The supercluster--void network II. An oscillating cluster correlation function

Abstract

We use rich clusters of galaxies in the Northern and Southern Galactic hemispheres up to a redshift z=0.12 to determine the cluster correlation function. We show that superclusters of galaxies and voids between them form a moderately regular network. As a result the correlation function determined for clusters located in rich superclusters oscillates: it has a series of regularly spaced secondary maxima and minima. The scale of the supercluster-void network, determined from the period of oscillations, is P=115 Mpc. The amplitude of oscillations is about 3 times larger than the estimated error. We compare the observed cluster correlation function with similar functions derived for popular models of structure formation. We find that the production of the observed cluster correlation function in any model with a smooth transition of the power spectrum from a Harrison-Zeldovich regime with positive spectral index on long wavelengths to a negative spectral index on short wavelengths is highly unlikely. The power spectrum must have an extra peak located at the wavelength equal to the period of oscillations of the correlation function.