Objective detection of voids and high-density structures in the first CfA redshift survey slice

Voids of galaxies delineated by sharp one- or two-dimensional structures are the main features of the large-scale clustering of galaxies. In order to objectively identify the significant structures in the first slice of the Center for Astrophysics redshift survey, we perform a space-scale analysis of this galaxy catalog by means of the wavelet transform. The wavelet coefficients allow us to detect on all scales within reach both over- and underdense structures. The confidence level of the detection is computed under the assumption that galaxies are distributed according to a Poissonian process with a nonuniform law. Significant voids and groups of galaxies are identified at different scales, and small-scale clustering is taken into account to further assess the reliability of the detection. The morphological parameters of the structures are estimated using an elliptical Gaussian model of the local galaxy distribution. The hierarchical clustering of the high-density regions is clearly exhibited. The structures identified on small scale are in good agreement with the published group catalog of the slice obtained by dynamical criteria. Significant structures are also detected at the location of the Abell clusters. Because the analysis is isotropic, the large-scale structures are traced by the alignment of contiguous smaller structures. Voids are identified at a 99.5% confidence level and a selection criterion is applied to take into account the multiple detections inherent to the analysis. We obtain a catalog of the astrophysical voids in the slice.