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The Redshift Evolution of Clustering in the HDF

We present a correlation function analysis for the catalogue of photometric red-shifts obtained from the Hubble Deep Field image by Fernandez-Soto et al., 1998. By dividing the catalogue into redshift bins of width ∆z = 0.4 we measured the angular correlation function w(θ) as a function of redshift up to z ∼ 4. From these measurements we derive the values for the r.m.s. density fluctuations in 8h −1 Mpc spheres, σ 8 (z). We find that σ 8 (z) is roughly constant with look-back time up to z ≃ 2, and then increases to higher values at z ∼ > 2.4. We estimate the comoving correlation length r 0 , assuming ξ(r, z) = (r/r 0 (z)) −γ , γ = 1.8 and Ω 0 = 1, and find r 0 (z = 2.6) ≃ 3.93h −1 Mpc and r 0 (z = 3.0) ≃ 3.45h −1 Mpc, in excellent agreement with the values obtained from analysis of the Lyman Break Galaxies.