Hubble space telescope and spitzer observations of the afterglow and host galaxy of GRB 050904 at z = 6.295

We present deep Hubble Space Telescope (HST) and Spitzer Space Telescope observations of GRB 050904 at z = 6.295. We detect the afterglow in the H band more than 3 weeks after the burst and confirm the presence of a jet break at t ≈ 2.1 days. This leads to an estimated opening angle of about 4° and a beaming-corrected energy of about 10⁵¹ ergs, similar to those of lower redshift gamma-ray bursts (GRBs). We do not detect an underlying host galaxy with either HST or Spitzer. From the upper limits we infer an extinction-corrected absolute magnitude M_UV ≳ -20.3 mag, or L ≲ L*, a star formation rate of ≲5.7 M_⊙ yr ^-1, and a stellar mass of ≲ few × 10⁹ M _⊙. A comparison to spectroscopically confirmed galaxies at z > 5.5 reveals that the host of GRB 050904 is fainter and has a lower star formation rate than at least 80% of these objects. Finally, using our luminosity limits, and the metallicity of about 0.05 Z_⊙ inferred from the afterglow absorption spectrum, we place the first limit on the luminosity-metallicity relation at z > 6. Future afterglow and host galaxy observations of z ≳ 4 GRBs should elucidate whether the mass- and luminosity-metallicity relations continue to evolve beyond the present limits of z ≲ 2.