The faint-galaxy hosts of gamma-ray bursts

The observed redshifts and magnitudes of the host galaxies of gamma-ray bursts (GRBs) are compared with the predictions of three basic GRB models, in which the comoving rate density of GRBs is (1) proportional to the cosmic star formation rate density, (2) proportional to the total integrated stellar density, and (3) constant. All three models make the assumption that at every epoch the probability of a GRB occurring in a galaxy is proportional to that galaxy's broadband luminosity. No assumption is made that GRBs are standard candles or even that their luminosity function is narrow. All three rate-density models are consistent with the observed GRB host galaxies to date, although model (2) is slightly disfavored relative to the others. Models (1) and (3) make very similar predictions for host galaxy magnitude and redshift distributions; these models probably will not be distinguished without measurements of host galaxy star formation rates. The fraction of host galaxies fainter than 28 mag may constrain the faint end of the galaxy luminosity function at high redshift, or, if the fraction is observed to be low, may suggest that the bursters are expelled from low-luminosity hosts. In all models, the probability of finding a z < 0.008 GRB among a sample of 11 GRBs is less than 10(-4), strongly suggesting that GRB 980425, if associated with SN 1998bw, represents a distinct class of GRBs.