The cross-correlation of Abell clusters with the Lick galaxy counts

We present an analysis of the cross-correlations between Abell clusters and the 10×10arcmin Lick galaxy counts. The main new features of our analysis are as follows: (i) we correct for gradients in the Lick counts that depend only on galactic latitude; (ii) we check the effects of applying a filter to the Lick counts to remove (likely artificial) gradients on scales >20°; (iii) redshifts for Abell clusters are used to compute a cross-correlation function $$W_\text{cg}(\sigma)$$, where $$\sigma \equiv\upsilon\theta/H_0$$ is the projected separation between a cluster with recession speed υ and a galaxy at angular distance θ from the cluster centre; (iv) the amplitude of the spatial cross-correlation function $$\xi_\text{cg}(r)$$ is estimated using modern determinations of the galaxy luminosity function. Our results show that the shape of $$\xi_\text{cg}$$ is reasonably well determined on scales r<20h⁻¹ Mpc ($$h\equiv H_0/100 \text{km s}^{-1} \text {Mpc}^{-1}$$). On larger scales, the results depend sensitively on the corrections for large-scale gradients in the Lick counts. The results based on $$W_\text{cg}(\sigma)$$ are well described by a power-law model $$\xi_\text{cg}(r)\approx(r/8.8h^{-1} \text{Mpc})^{-2.2}$$, while the angular cross-correlations for Abell clusters in distance class D = 5 are better described by the model $$\xi_\text{cg}(r)\approx(r/6h^{-1} \text{Mpc})^{-2.3}+(r/7h^{-1} \text {Mpc})^{-1.7}$$. Seldner & Peebles derived a larger amplitude for $$\xi_{\text {cg}}$$ because they assumed a different luminosity function. We compare these results with theoretical predictions of $$\xi_{\text {cg}}$$ in the Ω = l biased cold dark matter (CDM) model. On scales 1 h⁻¹ Mpc≲r≲10h⁻¹ Mpc, the theoretical predictions for $$\xi_{\text {cg}}$$ are in surprisingly good agreement with our observational estimates. On smaller scales, the CDM model gives too high an amplitude whereas on larger scales the predicted amplitude is too low. We argue that neither of these discrepancies is particularly serious.