ON THE MEASUREMENT OF A COSMOLOGICAL DIPOLE IN THE PHOTON NUMBER COUNTS OF GAMMA-RAY BURSTS

If gamma-ray bursts are cosmological or in a halo distribution their p roperties are expected to be isotropic (at least to first order). Howe ver, our motion with respect to the burst parent population (whose pro per frame is expected to be that of the cosmic microwave background [C MB], or that of a static halo) will cause a dipole effect in the distr ibution of bursts and in their photon number counts (together termed a Compton-Getting effect). We argue that the photon number count inform ation is necessary to distinguish a genuine Compton-Getting effect fro m some other anisotropy and to fully test the proper-frame isotropy of the bursts. Using Monte Carlo simulations we obtain probability distr ibutions for the statistics of dipole alignment, angular power, and di pole aligned component. We demonstrate the agreement expected between number distribution and photon count distribution dipoles in the prese nce of noise. It is estimated that of the order of 10(4) bursts would be necessary to constrain a dipole effect of 1%. However, we can test the consistency of number and photon count distributions for a catalog of any size. Using the 2B catalog (Meegan et al. 1994, available in e lectronic form via ftp from grossc.gsfc.nasa.gov, user name gronews) o f bursts observed with the COMPTON/BATSE instrument (Fishman et al. 19 89) (in the energy band 20-50 keV), and the dipole determined from the CMB, we find the surprising result that although the number-weighted distribution is consistent with isotropy, the fluence-weighted dipole has a correlation with the CMB dipole that has a probability of occurr ing only 10% of the time for an isotropic photon distribution. Further more, the photon and number dipoles are inconsistent under the hypothe sis of isotropy, at the 2 sigma level. Taken together this could be an indication that a nonnegligible fraction of gamma-ray bursts originat e in the local, anisotropic universe. These results suggest that futur e analyses of the angular distribution of gamma-ray bursts should incl ude both photon count and number weighting and that larger catalogs sh ould be used to test the robustness of the apparent inconsistency with isotropy found here.