The Spatial Distribution of Gamma-Ray Bursts with Measured Redshifts from 24 Years of Observation.

Gamma-ray bursts (GRBs) are the most luminous objects known: they outshine their host galaxies, making them ideal candidates for probing large-scale structure. Our aim is to determine the Spatial Two-Point Correlation Function of the GRBs with spectroscopic redshifts. We used all observations till 4 June 2021, and we also split the data according to the origin of the redshift (afterglow or host galaxy). We analyzed the possible correlation between the GRB redshift and sky position. There is only one region, called the Faraway GRB Patch, where nine distant GRBs shows deviation from the randomness with an ≈1% significance, showing that the sky and the radial component of the GRB distribution could be factorized and both can be determined independently. The GRBs' cumulative monthly distribution was used to show that it is impossible to synthesize the Sky Exposure Function, even from the perfect observational logs. We estimated the Sky Exposure Function using the Gaussian kernel, and with the radial distribution, it was used for the estimation of the Spatial Two-Point Correlation Function. Monte Carlo simulations were used to determine the Poissonian errors. Our result shows that the current Spatial Two-Point Correlation Function estimations are consistent with zero for the full and the afterglow/host galaxy datasets. [ABSTRACT FROM AUTHOR]