THE SHAPE OF THE 2-POINT CORRELATION-FUNCTION - EVIDENCE FOR A DOUBLE POWER LAW

We examine the two-point galaxy correlation functions of the Zwicky/CfA1, the Southern Sky Redshift Survey catalogs, and a sample of IRAS galaxies. To minimize the effects of peculiar velocities, we examine the angular and projected correlation functions and obtain the spatial correlation function for the CfA1 and SSRS samples by inverting the projected function. From the chi2 analysis, we find that a double power law model for 1 + xi(r) is a fair generalization over the range of large separations (5 h-1 < r < 30 h-1 Mpc) of the single power law model for xi(r), where xi(r) is the two-point correlation function of galaxies. Indeed, the double power law fits the data over a factor of 2 larger in separation (approximately 30 h-1 Mpc). The fit we obtain agrees well with those found by Dekel & Aarseth for the CfA1 survey and by Guzzo et al. for the Perseus-Pisces redshift catalog, based on redshift separations. Our analysis demonstrates that the double power law nature is geometrical and not a consequence of peculiar motions. We find the function 1 + xi(r) for clusters of galaxies exhibits the same power law as that for the galaxies on large scales. We consider some consequences of such large-scale clustering, including a different normalization of the power spectrum of primordial density fluctuations.