DETECTABILITY OF GAMMA-RAY BURST EXCESS TOWARD M31

We calculate the expected excess of gamma ray bursts (GRBs) from the d irection of M31 assuming that GRBs come from an extended halo around b oth M31 and our own Galaxy. Specifically, we consider the delayed turn -on and halo-beaming models for GRBs. We express the ratio of GRB rate from M31 to our Galaxy as a function of instrument sensitivities, the observing solid angles toward M31, and the burst luminosity functions . This ratio tends to be much larger than 1 for a small observing angl e (<10 degrees) when the instrument can sample close to the distance o f M31. Assuming that a hypothetical gamma-ray instrument is 10 times m ore sensitive than BATSE, we find in a 1 yr observation, for both imag ing or nonimaging instruments, that the delayed turn-on model might be tested but no statistically significant signal is expected for the ha lo-beaming model. Thus, it is extremely difficult to rule out the halo -beaming model by observing M31.