A Constraint on the Distance Scale to Cosmological Gamma-Ray Bursts

If \g--ray bursts are cosmological in origin, the sources are expected totrace the large--scale structure of luminous matter in the universe. I use anew likelihood method that compares the counts--in--cells distribution of\g--ray bursts in the BATSE 3B catalog with that expected from the knownlarge--scale structure of the universe, in order to place a constraint on thedistance scale to cosmological bursts. I find, at the 95\% confidence level,that the comoving distance to the ``edge'' of the burst distribution is greaterthan $630~h^{-1}$~Mpc ($z > 0.25$), and that the nearest burst is farther than$40~h^{-1}$~Mpc. The median distance to the nearest burst is $170~h^{-1}$~Mpc,implying that the total energy released in \g--rays during a burst event is oforder $3\times 10^{51}~h^{-2}$ ergs. None of the bursts that have been observedby BATSE are in nearby galaxies, nor is a signature from the Coma cluster orthe ``Great Wall'' likely to be seen in the data at present.Comment: 15 LaTeX pages with 2 encapsulated Postscript figures included, uses AASTeX (v. 4.0) available at ftp://ftp.aas.org/pubs