The Large-Scale and Small-Scale Clustering of Lyman Break Galaxies at 3.5 ⩽ z ⩽ 5.5 from the GOODS Survey

We report on the angular correlation function of Lyman break galaxies (LBGs) at z ~ 4 and 5 from deep samples obtained from the Great Observatories Deep Origins Survey (GOODS). As for LBGs at z ~ 3, the shape of w(θ) of the GOODS LBGs is well approximated by a power law with a slope β ≈ 0.6 at angular separation θ ≥ 10''. The clustering strength of the z ~ 4 and 5 LBGs depends on the rest-frame UV luminosity similar to that of z ~ 3 LBGs, with brighter galaxies more strongly clustered than fainter ones. At smaller separations, w(θ) significantly exceeds the extrapolation of the large-scale power-law fit, implying enhanced spatial clustering on comoving scales r ≤ 1 Mpc. We also find that bright LBGs statistically have more faint companions on scales θ ≲ 20'' than fainter ones. The enhanced small-scale clustering is very likely due to substructure, reflecting multiple galaxies within the same massive halos. A simple model for the halo occupation distribution along with the halo mass function in a ΛCDM cosmology reproduces well the observed w(θ). The scaling relationship of the clustering strength with volume density and redshift is quantitatively consistent with that of CDM halos. If we associate LBGs with dark matter halos that have the same clustering strength, this luminosity dependence of w(θ) implies a close correlation between the halo mass and the star formation rate. A comparison of the clustering strength of three samples of equal luminosity limit at z ~ 3, 4, and 5 shows that the LBGs at z ~ 5 are hosted in halos about 5-10 times less massive than those at z ~ 3-4, suggesting that star formation was more efficient at z ~ 5.