Voids in the Point Source Catalogue Survey and the Updated Zwicky Catalog

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Abstract
We describe an algorithm to detect voids in galaxy redshift surveys. The method is based on the void finder algorithm of El-Ad & Piran. We apply a series of tests to determine how accurately we are able to recover the volumes of voids using our detection method. We simulate voids of different ellipticity and find that if voids are approximately spherical, our algorithm will recover 100% of the volume of the void. The more elliptical the void, the smaller the fraction of the volume we can recover. We insist that voids lie completely within the survey. Voids close to the edge of the survey will therefore be underestimated in volume. By considering a deeper sample, we estimate that the maximal sphere diameters are correct to within 30%. We apply the algorithm to the Point Source Catalog redshift (PSCz) survey and the Updated Zwicky Catalog (UZC). The PSCz survey is an almost all-sky survey with objects selected from the IRAS catalog. The UZC covers a smaller area of sky but is optically selected and samples the structures more densely. We detect 35 voids in the PSCz and 19 voids in the UZC with diameter larger than 20 h-1 Mpc. Using this minimum size threshold, we find that voids have an average effective diameter of 29.8 ± 3.5 h-1 Mpc (PSCz) and 29.2 ± 2.7 h-1 Mpc (UZC) and that they are underdense regions with δρ/ρ values of -0.92 ± 0.03 (PSCz) and -0.96 ± 0.01 (UZC), respectively. Using this quite stringent threshold for void definition, voids fill up to 40% of the volume of the universe.
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