Statistical analysis of the Perseus-Pisces redshift survey: spatial and luminosity properties

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) Γ(r) is a power law up to the sample effective depth ( 30 h−1 Mpc), showing the fractal nature of the galaxy distribution in this catalog. The fractal dimension turns out to be D 2. We also consider the CF ξ(r) and in particular the behavior of the “correlation length” r0 (ξ(r0) 1) as function of the sample size. In this respect we find, unambiguously, that the luminosity segregation effect is not supported by any experimental evidence. In addition we have studied the galaxian number-density (n(r)) and number-counts (N(m)) in the VL subsamples finding a good agreement with the properties of a fractal distribution. In particular our conclusion is that the n(r) relation permits to extend the analysis of the fractal nature up to a deeper depth than that reached by the CF analysis, and, we find evidence for fractal properties up to the limiting depth of 130 h−1 Mpc. We clarify the role of the small-scale fluctuations in the determination of the galaxy counts. Even in this case the results are in agreement with the previous ones. Finally we have considered the correlations between galaxy positions and luminosities by means of the multifractal analysis. We find clear evidence for self-similar behavior of the whole luminosity-space distribution. These results confirm and extend those of Coleman and Pietronero (1992).