Properties of Voids in the 2dFGRS Galaxy Survey

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Abstract
A method for detecting voids in the galaxy distribution is presented. Using this method, we have identified 732 voids with a radius of the seed sphere Rseed > 4.0h^{-1}Mpc in a volume-limited sample of galaxies from the southern part of the 2dFGRS survey. 110 voids with Rseed > 9.0h^{-1}Mpc have a positive significance. The mean volume of such voids is 19000 h^{-3}Mpc^3. Voids with Rseed > 9.0h^{-1}Mpc occupy 55% of the sample volume. We construct a dependence of the volumes of all the identified voids on their ranks and determine parameters of the galaxy distribution. The dependence of the volume of voids on their rank is consistent with a fractal model (Zipf's power law) of the galaxy distribution with a fractal dimension D ~ 2.1 (given the uncertainty in determining the dimension using our method and the results of a correlation analysis) up to scales of 25h^{-1}Mpc with the subsequent transition to homogeneity. The directions of the greatest elongations of voids and their ellipticities (oblateness) are determined from the parameters of equivalent ellipsoids. The directions of the greatest void elongations have an enhanced concentration to the directions perpendicular to the line of sight.

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