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 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)

Properties of the intermediate type of gamma-ray bursts

Gamma-ray bursts can be divided into three groups ("short", "intermediate", "long") with respect to their durations. The third type of gamma-ray bursts - as known - has the intermediate duration. We show that the intermediate group is the softest one. An anticorrelation between the hardness and the duration is found for this subclass in contrast to the short and long groups.Comment: In Sixteenth Maryland Astrophysics Conferenc

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 non-zero 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 increased attention on the related hardness ratio $H43$ appears 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 performing various corrections on available measurementsComment: Ap.J., accepted 12/9/97; revised version contains a new appendix, somewhat expanded discussion; latex, aaspp4, 15 page