Improved correlation between the variability and peak luminosity of gamma-ray bursts

A new procedure for smoothing a gamma-ray burst (GRB) light curve and calculating its variability is presented. Applying the procedure to a sample of 25 long GRBs, we have obtained a very tight correlation between the variability and the peak luminosity. The only significant outlier in the sample is GRB 030329. With this outlier excluded, the data scatter is reduced by a factor of ∼3 compared to that of Guidorzi et al., measured by the deviation of fit. Possible causes for the outlier are discussed.     

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.     

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.     

A statistical study of gamma-ray burst afterglows measured by the Swift Ultraviolet Optical Telescope

We present the first statistical analysis of 27 Ultraviolet Optical Telescope (UVOT) optical/ultraviolet light curves of gamma-ray burst (GRB) afterglows. We have found, through analysis of the light curves in the observer's frame, that a significant fraction rise in the first 500 s after the GRB trigger, all light curves decay after 500 s, typically as a power law with a relatively narrow distribution of decay indices, and the brightest optical afterglows tend to decay the quickest. We find that the rise could be either produced physically by the start of the forward shock, when the jet begins to plough into the external medium, or geometrically where an off-axis observer sees a rising light curve as an increasing amount of emission enters the observers line of sight, which occurs as the jet slows. We find that at 99.8 per cent confidence, there is a correlation, in the observed frame, between the apparent magnitude of the light curves at 400 s and the rate of decay after 500 s. However, in the rest frame, a Spearman rank test shows only a weak correlation of low statistical significance between luminosity and decay rate. A correlation should be expected if the afterglows were produced by off-axis jets, suggesting that the jet is viewed from within the half-opening angle θ or within a core of a uniform energy density  θ_c  . We also produced logarithmic luminosity distributions for three rest-frame epochs. We find no evidence for bimodality in any of the distributions. Finally, we compare our sample of UVOT light curves with the X-ray Telescope (XRT) light-curve canonical model. The range in decay indices seen in UVOT light curves at any epoch is most similar to the range in decay of the shallow decay segment of the XRT canonical model. However, in the XRT canonical model, there is no indication of the rising behaviour observed in the UVOT light curves.     

Evidence for luminosity evolution of long gamma-ray bursts in Swift data

We compute the luminosity function (LF) and the formation rate of long gamma-ray bursts (GRBs) by fitting the observed differential peak flux distribution obtained by the Burst and Transient Source Experiment (BATSE) in two different scenarios: (i) the GRB luminosity evolves with redshift and (ii) GRBs form preferentially in low-metallicity environments. In both cases, model predictions are consistent with the Swift number counts and with the number of detections at   z > 2.5  and >3.5. To discriminate between the two evolutionary scenarios, we compare the model results with the number of luminous bursts (i.e. with isotropic peak luminosity in excess of 10⁵³ erg s⁻¹) detected by Swift in its first 3 yr of mission. Our sample conservatively contains only bursts with good redshift determination and measured peak energy. We find that pure luminosity evolution models can account for the number of sure identifications. In the case of a pure density evolution scenario, models with   Z _th > 0.3 Z_⊙  are ruled out with high confidence. For lower metallicity thresholds, the model results are still statistically consistent with available lower limits. However, many factors can increase the discrepancy between model results and data, indicating that some luminosity evolution in the GRB LF may be needed also for such low values of Z _th. Finally, using these new constraints, we derive robust upper limits on the bright end of the GRB LF, showing that this cannot be steeper than ∼2.6.     

Jet breaks in the X-ray light-curves of Swift gamma-ray burst afterglows

In the set of 236 gamma-ray burst (GRB) afterglows observed by Swift between 2005 January and 2007 March, we identify 30 X-ray light-curves that have power-law fall-offs that exhibit a steepening ('break') at 0.1–10 d after they are triggered, to a decay steeper than t ^−1.5. For most of these afterglows, the X-ray spectral slope and the decay indices before and after the break can be accommodated by the standard jet model although a different origin of the breaks cannot be ruled out. In addition, there are 27 other afterglows which have X-ray light-curves that may also exhibit a late break to a steep decay, but the evidence is not that compelling. The X-ray emissions of 38 afterglows decay slower than t ^−1.5 until after 3 d, half of them exhibiting such a slow decay until after 10 d. Therefore, the fraction of well-monitored Swift afterglows with potential jet breaks is around 60 per cent, whether we count only the strongest cases for each type or all of them. This fraction is comparable to the 75 per cent of pre-Swift afterglows which have optical light-curves that displayed similar breaks at ∼1 d. The peak energy of the GRB spectrum of Swift afterglows with light-curve breaks shows the same correlations with the burst isotropic output (Amati relation) and with the burst collimated output (Ghirlanda relation) as previously found for pre- Swift optical afterglows with light-curve breaks. However, we find that the Ghirlanda relation is largely a consequence of Amati's and that the use of the jet-break time leads to a stronger Ghirlanda correlation only when the few objects that do not satisfy the Amati relation are included.     

Tail emission of prompt gamma-ray burst jets

Tail emission of the prompt gamma-ray burst (GRB) is discussed using a multiple emitting sub-shell (inhomogeneous jet, sub-jets or mini-jets) model, where the whole GRB jet consists of many emitting sub-shells. One may expect that such a jet with angular inhomogeneity should produce spiky tail emission. However, we found that the tail is not spiky but is decaying roughly monotonically. The global decay slope of the tail is not so much affected by the local angular inhomogeneity but affected by the global sub-shell energy distribution. The fact that steepening GRB tail breaks appeared in some events prefers the structured jets. If the angular size of the emitting sub-shell is around 0.01–0.02 rad, some bumps or fluctuations appear in the tail emission observed frequently in long GRBs. If the parameter differences of sub-shell properties are large, the tail has frequent changes of the temporal slope observed in a few bursts. Therefore, the multiple emitting sub-shell model has the advantage of explaining the small-scale structure in the observed rapid decay phase.     

Are there cosmological evolution trends on gamma-ray burst features?

The variability of a gamma-ray burst (GRB) is thought to be correlated with its absolute peak luminosity, and this relation had been used to derive an estimate of the redshifts of GRBs. Recently, Amati et al. presented the results of spectral and energetic properties of several GRBs with known redshifts. Here, we analyse the properties of two groups of GRBs: one group with known redshift from afterglow observation and another group with redshift derived from the luminosity–variability relation. We study the redshift dependence of various GRBs features in their cosmological rest frames, including the burst duration, the isotropic luminosity and radiated energy, and the peak energy E_p of ν F _ν spectra. We find that, for these two groups of GRBs, their properties are all redshift-dependent, i.e. their intrinsic duration, luminosity, radiated energy and peak energy E_p are all correlated with the redshift, which means that there are cosmological evolution effects on gamma-ray burst features, and this can provide an interesting clue to the nature of GRBs. If this is true, then the results also imply that the redshift derived from the luminosity–variability relation may be reliable.     

Reverse shock emission as a probe of gamma-ray burst ejecta

We calculate the reverse shock (RS) synchrotron emission in the optical and the radio wavelength bands from electron–positron pair-enriched gamma-ray burst ejecta with the goal of determining the pair content of gamma-ray bursts (GRBs) using early-time observations. We take into account an extensive number of physical effects that influence radiation from the RS-heated GRB ejecta. We find that optical/infrared flux depends very weakly on the number of pairs in the ejecta, and there is no unique signature of ejecta pair enrichment if observations are confined to a single wavelength band. It may be possible to determine if the number of pairs per proton in the ejecta is ≳100 by using observations in optical and radio bands; the ratio of flux in the optical and radio at the peak of each respective RS light curve is dependent on the number of pairs per proton. We also find that over a large parameter space, RS emission is expected to be very weak; GRB 990123 seems to have been an exceptional burst in that only a very small fraction of the parameter space produces optical flashes this bright. Also, it is often the case that the optical flux from the forward shock is brighter than the RS flux at deceleration. This could be another possible reason for the paucity of prompt optical flashes with a rapidly declining light curve at early times as was seen in GRBs 990123 and 021211. Some of these results are a generalization of similar results reported in Nakar & Piran.