Correlation analysis of the space and surface distribution of galaxies

Abstract

AbstractThe paper presents a number of calculations which are useful for the interpretation of catalogues of galaxies. It is suggested that a correlation function approach based on a MAYER cluster expansion for the N‐point probability function of galaxies leads to a complete description of galaxy clustering. Other statistical measures of clustering such as the distribution function for the cell population or the distribution of the next neighbour distances are shown to be reducible to a correlation approach. For the classical cell count method smoothing effect estimates are given and the ZWICKY dispersion curve technique is studied. The relation between the space distribution and the surface distribution of galaxies is discussed in cosmological models of FRIEDMANN type. Deviations from PEEBLES' scaling law occur for catalogues extending to faint magnitudes and suggest the existence of strong evolutionary effects in the distribution of galaxies. From the DODD et al. field and the Jagiellonian field one derives — comparing the data with those of the ZWICKY catalogue — that the clustering amplitude decreases like (I + z)‐s within increasing redshift, where s is of the order 6. Since the catalogues extend to small redshifts only, it is not clear if this behaviour continues to larger redshifts. Within the observationally accessible range of z, the value of s does not essentially depend neither on the galaxian luminosity function nor on the deceleration parameter q0, it depends weakly on the assumed K correction.