The power spectrum of rich clusters of galaxies on large spatial scales

A B STR A CT We present an analysis of the redshift-space power spectrum, P (k), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P (k) can be approximated by a power law, P (k);k n , with n2—1.6 over the wavenumber range 0.04sks0.1 h Mpc —1 . Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k10.03 h Mpc —1 . We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N-body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers kz0.02 h Mpc —1 . These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a nearscale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.