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