Measuring and Modelling the Redshift Evolution of Clustering: the Hubble Deep Field North

(abridged) The evolution of galaxy clustering from z=0 to z=4.5 is analyzed using the angular correlation function and the photometric redshift distribution of galaxies brighter than I_{AB}\le 28.5 in the HDF 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 has a small decrease in the range 0<z<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 CDM. The 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\simeq 2 at z=2 and b\simeq 5 at z=4. A comparison of the clustering amplitudes that we measured at z=3 with those reported for LBG 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=3 are consistent with the expected density of massive haloes predicted for the various cosmologies here considered. At z=4, the strong clustering observed in the HDF 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.