Scaling analysis of galaxy distribution in the Las Campanas Redshift Survey data

¹ Department of Physics, Ochanomizu University, 2-2-1 Otsuka, Bunkyo, Tokyo 112-8610, Japan
² Institute for Gender Studies, Ochanomizu University, 2-2-1 Otsuka, Bunkyo, Tokyo 112-8610, Japan
³ Meteorological Research Institute, 1-1 Nagamine, Tsukuba 305-0052, Japan

Corresponding author: T. Kurokawa, perle@cosmos.phys.ocha.ac.jp

Received: 14 December 1999
Accepted: 23 November 2000

Abstract

The Las Campanas Redshift Survey data are used to investigate structures ofthe galaxy number distribution. We construct two volume-limited samples with sizes of and h^-1 Mpc, and calculate the second- to ninth-order moments with the count-in-cell method. The galaxy distribution at ≥30 h^-1 Mpc is found to be statistically homogeneous. On the other hand, we find a multifractal scaling at <30 h^-1 Mpc. From the scaling exponent, we obtain the generalized dimension, which decreases from 2 toward 1 as the order is increased from 2 to 9. Galaxies are known to lie, around voids, in planar structures with filamentary dense regions. The present result indicates that these void-filament structures are predominant up to 30 h^-1 Mpc. Statistically, they appear to be the largest-scale significant structures in the Universe.