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.

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Abstract. We argue that the distributions of both the intrinsic fluence and the intrinsic duration of the γ-ray emission in gammaray 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.

Abstract. It is known that, theoretically, the Rees-Sciama effect may cause arbitrarily large additional redshifts in the cosmic microwave background radiation due to transparent expanding voids having sizes comparable with the size of horizon. Therefore, again theoretically, eventual huge voids existing immediately after the recombination may essentially change the predictions of the theory of big bang nucleosynthesis. If this eventuality holds, then the dark matter can be dominantly baryonic and, simultaneously, one can be in accordance with the predictions of primordial nucleosynthesis theory. Studying this eventuality one arrives at the result that the observed extreme isotropy of the cosmic microwave background radiation rejects the existence of any such huge voids, and hence this eventuality does not hold.

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 BATSE's 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).

Gamma-ray bursts 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 gamma-ray bursts. We give a new, probabilistic definition for this class of events.

In the article a test is developed, which allows to test the null-hypothesis of the intrinsic randomness in the angular distribution of gamma-ray bursts collected at the Current BATSE Catalog. The method is a modified version of the well-known counts-in-cells test, and fully eliminates the non-uniform skyexposure function of BATSE instrument. Applying this method to the case of 1 all gamma-ray bursts no intrinsic non-randomness was found. The test also did not find intrinsic non-randomnesses for the short and long gamma-ray bursts, respectively. On the other hand, using the method to the new intermediate subclass of gamma-ray bursts, the null-hypothesis of the intrinsic randomness for 181 intermediate gamma-ray bursts is rejected on the 96.4% confidence level. Taking 92 dimmer bursts from this subclass itself, we obtain the surprising result: This "dim" subclass of the intermediate subclass has an intrinsic non-randomness on the 99.3% confidence level. On the other hand, the 89 "bright" GRBs show no intrinsic non-randomness.