We report the discovery of a luminous z = 5.78 star-forming galaxy in the Chandra Deep Field South. This galaxy was selected as an `i -drop' from the GOODS public survey imaging with the Hubble Space Telescope/Advanced Camera for Surveys (object 3 in the work of (Stanway, Bunker & McMahon, 2003). The large colour of (i'-z')AB= 1.6 indicated a spectral break consistent with the Lyman α forest absorption shortward of Lyman α at z ~ 6. The galaxy is very compact (marginally resolved with ACS with a half-light radius of 0.08 arcsec, so rhl< 0.5 h –170kpc). We have obtained a deep (5.5 h) spectrum of this z'AB= 24.7 galaxy with the DEIMOS optical spectrograph on the Keck Telescope, and here we report the discovery of a single emission line centred on 8245 Å detected at 20σ with a flux of f ~ 2x10–17 erg/cm2/s. The line is clearly resolved with detectable structure at our resolution of better than 55 km/s, and the only plausible interpretation consistent with the ACS photometry is that we are seeing Lyman α emission from a z = 5.78 galaxy. This is the highest redshift galaxy to be discovered and studied using HST data. The velocity width (ΔvFWHM= 260 km/s) and rest-frame equivalent width (W Lyαrest= 20 Å) indicate that this line is most probably powered by star formation, as an AGN would typically have larger values. The starburst interpretation is supported by our non-detection of the high-ionization N vλ1240-Å emission line, and the absence of this source from the deep Chandra X-ray images. The star formation rate inferred from the rest-frame UV continuum is 34 h –270M☉yr–1 (ΩM= 0.3, ΩΛ= 0.7). This is the most luminous starburst known at z > 5. Our spectroscopic redshift for this object confirms the validity of the i'-drop technique of (Stanway et al) to select star-forming galaxies atz ~ 6.
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