The Redshift Evolution of Clustering in the HDF

We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto et al., 1998. By dividing the catalogue into redshift bins of width $\mathrm{\Delta }z=0.4$ we measured the angular correlation function $w(\theta )$ as a function of redshift up to $z\sim 4.8$. From these measurements we derive the trend of the correlation length $r_0$. We find that $r_0(z)$ is roughly constant with look-back time up to $z\simeq 2$, and then increases to higher values at $z\text{simgt}2.4$. We estimate the values of $r_0$, assuming $\xi (r,z)=(r\mathrm{/}{r}_0(z){)}^{-\gamma }$, $\gamma =1.8$ and different geometries. For ${\mathrm{\Omega }}_0=1$ we find $r_0(z=3)\simeq 7.00\pm 4.87h^{-1}$ Mpc, in good agreement with the values obtained from analysis of the Lyman Break Galaxies.