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Evidence for Brightness-Dependent Anisotropy of Gamma Ray Bursts and Its Galactic Intepretation

We show that the brighter gamma-ray bursts (GRBs) in the BATSE 3B catalog concentrate slightly toward the Galactic plane and center, suggesting that at least some bursts originate within the Galaxy. To develop an interpretation of this brightness-dependent anisotropy, we consider GRBs distributed in a thick disk centered on the Galaxy. As an approximation to the true luminosity distribution, we divide bursts into two distinct luminosity classes. Most bursts originate from low-luminosity, nearby sources while the relatively few high-luminosity sources trace the shape of the thick disk. We find that characteristic disk dimensions as small as 20 kpc in thickness and 30 kpc in radial extent can match the observed brightness-dependent anisotropy as well as the number-flux distribution; these dimensions are smaller than previously considered viable. For bursts distributed in a disk of these compact dimensions, the low-luminosity sources must have peak powers of $\lapprox 5\times 10^{40}$ erg s$^{-1}$ and rate densities of $\gapprox 5\times 10^{-3}$ yr$^{-1}$ kpc$^{-3}$. The high-luminosity sources must have a peak luminosity of $\simeq 10^{42}$ erg s$^{-1}$ but their rate density need be only 5% or less than that of the low-luminosity sources. If the Andromeda Galaxy contained a similar population of high-luminosity sources, their peak gamma-ray fluxes would be less than $\sim 0.1$ s$^{-1}$ cm$^{-2}$, making their detection problematic. Statistical analyses of the gamma-ray burst events obtained since the compilation of the 3B catalog will determine whether the thick-disk interpretation is preferred over the isotropic one.