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One of the strongest pieces of evidence for the cosmological origin of $\gamma$-ray bursts would be the observation of a photon number count dipole (a Compton-Getting effect) due to our motion with respect to a distant burst parent population. Such an effect is the product of a dipole anisotropy in the distribution of bursts (Maoz 1994, ApJ 428, 454) and a dipole anisotropy due to counting photons in a finite energy bandwidth. The form of the Compton-Getting effect is discussed and Monte-Carlo simulations are performed to estimate the likelihood of its measurement under different circumstances. Using a catalogue of 410 bursts observed by the COMPTON/BATSE instrument (in the energy band 20-50$keV$), and the dipole determined from the Cosmic Microwave Background, we find that the observed dipole-aligned component has only a $\sim 10$\% chance of occuring for the null hypothesis of no Compton-Getting effect. However at the 90\% confidence level we can only constrain the Compton-Getting effect to be $> 0$\% and $< 40$\% in magnitude. Of the order of $10^{4}$ bursts would be necessary for a robust confirmation of the expected 1-2\% Compton-Getting effect. In addition the observed correlation with the direction of the Local Group motion has only a $\sim 5$\% probability of occuring by chance. These results are intriguing and suggest that future analyses of the angular distribution of $\gamma$-ray bursts should include photon number weighting.
C.A.S. acknowledges the NRC for their support through a Research Associateship.
