Measuring and modelling the redshift evolution of clustering:: the Hubble Deep Field North

The evolution of galaxy clustering from z = 0 to z similar or equal to 4.5 is analysed using the angular correlation function and the photometric redshift distribution of galaxies brighter than I-AB less than or equal to 28.5 in the Hubble Deep Field North. The reliability of the photometric redshift estimates is discussed on the basis of the available spectroscopic redshifts, comparing different codes and investigating the effects of photometric errors. The redshift bins in which the clustering properties are measured are then optimized to take into account the uncertainties of the photometric redshifts. The results show that the comoving correlation length r(0) has a small decrease in the range 0 less than or similar to z less than or similar to 1 followed by an increase at higher z. We compare these results with the theoretical predictions of a variety of cosmological models belonging to the general class of Cold Dark Matter scenarios, including Einstein-de Sitter models, an open model and a flat model with non-zero cosmological constant. Comparison with the expected mass clustering evolution indicates that the observed high-redshift galaxies are biased tracers of the dark matter with an effective bias b strongly increasing with redshift. Assuming an Einstein-de Sitter universe, we obtain b similar or equal to 2.5 at z similar or equal to 2 and b similar or equal to 5 at z similar or equal to 4. These results support theoretical scenarios of biased galaxy formation in which the galaxies observed at high redshift are preferentially located in more massive haloes. Moreover, they suggest that the usual parameterization of the clustering evolution as xi(r,z) = xi(r,0)(1+z)(-(3+epsilon)) is not a good description for any value of epsilon. Comparison of the clustering amplitudes that we measured at z similar or equal to 3 with those reported by Adelberger et al. and Giavalisco et al., based on a different selection, suggests that the clustering depends on the abundance of the objects: more abundant objects are less clustered, as expected in the paradigm of hierarchical galaxy formation. The strong clustering and high bias measured at z similar or equal to 3 are consistent with the expected density of massive haloes predicted in the frame of the various cosmologies considered here. At z similar or equal to 4, the strong clustering observed in the Hubble Deep Field requires a significant fraction of massive haloes to be already formed by that epoch. This feature could be a discriminant test for the cosmological parameters if confirmed by future observations.