THE SUPERDUSTER-VOID NETWORK .2. 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 correl ation function for a separation interval approximate to 650h(-1) Mpc ( h is the Hubble constant in units of 100 kms(-1) Mpc(-1)). We show tha t superclusters of galaxies and voids between them form a moderately r egular network. Asa result the correlation function determined for clu sters located in rich superclusters oscillates: it has a series of reg ularly spaced secondary maxima and minima. The scale of the superclust er-void network, determined from the period of oscillations, is P = 11 5 +/- 15 h(-1) Mpc, Five periods are observed, The correlation functio n 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 ampli tude of oscillations for clusters in the Southern hemisphere is larger by a factor of about 1.5. We investigate the influence of possible er rors in the correlation function. The amplitude of oscillations for cl usters in very rich superclusters is about 3 times larger than the est imated error, We argue that the oscillations in the correlation functi on 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 geome trical models of cluster distribution. We find that the production of the observed cluster con;elation function in any model with a smooth t ransition of the power spectrum from a Harrison-Zeldovich regime with positive spectral index at long wavelengths to a negative spectral ind ex at short wavelengths is highly unlikely. The power spectrum must ha ve an extra peak located at a wavelength equal to the period of oscill ations of the correlation function. The relative amplitude of the peak over the smooth spectrum is probably of the order of a factor of at l east 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 understanding of structure f ormation needs revision.