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

Abstract

We have measured the angular correlation function w(theta) for a sample of 871 Lyman-break galaxies (LBGs) at z=3. Fitting a power-law to a weighted average of w(theta) from 5 fields, we find the amplitude to be A_w=2 arcsec^β and the slope β=0.9. The slope is the same as in the local and moderate redshift universe. 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 redshifts, the real-space correlation function can be derived from the angular one through the Limber transform. This inversion is rather insensitive to the still relatively large errors on A_w and β, and the spatial correlation length is much more tightly constrained than either of these parameters. We estimate r_0=3.3 -0.6 +0.7 (2.1 -0.5 +0.4) h^{-1} Mpc (comoving) for q_0=0.1 (0.5) at z=3.04 (h is in units of 100 km/s/Mpc). The correlation length of LBGs at z=3 is comparable to that of present-day spiral galaxies and is only about 50% smaller than that of the ellipticals; it is as large or larger than any measured in galaxy samples at 0.3<z<1. By comparing the observed galaxy correlation length to that of the mass predicted from CDM theory, we estimate a bias for LBGs of b\sim 1.5 (4.5) for q_0=0.1 (0.5), in 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 clustering of LBGs at z=3 emphasizes that apparent evolution of galaxy clustering may be due as much to variations in effective bias parameter among different samples as to evolution in the mass distribution through gravitational instability.