The Angular Clustering of Lyman-Break Galaxies at Redshift z ~ 3

We have measured the angular correlation function w(θ) for a sample of 871 Lyman-break galaxies (LBGs) in five fields at redshift z ~ 3. Fitting the power law Aw θ-β to a weighted average of w(θ) from the five fields over the range 12'' ≲ θ ≲ 330'', we find Aw ~ 2 arcsecβ and β ~ 0.9. The slope is, within the errors, the same as for galaxy samples in the local and intermediate-redshift universe, and a slope β = 0.25 or shallower is ruled out by the data at the 99.9% confidence level. Because N(z) of LBGs is well determined from 376 spectroscopic LBG redshifts, the real-space correlation function can be accurately derived from the angular one through the Limber transform. The inversion of w(θ) is rather insensitive to the still relatively large uncertainties on Aω and β, and the spatial correlation length is much more tightly constrained than either of these parameters. We estimate r0=3.3+ 0.7−0.6(2.1+ 0.4−0.5) h-1 Mpc (comoving) for q0 = 0.1 (0.5) at the median redshift of the survey, =3.04 (h is in units of 100 km s-1 Mpc-1 throughout this paper). The observed comoving correlation length of LBGs at z ~ 3 is comparable to that of present-day spiral galaxies and is only ~50% smaller than that of present-day ellipticals; it is as large or larger than any measured in recent intermediate-redshift galaxy samples (0.3 ≲ z ≲ 1). By comparing the observed galaxy correlation length to that of the mass predicted from cold dark matter (CDM) theory, we estimate a linear bias for LBGs of b ~ 1.5 (4.5) for q0 = 0.1 (0.5), in broad agreement with our previous estimates based on preliminary spectroscopy. The strong clustering and the large bias of the LBGs are consistent with biased galaxy formation theories and provide additional evidence that these systems are associated with massive dark matter halos. The results of the clustering of LBGs at z ~ 3 emphasize that apparent evolution in the clustering properties of galaxies may be due as much to variations in effective light-to-mass bias parameter among different galaxy samples as to evolution in the mass distribution through gravitational instability.