Evolution of the Angular Correlation Function

Abstract

For faint photometric surveys, our ability to quantify the clustering of galaxies has depended on interpreting the angular correlation function as a function of the limiting magnitude of the data. Because of the broad redshift distribution of galaxies at faint magnitude limits, the correlation signal has been extremely difficult to detect and interpret. Here we introduce a new technique for measuring the evolution of clustering. We utilize photometric redshifts derived from multicolor surveys to isolate redshift intervals and to calculate the evolution of the amplitude of the angular two-point correlation function. Applying these techniques to the Hubble Deep Field, we find that the shape of the correlation function at z=1 is consistent with a power law with a slope of -0.8. For z > 0.4, the best fit to the data is given by a model of clustering evolution with a comoving r₀=2.37 h^-1 Mpc and =-0.4^{+ 0.37}_−0.65, which is consistent with published measures of the clustering evolution. To match the canonical value of r₀=5.4 h^-1 Mpc found for the clustering of local galaxies requires a value of =2.10^{+ 0.43}_−0.64 (significantly more than linear evolution). The log likelihood of this latter fit is 4.15 times smaller than that for the r₀=2.37 h^-1 Mpc model. We, therefore, conclude that the parameterization of the clustering evolution of (1+z)^-(3+) is not a particularly good fit to the data.