The real-space correlation function measured from the APM Galaxy Survey

We present a determination of the real-space galaxy correlation function, ξ(r), for galaxies in the APM Survey with 17 ɤbj ≤20. We have followed two separate approaches, based upon a numerical inversion of Limber 's equation. For Ω = 1 and clustering that is fixed in comoving coordinates, the correlation function on scales r ≤4 h−1 Mpc is well fitted by a power law ξ(r) = (r/4.5)−1.7. There is a shoulder in ξ(r) at 4 ɤr ≤25 h−1 Mpc, with the correlation function rising above the quoted power law, before falling and becoming consistent with zero on scales r ≥40 h−1 Mpc. The shape of the correlation function is unchanged if we assume that clustering evolves according to linear perturbation theory; the amplitude of ξ(r) increases, however, with r0 = 5.25 h−1 Mpc. We compare our results against an estimate of the real-space ξ(r) made by Loveday et al. from the Stromlo-APM Survey, obtained using a cross-correlation technique. We examine the scaling with depth of ξ(r), in order to make a comparison with the shallower Stromlo-APM Survey and find that the changes in ξ(r) are within the 1σ errors. The estimate of ξ(r) that we obtain is smooth on large scales, allowing us to estimate the distortion in the redshift-space correlation function of the Stromlo-APM Survey caused by galaxy peculiar velocities on scales where linear perturbation theory is only approximately correct. We find that β= Ω0.6/b= 0.61 with the 1 σ spread 0.38 ≤β ≤0.81, for Ω=1 and clustering that is fixed in comoving coordinates; b is the bias factor between fluctuations in the density and the light. For clustering that evolves according to linear perturbation theory, we recover β=0.20 with 1σ range −0.02 ≤ β ≤ 0.39. We rule out β= 1 at the 2 σ level. This implies that if Ω = 1, the bias parameter must have a value b >1 on large scales, which disagrees with the higher order moments of counts measured in the APM Survey (Gaztanaga).