Galaxies at z ~ 6: The UV Luminosity Function and Luminosity Density from 506 HUDF, HUDF Parallel ACS Field, and GOODS i-Dropouts^{* **}

We have detected 506 i-dropouts (z ~ 6 galaxies) in deep, wide-area HST ACS fields: HUDF, enhanced GOODS, and HUDF parallel ACS fields (HUDF-Ps). The contamination levels are ≲8% (i.e., ≳92% are at z ~ 6). With these samples, we present the most comprehensive, quantitative analyses of z ~ 6 galaxies yet and provide optimal measures of the UV luminosity function (LF) and luminosity density at z ~ 6, and their evolution to z ~ 3. We redetermine the size and color evolution from z ~ 6 to z ~ 3. Field-to-field variations (cosmic variance), completeness, flux, and contamination corrections are modeled systematically and quantitatively. After corrections, we derive a rest-frame continuum UV (~1350 Å) LF at z ~ 6 that extends to M_1350,AB ~ -17.5 (0.04L). There is strong evidence for evolution of the LF between z ~ 6 and z ~ 3, most likely through a brightening (0.6 ± 0.2 mag) of M* (at 99.7% confidence), although the degree depends on the faint-end slope. As expected from hierarchical models, the most luminous galaxies are deficient at z ~ 6. Density evolution (ϕ*) is ruled out at >99.99% confidence. Despite large changes in the LF, the luminosity density at z ~ 6 is similar to (0.82 ± 0.21 times) that at z ~ 3. Changes in the mean UV color of galaxies from z ~ 6 to z ~ 3 suggest an evolution in dust content, indicating that the true evolution is substantially larger: at z ~ 6 the star formation rate density is just ~30% of the z ~ 3 value. Our UV LF is consistent with z ~ 6 galaxies providing the necessary UV flux to reionize the universe.