Modeling The GRB Host Galaxy Mass Distribution: Are GRBs Unbiased
  Tracers of Star Formation?
  We model the mass distribution of long gamma-ray burst (GRB) host galaxies
given recent results suggesting that GRBs occur in low metallicity
environments. By utilizing measurements of the redshift evolution of the
mass-metallicity (M-Z) relationship for galaxies, along with a sharp host
metallicity cut-off suggested by Modjaz and collaborators, we estimate an upper
limit on the stellar mass of a galaxy that can efficiently produce a GRB as a
function of redshift. By employing consistent abundance indicators, we find
that sub-solar metallicity cut-offs effectively limit GRBs to low stellar mass
spirals and dwarf galaxies at low redshift. At higher redshifts, as the average
metallicity of galaxies in the Universe falls, the mass range of galaxies
capable of hosting a GRB broadens, with an upper bound approaching the mass of
even the largest spiral galaxies. We compare these predicted limits to the
growing number of published GRB host masses and find that extremely low
metallicity cut-offs of 0.1 to 0.5 solar are effectively ruled out by a large
number of intermediate mass galaxies at low redshift. A mass function that
includes a smooth decrease in the efficiency of producing GRBs in galaxies of
metallicity above 12+log(O/H)_(KK04) ~ 8.7 can, however, accommodate a majority
of the measured host galaxy masses. We find that at z ~ 1, the peak in the
observed GRB host mass distribution is inconsistent with the expected peak in
the mass of galaxies harboring most of the star formation. This suggests that
GRBs are metallicity biased tracers of star formation at low and intermediate
redshifts, although our model predicts that this bias should disappear at
higher redshifts due to the evolving metallicity content of the universe.
