Star Formation at z ~ 6: i-Dropouts in the Advanced Camera for Surveys Guaranteed Time Observation Fields^{* **}

Using an i - z dropout criterion, we determine the space density of z ~ 6 galaxies from two deep ACS GTO fields with deep optical-IR imaging. A total of 23 objects are found over 46 arcmin², or ~0.5 ± 0.1 objects arcmin^-2 down to z_AB ~ 27.3 (6 σ), or a completeness-corrected ~0.5 ± 0.2 objects arcmin^-2 down to z_AB ~ 26.5 (including one probable z ~ 6 active galactic nucleus). Combining deep ISAAC data for our RDCS 1252-2927 field (J_AB ~ 25.7 and K_s,AB ~ 25.0; 5 σ) and NICMOS data for the Hubble Deep Field-North (J_110,AB and H_160,AB ~ 27.3, 5 σ), we verify that these dropouts have relatively flat spectral slopes, as one would expect for star-forming objects at z ~ 6. Compared with the average-color (β = -1.3) U-dropout in the Steidel et al. z ~ 3 sample, i-dropouts in our sample range in luminosity from ~1.5L_* (z_AB ~ 25.6) to ~0.3L_* (z_AB ~ 27.3) with the exception of one very bright candidate at z_850,AB ~ 24.2. The half-light radii vary from 009 to 021, or 0.5 kpc to 1.3 kpc. We derive the z ~ 6 rest-frame UV luminosity density (or star formation rate density) by using three different procedures. All three procedures use simulations based on a slightly lower redshift (z ~ 5) V₆₀₆-dropout sample from Chandra Deep Field-South ACS images. First, we make a direct comparison of our findings with a no-evolution projection of this V-dropout sample, allowing us to automatically correct for the light lost at faint magnitudes or lower surface brightnesses. We find 23% ± 25% more i-dropouts than we predict, consistent with no strong evolution over this redshift range. Adopting previous results to z ~ 5, this works out to a mere 20% ± 29% drop in the luminosity density from z ~ 3 to z ~ 6. Second, we use the same V-dropout simulations to derive a detailed selection function for our i-dropout sample and compute the UV-luminosity density [(7.2 ± 2.5) × 10²⁵ ergs s^-1 Hz^-1 Mpc^-3 down to z_AB ~ 27]. We find a 39% ± 21% drop over the same redshift range (z ~ 3-6), consistent with the first estimate. This is our preferred value and suggests a star formation rate of 0.0090 ± 0.0031 M_☉ yr^-1 Mpc^-3 to z_AB ~ 27, or ~0.036 ± 0.012 M_☉ yr^-1 Mpc^-3 by extrapolating the luminosity function to the faint limit, assuming α = -1.6. Third, we follow a very similar procedure, except that we assume no incompleteness, and find a rest-frame continuum luminosity that is ~2-3 times lower than our other two determinations. This final estimate is to be taken as a lower limit and is important if there are modest changes in the colors or surface brightnesses from z ~ 5 to z ~ 6 (the other estimates assume no large changes in the intrinsic selectability of objects). We note that all three estimates are well within the canonical range of luminosity densities necessary for reionization of the universe at this epoch by star-forming galaxies.