HST and Spitzer Observations of the Host Galaxy of GRB 050904: A Metal-Enriched, Dusty Starburst at z=6.295

We present deep Hubble Space Telescope and Spitzer Space Telescope observations of the host galaxy of GRB 050904 at z=6.295. The host is detected in the H-band and marginally at 3.6 micron. From these detections, and limits in the z'-band and 4.5 micron, we infer an extinction-corrected absolute magnitude, M(UV)=-20.7 mag, or ~L*, a substantial star formation rate of 15 solar masses per year, and a stellar mass of a few 10^9 solar masses. A comparison to the published sample of spectroscopically-confirmed galaxies at z>5.5 reveals that the host of GRB 050904 would evade detection and/or confirmation in any of the current surveys due to the lack of detectable Ly-alpha emission, which is likely the result of dust extinction (A[1200]~1.5 mag). This suggests that not all luminous starburst galaxies at z~6 are currently being accounted for. Most importantly, using the metallicity of Z~0.05 solar inferred from the afterglow absorption spectrum, our observations indicate for the first time that the observed evolution in the mass- and luminosity-metallicity relations from z=0 to z~2 continues on to z>6. The ease of measuring redshifts and metallicities from the afterglow emission suggests that in tandem with the next generation ground- and space-based telescopes, a GRB mission with dedicated near-IR follow-up can provide unique information on the evolution of stars and galaxies through the epoch of re-ionization.