The APM cluster--galaxy cross-correlation function: constraints on   and galaxy bias

We estimate the clustergalaxy cross-correlation function (y cg ), from the APM galaxy and galaxy cluster surveys. We obtain estimates both in real space from the inversion of projected statistics and in redshift space using the galaxy and cluster redshift samples. The amplitude of y cg is found to be almost independent of cluster richness. At large separations, r * 5 h 1 Mpc (h H 0 =100 km s 1 Mpc 1 , where H 0 is the Hubble constant), y cg has a similar shape to the galaxygalaxy and clustercluster autocorrelation functions. y cg in redshift space can be related to the real-space y cg by convolution with an appropriate velocity eld model. Here we apply a spherical collapse model, which we have tested against N-body simulations, nding that it provides an accurate description of the averaged infall velocity of matter into galaxy clusters. We use this model to estimate b (b Q 0:6 =b, where b is the linear bias parameter), and nd that it tends to overestimate the true result in simulations by only ,1030 per cent. Application to the APM results yields b 0:46 with b < 0:73 at 95 per cent condence. This measure is complementary to the estimates made of the density parameter from larger scale bulk ows and from the virialized regions of clusters on smaller scales. We also compare the APM y cg and galaxy autocorrelations directly with the mass correlation and cluster-mass correlations in COBE-normalized simulations of popular cosmological models, and derive two independent estimates of the galaxy biasing expected as a function of scale. This analysis reveals that both low-density and critical-density COBE-normalized cold dark matter (CDM) models require anti-biasing by a factor ,2 on scales r # 2 h 1 Mpc, and that the mixed dark matter (MDM) model is consistent with a constant biasing factor on all scales. The criticaldensity CDM model also suffers from the usual decit of power on large scales (r * 20 h 1 Mpc). We use the velocity elds predicted from the different models to distort the APM real-space cross-correlation function. Comparison with the APM redshift-space y cg yields an estimate of the value of Q 0:6 needed in each model. We nd that only the low-Q model is fully consistent with observations, with MDM marginally excluded at the ,2j level.