Lajos G. Balázs

A new definition of the intermediate group of gamma-ray bursts

Gamma-ray bursts can be divided into three groups (short, intermediate, long) with respect to their durations. This classification is somewhat imprecise, since the subgroup of intermediate duration has an admixture of both short and long bursts. In this paper a physically more reasonable definition of the intermediate group is presented, using also the hardnesses of the bursts. It is shown again that the existence of the three groups is real, no further groups are needed. The intermediate group is the softest one. From this new definition it follows that 11% of all bursts belong to this group. An anticorrelation between the hardness and the duration is found for this subclass in contrast to the short and long groups. Despite this difference it is not clear yet whether this group represents a physically different phenomenon.

Classification of Swift's gamma-ray bursts

Context. Two classes of gamma-ray bursts have been identified in the BATSE catalogs characterized by durations shorter and longer than about 2 seconds. There are, however, some indications for the existence of a third class. Swift satellite detectors have different spectral sensitivity than pre-Swift ones for gamma-ray bursts. Therefore we reanalyze the durations and their distribution and also the classification of GRBs. Aims. We analyze the bursts duration distribution, published in The First BAT Catalog, whether it contains two, three or more groups. Methods. Using The First BAT Catalog the maximum likelihood estimation was used to analyze the duration distribution of GRBs. Results. The three log-normal fit is significantly (99.54% probability) better than the two for the duration distribution. Monte-Carlo simulations also confirm this probability (99.2%). Similarly, in previous results we found that the fourth component is not needed. The relative frequencies of the distribution of the groups are 7% short 35% intermediate and 58% long. Conclusions. Similarly to the BATSE data, three components are needed to explain the BAT GRBs’ duration distribution. Although the relative frequencies of the groups are different than in the BATSE GRB sample, the difference in the instrument spectral sensitivities can explain this bias. This means theoretical models may be needed to explain three different type of gamma-ray bursts.

On the difference between the short and long gamma-ray bursts

We argue that the distributions of both the intrinsic fluence and the intrinsic duration of the γ-ray emission in gamma- ray bursts from the BATSE sample are well represented by log-normal distributions, in which the intrinsic dispersion is much larger than the cosmological time dilatation and redshift effects. We perform separate bivariate log-normal distribution fits to the BATSE short and long burst samples. The bivariate log-normal behaviour results in an ellipsoidal distribution, whose major axis determines an overall statistical relation between the fluence and the duration. We show that this fit provides evidence for a power-law dependence between the fluence and the duration, with a statistically significant different index for the long and short groups. We discuss possible biases, which might affect this result, and argue that the effect is probably real. This may provide a potentially useful constraint for models of long and short bursts.

A DISTINCT PEAK-FLUX DISTRIBUTION OF THE THIRD CLASS OF GAMMA-RAY BURSTS: A POSSIBLE SIGNATURE OF X-RAY FLASHES?

Gamma-ray bursts (GRBs) are the most luminous events in the universe. Going beyond the short-long classification scheme, we work in the context of three burst populations with the third group of intermediate duration and softest spectrum. We are looking for physical properties which discriminate the intermediate duration bursts from the other two classes. We use maximum likelihood fits to establish group memberships in the duration-hardness plane. To confirm these results we also use k-means and hierarchical clustering. We use Monte Carlo simulations to test the significance of the existence of the intermediate group and we find it with 99.8% probability. The intermediate duration population has a significantly lower peak flux (with 99.94% significance). Also, long bursts with measured redshift have higher peak fluxes (with 98.6% significance) than long bursts without measured redshifts. As the third group is the softest, we argue that we have related them with X-ray flashes among the GRBs. We give a new, probabilistic definition for this class of events.

Testing the randomness in the sky-distribution of gamma-ray bursts

We have studied the complete randomness of the angular distribution of gamma-ray bursts (GRBs) detected by the Burst and Transient Source Experiment (BATSE). Because GRBs seem to be a mixture of objects of different physical nature, we divided the BATSE sample into five subsamples (short1, short2, intermediate, long1, long2) based on their durations and peak fluxes, and we studied the angular distributions separately. We used three methods, Voronoi tesselation, minimal spanning tree and multifractal spectra, to search for non-randomness in the subsamples. To investigate the eventual non-randomness in the subsamples, we defined 13 test variables (nine from the Voronoi tesselation, three from the minimal spanning tree and one from the multifractal spectrum). Assuming that the point patterns obtained from the BATSE subsamples are fully random, we made Monte Carlo simulations taking into account the BATSEs sky-exposure function. The Monte Carlo simulations enabled us to test the null hypothesis (i.e. that the angular distributions are fully random). We tested the randomness using a binomial test and by introducing squared Euclidean distances in the parameter space of the test variables. We concluded that the short1 and short2 groups deviate significantly (99.90 and 99.98 per cent, respectively) from the full randomness in the distribution of the squared Euclidean distances; however, this is not the case for the long samples. For the intermediate group, the squared Euclidean distances also give a significant deviation (98.51 per cent).

The Swift satellite and redshifts of long gamma-ray bursts

Until 6 October 2005 sixteen redshifts had been measured of long gamma-ray bursts discovered by the Swift satellite. Further 45 redshifts have been measured of the long gamma- ray bursts discovered by other satellites. Here we perform five statistical tests comparing the redshift distributions of these two samples assuming as the null hypothesis an identical distribution for the two samples. Three tests (Students t-test, Mann-Whitney test, Kolmogorov-Smirnov test) reject the null hypothesis at significance levels between 97.19 and 98.55%. Two different comparisons of the medians show extreme (99.78 - 99.99994)% significance levels of rejection. This means that the redshifts of the Swift sample and the redshifts of the non-Swift sample are distributed differently - in the Swift sample the redshifts are on average larger. This statistical result suggests that the long GRBs should on average be at the higher redshifts of the Swift sample.

A Principal Component Analysis of the 3B Gamma-Ray Burst Data

We have carried out a principal component analysis for 625 gamma-ray bursts in the BATSE 3B catalog for which nonzero values exist for the nine measured variables. This shows that only two out of the three basic quantities of duration, peak flux, and fluence are independent, even if this relation is strongly affected by instrumental effects, and these two account for 91.6% of the total information content. The next most important variable is the fluence in the fourth energy channel (at energies above 320 keV). This has a larger variance and is less correlated with the fluences in the remaining three channels than the latter correlate among themselves. Thus a separate consideration of the fourth channel and an increased attention paid to the related hardness ratio H43 appear useful for future studies. The analysis gives the weights for the individual measurements needed to define a single duration, peak flux, and fluence. It also shows that, in logarithmic variables, the hardness ratio H32 is significantly correlated with peak flux, while H43 is significantly anticorrelated with peak flux. The principal component analysis provides a potentially useful tool for estimating the improvement in information content to be achieved by considering alternative variables or for performing various corrections on available measurements.

A giant ring-like structure at 0.78 <z <0.86 displayed by GRBs

According to the cosmological principle, Universal large-scale structure is homogeneous and isotropic. The observable Universe, however, shows complex structures even on very large scales. The recent discoveries of structures significantly exceeding the transition scale of 370 Mpc pose a challenge to the cosmological principle. We report here the discovery of the largest regular formation in the observable Universe; a ring with a diameter of 1720 Mpc, displayed by 9 gamma ray bursts (GRBs), exceeding by a factor of five the transition scale to the homogeneous and isotropic distribution. The ring has a major diameter of 43 o and a minor diameter of 30 o at a distance of 2770 Mpc in the 0.78 < z < 0.86 redshift range, with a probability of 2 × 10 6 of being the result of a random fluctuation in the GRB count rate. Evidence suggests that this feature is the projection of a shell onto the plane of the sky. Voids and string-like formations are common outcomes of large-scale structure. However, these structures have maximum sizes of 150 Mpc, which are an order of magnitude smaller than the observed GRB ring diameter. Evidence in support of the shell interpretation requires that temporal information of the transient GRBs be included in the analysis. This ring-shaped feature is large enough to contradict the cosmological principle. The physical mechanism responsible for causing it is unknown.

An intrinsic anisotropy in the angular distribution of gamma-ray bursts

The anisotropy of the sky distribution of 2025 gamma-ray bursts (GRBs) collected in Current BATSE catalog is confirmed. It is shown that the quadrupole term being proportional to similar to sin 2b sin I is non-zero with a probability 99.9%. The occurrence of this anisotropy term is then supported by the binomial test even with the probability 99.97%. It is also argued that this anisotropy cannot be caused exclusively by instrumental effects due to the non-uniform sky exposure of BATSE instrument; there should exist also some intrinsic anisotropy in the angular distribution of GRBs. Separating GRBs into short and long subclasses, it is shown that the 251 short ones are distributed anisotropically, but the 681 long ones seem to be distributed still isotropically. The 2-sample Kolmogorov Smirnov test shows that they are distributed differently with a 98.7% probability. The character of anisotropy suggests that the cosmological origin of short GRBs further holds, and there is no evidence for their Galactical origin. The work in essence contains the key ideas and results of a recently published paper (Balazs et al. 1998), to which the new result following from the 2-sample Kolmogorov-Smirnov test is added, too.

Redshift distribution of gamma-ray bursts and star formation rate

Aims. The redshift distribution of gamma-ray bursts collected in the BATSE Catalog is compared with the star formation rate.We aim to clarify the accordance between them. We also study the case of comoving number density of bursts monotonously increasing up to redshift \simeq �(6−20). Methods. A method independent of the models of the gamma-ray bursts is used. The short and the long subgroups are studied separately. Results. The redshift distribution of the long bursts may be proportional to the star formation rate. For the short bursts this can also happen, but the proportionality is less evident. For the long bursts the monotonously increasing scenario is also less probable but still can occur. For the short bursts this alternative seems to be excluded.