Spheroidal Resampling Analysis of High-Redshift Gamma-Ray Burst Spatial Densities
Gamma-ray bursts (GRBs) are bright transient sources that can be observed at high redshift. They can therefore be used as tracers of the distant large-scale structure, although the GRB redshift sample is sparse and affected by strong selection effects. We analyze the three-dimensional distribution of 542 GRBs with spectroscopic redshifts. The method extends our earlier spherical-window search by replacing spherical counting volumes with axisymmetric spheroids. The angular positions of the observed GRBs are kept fixed in the Monte-Carlo null samples, while the redshifts are shuffled within each Galactic hemisphere. In the Northern Galactic hemisphere, the overdensity associated with the Hercules--Corona Borealis Great Wall remains significant for a range of spheroidal shapes. This supports the stability of the previously reported signal and shows that it is not only a consequence of using spherical counting volumes. In the Southern Galactic hemisphere, the same method finds no structure with comparable significance. A small candidate grouping is present, but its significance is only marginal, and it is sensitive to the small number of events. We conclude that spheroidal resampling is a useful check of GRB overdensity searches, but the physical nature of any candidate structure still requires confirmation with independent tracers such as galaxy or quasar samples.