The Angular Power Spectrum of BATSE 3B Gamma-Ray Bursts

We compute the angular power spectrum C_l from the BATSE 3B catalog of 1122gamma-ray bursts, and find no evidence for clustering on any scale. Theseconstraints bridge the entire range from small scales (which probe sourceclustering and burst repetition) to the largest scales (which constrainpossible anisotropies from the Galactic halo or from nearby cosmological largescale structures). We develop an analysis technique that takes the angularposition errors into account, which enables us to place tight upper limits onthe clustering down to scales l\approx 60, corresponding to a few degrees onthe sky. The minimum-variance burst weighting that we employ is graphicallyvisualized as an all-sky map where each burst is smeared out by an amountcorresponding to its position uncertainty. We also present separate band-passfiltered sky maps for the quadrupole term and for the multipole-ranges l=3-10and l=11-30, so that the fluctuations on different angular scales can beseparately inspected for visual features such as localized ``hot spots" orstructures aligned with the Galactic plane. These filtered maps reveal noapparent deviations from isotropy.