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

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 for a separation interval =650h-1 Mpc (h is the Hubble constant in units of 100 kms-1Mpc-1). 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 ± 15 h-1 Mpc. Five periods are observed. The correlation function found for clusters in poor and medium-rich superclusters is zero on large scales. The correlation functions calculated separately for the Northern and Southern Galactic hemispheres are similar; only the amplitude of oscillations for clusters in the Southern hemisphere is larger by a factor of about 1.5. We investigate the influence of possible errors in the correlation function. The amplitude of oscillations for clusters in very rich superclusters is about 3 times larger than the estimated error. We argue that the oscillations in the correlation function are due neither to the double­ cone shape of the observed volume of space, nor to the inaccuracy in the selection function. 'We compare the observed cluster correlation function with similar functions derived for popular models of structure formation, as well as for simple geometrical models of cluster distribution. 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 at long wavelengths to a negative spectral index at short wavelengths is highly unlikely. The power spectrum must have an extra peak located at a wavelength equal to the period of oscillations of the correlation function. The relative amplitude of the peak over the smooth spectrum is probably of the order of a factor of at least 1.25. These quantitative tests show that high-density regions in the Universe marked by rich clusters of galaxies are distributed more regularly than expected. Thus our present under­ standing of structure formation needs revision.