Clustering at High Redshift: Precise Constraints from a Deep, Wide-Area Survey

We present constraints on the evolution of large-scale structure from a catalog of 710,000 galaxies with I_AB ≤ 24 derived from a KPNO 4 m CCD imaging survey of a contiguous 4° × 4° region. The advantage of using large contiguous surveys for measuring clustering properties on even modest angular scales is substantial: the effects of cosmic scatter are strongly suppressed. We provide highly accurate measurements of the two-point angular correlation function, ω(θ), as a function of magnitude on scales up to 15. The amplitude of ω(θ) declines by a factor of ~10 over the range 16 ≤ I ≤ 20 but only by a factor of 2-3 over the range 20 < I ≤ 23. For a redshift dependence of the spatial correlation function, ξ(r), parameterized as ξ(r, z) = (r/r₀)^-γ(1 + z)^-(3+), we find r₀ = 5.2 ± 0.4 h^-1 Mpc, and 0 for I ≤ 20. This is in good agreement with the results from local redshift surveys. At I > 20, our best-fit values shift toward lower r₀ and more negative . A strong covariance between r₀ and prevents us from rejecting > 0 even at faint magnitudes, but if > 1, we strongly reject r₀ 4 h^-1 Mpc (comoving). The above expression for ξ(r, z) and our data give a correlation length of r₀(z = 0.5) ≈ 3.0 ± 0.4 h^-1 Mpc, about a factor of 2 larger than the correlation length at z = 0.5 derived from the Canada-France Redshift Survey (CFRS). The small volume sampled by the CFRS and other deep redshift probes, however, makes these spatial surveys strongly susceptible to cosmic scatter and will tend to bias their derived correlation lengths toward the low end. Our results are consistent with redshift distributions in which ~30%-50% of the galaxies at I = 23 lie at z > 1. The best-fit power-law slope of the correlation function remains independent of I magnitude for I ≤ 22. At fainter limits, there is a suggestive trend toward flatter slopes that occurs at fluxes consistent with similar trends seen by Neuschaffer & Windhorst and Campos and coworkers. The galaxy counts span 11 magnitudes and provide an accurate calibration of the galaxy surface density. We find evidence for mild galaxy evolution: about 1 mag of brightening or a doubling of the density by I = 23 relative to an Ω₀ = 1 no-evolution model, about 0.5 mag of brightening or a factor of 1.5 increase in surface density relative to an open model. Our galaxy counts agree well with those from the Hubble Deep Field survey and, thus, argue against a significant inclusion of subgalactic components in the latter census for I < 24.