Exploring the Galaxy Mass-Metallicity Relation at z~3-5
  Long-duration gamma-ray bursts (GRBs) provide a premier tool for studying
high-redshift star-forming galaxies thanks to their extreme brightness and
association with massive stars. Here we use GRBs to study the galaxy stellar
mass-metallicity (M*-Z) relation at z~3-5, where conventional direct
metallicity measurements are extremely challenging. We use the ISM
metallicities of LGRB hosts derived from afterglow absorption spectroscopy
(Z~0.01-1 solar), in conjunction with host galaxy stellar masses determined
from deep Spitzer 3.6 micron observations of 20 GRB hosts. We detect about 1/4
of the hosts with I-band magnitudes ~ -21.5 to -22.5 AB mag, and place a limit
of M > -19 mag on the remaining hosts from a stacking analysis. Using these
observations, we present the first rest-frame optical luminosity distribution
of long GRB hosts at z>3 and find that it is similar to the distribution of
long GRB hosts at z~1. In comparison to Lyman-break galaxies at the same
redshift, GRB hosts are generally fainter, but the sample is too small to rule
out an overall similar luminosity function. On the other hand, the GRB hosts
appear to be more luminous than the population of Lyman-alpha emitters at
z~3-4. Using a conservative range of mass-to-light ratios for simple stellar
populations (with ages of 70 Myr to ~2 Gyr), we infer the host stellar masses
and present mass-metallicity measurements at z~3-5 (<z> ~ 3.5). We find that
the detected GRB hosts, with M*~2e10 solar masses, display a wide range of
metallicities, but that the mean metallicity at this mass scale, Z~0.1 solar,
is lower than measurements at z<3. Combined with stacking of the non-detected
hosts with M*< 3e9 solar masses and Z<0.03 solar, we find evidence for the
existence of an M*-Z relation at z~3.5 and continued evolution of this relation
to systematically lower metallicities from z~2.
