The cross-correlation of IRAS galaxies with Abell clusters and radio galaxies

We analyse the cross-correlation of IRAS galaxies (QDOT sample) with Abell clusters and radio galaxies, using redshift samples. The large and uniformly selected QDOT sample enables us to determine reliably the cross-correlation functions on large scales, independent of possible non-uniformities in the cluster catalogues. The results give accurate information on the shape of the power spectrum of the galaxy density field on large scales, and on how different objects trace the large-scale structure of the Universe. Our statistical analysis is based on the average two-point cross-correlation function |ξ̄AB(r)=(3/r³)∫₀ʳx²ξ AB(x)\, dx|⁠, where ξAB(x) is the two-point cross-correlation function between objects of types A and B. We find that the shapes of |ξ ̄AB(r)| for different samples are similar and can be well described at small separations by a power law |ξ̄AB| ∝ r–α with α = 1.7 ± 0.2; the average cross-correlation functions have a break below this power law at r = (57 ± 5) h–1 Mpc (h ≡ H0 /100 km s–1 Mpc–1). These results show that different objects trace the same large-scale structure. The best fit of the results shows that the power spectrum of the galaxy density field has a slope n ≃ – 1.3 for wavelengths λ. < (160 ± 30) h–1 Mpc and breaks to n ≃ 1 for larger wavelengths. When normalized at r = 10 h–1 Mpc, our results are inconsistent with the standard CDM model (i.e. Ω h = 0.5) for r > 20 h–1Mpc. The best fit of the results with a model of adiabatic scale-invariant CDM fluctuations gives Ω h = 0.32 ± 0.07. The amplitude of the cross-correlation function depends significantly on the richness of clusters. The ratios of the cross-correlation functions are ξ(radio): |ξ ̄(R = 0): ξ ̄(R ≥ 0): ξ ̄(R ≥ 0)≈| 1:0.9:1.7:3.2. These ratios do not change significantly with r for r ≤ 50 h–1 Mpc, suggesting that the Kaiser mechanism may be a reasonable approximation on large scales, and providing a powerful argument in favour of Gaussian statistics for the large-scale density field.