A STATISTICAL TREATMENT OF THE GAMMA-RAY BURST NO HOST GALAXY PROBLEM- I - METHODOLOGY

If gamma-ray bursts originate in galaxies at cosmological distances, t he host galaxy should be detected if a burst error box is searched dee ply enough; are the host galaxies present? We present and implement a statistical methodology that evaluates whether the observed galaxy det ections in a burst's error box are consistent With the presence of the host galaxy, or whether all the detections can be attributed to unrel ated background galaxies. This methodology requires the model-dependen t distribution of host-galaxy fluxes. While our methodology was derive d for galaxies in burst error boxes, it can be applied to other candid ate host objects (e.g., active galaxies) and to other types of error b oxes. As examples, we apply this methodology to two published studies of burst error boxes. We find that the nine error boxes observed by La rson and McLean are too large to discriminate between the presence or absence of host galaxies, while the absence of bright galaxies in the four significantly smaller error boxes observed by the Hubble Space Te lescope (Schaefer et al.) does confirm that there is a ''no host galax y'' problem within the ''minimal'' host-galaxy model.