THE REAL-SPACE CORRELATION-FUNCTION MEASURED FROM THE APM GALAXY SURVEY

We present a determination of the real-space galaxy correlation functi on, xi(r), for galaxies in the APM Survey with 17 less than or equal t o b(J) less than or equal to 20. We have followed two separate approac hes, based upon a numerical inversion of Limber's equation. For Omega= 1 and clustering that is fixed in comoving coordinates, the correlatio n function on scales r less than or equal to 4 h(-1) Mpc is well fitte d by a power law xi(r)=(r/4.5)(-1.7). There is a shoulder in xi(r) at 4 less than or equal to r less than or equal to 25 h(-1) Mpc, with the correlation function rising above the quoted power law, before fallin g and becoming consistent with zero on scales r greater than or equal to 40 h(-1) Mpc. The shape of the correlation function is unchanged if we assume that clustering evolves according to linear perturbation th eory; the amplitude of xi(r) increases, however, with r(0)=5.25 h(-1) Mpc. We compare our results against an estimate of the real-space xi(r ) made by Loveday et al. from the Stromlo-APM Survey, obtained using a cross-correlation technique. We examine the scaling with depth of xi( r), in order to make a comparison with the shallower Stromlo-APM Surve y and find that the changes in xi(r) are within the 1 sigma errors. Th e estimate of xi(r) that we obtain is smooth on large scales, allowing us to estimate the distortion in the redshift-space correlation funct ion of the Stromlo-APM Survey caused by galaxy peculiar velocities on scales where linear perturbation theory is only approximately correct. We find that beta=Omega(0.6)/b=0.61 with the 1 sigma spread 0.38 less than or equal to beta less than or equal to 0.81, for Omega=1 and clu stering that is fixed in comoving coordinates; b is the bias factor be tween fluctuations in the density and the light. For clustering that e volves according to linear perturbation theory, we recover beta=0.20 w ith 1 sigma range - 0.02 less than or equal to beta less than or equal to 0.39. We rule out beta=1 at the 2 sigma level. This implies that i f Omega=1, the bias parameter must have a value b>1 on large scales, w hich disagrees with the higher order moments of counts measured in the APM Survey (Gaztanaga).