution of the correlation coefficient is evaluated using a Markov chain Monte Carlo method. The mean values of the posterior distributions range from −0.33 to about zero, depending on the specifics of the supernova (SN) peak brightness distribution. The implication is that the existing data favour a modest correlation between the GRB peak energy and the SN peak brightness; confidence intervals are very wide and include zero.     

The visibility of gamma-ray burst afterglows in dusty star-forming regions

Recent observations of the environments of gamma-ray bursts (GRBs) favour massive stars as their progenitors, which are likely to be surrounded by gas and dust. The visibility of the optical and UV emission of a GRB is expected to depend on the characteristics of both the dust and the GRB emission itself. A reasonable distribution of surrounding dust is capable of absorbing all the optical and UV emission of the optical flash and afterglow of a GRB, unless the optical flash has a peak isotropic luminosity L _peak≳10⁴⁹ erg s⁻¹ . This means that dark bursts should exist and these bursts will have to be studied at infrared rather than optical wavelengths. In this paper details will be given about the infrared GRB dust emission. The reprocessed dust emission peaks at a rest-frame wavelength of about 8 μm. Forthcoming space telescopes, in particular the IRAC camera on board the Space Infrared Telescope Facility , could detect this emission out to a redshift of about two. However, an accurate position of the GRB afterglow must be provided for this emission to be identified, because the light curve of the reprocessed dust emission does not vary on time-scales less than several years.     

The rest-frame ultraviolet spectra of GRBs from massive rapidly rotating stellar progenitors

The properties of a massive star prior to its final explosion are imprinted in the circumstellar medium (CSM) created by its wind and termination shock. We perform a detailed, comprehensive calculation of the time-variable and angle-dependent transmission spectra of an average-luminosity gamma-ray burst (GRB) which explodes in the CSM structure produced by the collapse of a  20 M_⊙  , rapidly rotating,   Z = 0.001  progenitor star. We study both the case in which metals are initially in the gaseous phase and the situation in which they are heavily depleted into dust. We find that high-velocity lines from low-ionization states of silicon, carbon and iron are initially present in the spectrum only if the metals are heavily depleted into dust prior to the GRB explosion. However, such lines disappear on time-scales of a fraction of a second for a burst observed on-axis, and of a few seconds for a burst seen at high latitude, making their observation virtually impossible. Rest-frame lines produced in the termination shock are instead clearly visible in all conditions. We conclude that time-resolved, early-time spectroscopy is not a promising way in which the properties of the GRB progenitor wind can be routinely studied. Previous detections of high-velocity features in GRB ultraviolet spectra must have been either due to a superposition of a physically unrelated absorber or due to a progenitor star with very unusual properties.     

Status of the ROTSE‐III telescope network

ROTSE‐III is a homogeneous worldwide array of 4 robotic telescopes. They were designed to provide optical observations of γ ‐ray burst (GRB) afterglows as close as possible to the start of γ ‐ray emission. ROTSE‐III is fulfilling its potential for GRB science, and provides optical observations for a variety of astrophysical sources in the interim between GRB events. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)