A Possible Effect of the Period of Galaxy Formation on the Angular Correlation Function

Abstract

During the epoch of galaxy formation, the formation of the first galaxies in regions of high overdensity may lead to an initial amplitude of the spatial correlation function of galaxies, $ξ_0,$ much higher than that expected in linear perturbation theory. This initially high ``bias'' would consequently decrease to the near-unityvalues expected from local observations. Such a ``Decreasing Correlation Period'' (DCP), detected in N-body simulations under certain conditions by several authors, is parametrised in a simple way, ending at a ``transition'' redshift $z_t.$ Consequences on $w_0,$ the amplitude of the angular correlation function of faint galaxies (for a fixed apparent magnitude range), have been estimated. The sensitivity of $w_0$ to $z_t,$ and how this is affected by the redshift distribution of the galaxies in the sample, by low redshift spatial correlation function behaviour, by cosmology, and by the rate at which $ξ_0$ decreases during the DCP, are shown and discussed. This simple model is intended as a first exploration of the effects of the DCP for a likely range of parameter space. Comparison with the Hubble Deep Field (HDF) estimate of $w_0$ (Villumsen et al. 1996) indicates that the DCP is compatible with observation for values of $z_t$ in the theoretically expected range $z_t \gtapprox 1.$ However, tighter observational constraints on the HDF redshift distribution and on low redshift correlation function growth will be needed either to detect the DCP unambiguously or to constrain $z_t$ to redshifts greater than those of galaxies in existing surveys.