The Two-Point Correlation Function of Gamma-ray Bursts

Abstract

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), $\xi (r)$ 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 $\Lambda$, with $({\Omega }_{\mathrm{m}},{\Omega }_{\mathrm{\Lambda }})=(0.28,0.72)$ and an Einstein-de Sitter (EdS) universe, with $({\Omega }_{\mathrm{m}},{\Omega }_{\mathrm{\Lambda }})=(1,0)$. 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 $\xi (r)=(r/r_0{)}^{-\gamma }$ to the measured $\xi (r)$ and obtain an amplitude and slope of $r_0=1235.2\pm 342.6h^{-1}$ Mpc and $\gamma =0.80\pm 0.19$ ($1\sigma$ 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 $200h^{-1}$ Mpc is usually described by the correlation function of galaxies.

25 pages, 7 figures, 3 tables

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