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

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  • Sylos Labini, F.
  • Montuori, M.
  • Pietronero, L.

Abstract

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).

Suggested Citation

  • Sylos Labini, F. & Montuori, M. & Pietronero, L., 1996. "Statistical analysis of the Perseus-Pisces redshift survey: spatial and luminosity properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 336-358.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:3:p:336-358
    DOI: 10.1016/0378-4371(96)00076-3
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    References listed on IDEAS

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    1. Caldarelli, G. & Vespignani, A. & Pietronero, L., 1995. "Fixed scale transformation for fracture growth processes governed by vectorial fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(3), pages 223-232.
    2. Amendola, Mario & Froeschle, Claude & Gaffard, Jean-Luc, 1996. "Structure and cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 29(3), pages 409-432, May.
    3. Labini, Paolo Sylos, 1995. "Why the interpretation of the Cobb-Douglas production function must be radically changed," Structural Change and Economic Dynamics, Elsevier, vol. 6(4), pages 485-504, December.
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