The Two-Point Correlation Function of Gamma-ray Bursts

In this paper, we examine the spacial distribution of gamma-ray bursts (GRBs) using a sample of 373 objects. We subdivide the GRB data into two redshift intervals over the redshift range $0<z< 6.7$. We measure the two-point correlation function (2PCF), $ξ(r)$ of the GRBs. In determining the separation distance of the GRB pairs, we consider two representative cosmological models: a cold dark matter universe plus a cosmological constant $Λ$, with $(Ω_{\rm m}, Ω_{\rm Λ})=(0.28,0.72)$ and an Einstein-de Sitter (EdS) universe, with $(Ω_{\rm m}, Ω_{\rm Λ})=(1,0)$. We find a $z$-decreasing correlation of the GRB distribution, which is in agreement with the predictions of the current structure formation theory. We fit a power-law model $ξ(r)=(r/r_0)^{-γ}$ to the measured $ξ(r)$ and obtain an amplitude and slope of $r_0= 1235.2 \pm 342.6~h^{-1}$ Mpc and $γ= 0.80\pm 0.19$ ($1σ$ confidence level) over the scales $r=200$ to $10^4~h^{-1}$ Mpc. Our result provide a supplement to the measurement of matter correlation on large scales, while the matter distribution below $200~h^{-1}$ Mpc is usually described by the correlation function of galaxies.

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