A 3-D Wavelet Analysis of the Coma Cluster

From a catalog of 798 galaxy redshifts in the region of the Coma cluster we look for the presence of substructure and voids at different scales ranging from $\sim 1$ to $\sim 16 h^{-1}$ Mpc, using a structure analysis method based on wavelet transforms and segmentation analysis. The wavelet transform allows us to find out structures on different scales and the segmentation method allows us a quantitative statistical and morphological analysis of the sample. Moreover, from the whole catalog we have selected 320 galaxies, with redshifts between $cz=5858$ km/s and $cz=8168$ km/s that we identify as belonging to the central region of Coma and on which we have performed a deeper analysis, on scales ranging from $180 h^{-1} $ Kpc to $1.44 h^{-1}$ Mpc. Our results are expressed in terms of number of structures or voids and sphericity for different values of the threshold detection and at all the scales investigated. According to our analysis, there is strong evidence for multiple hierarchical substructure on scales ranging from a few hundreds of Kpc to about $4 h^{-1} $ Mpc, and the substructure morphology is rather spherical. We find the two subclusters already described in previous papers, but we also find evidence for more clumps whose positions can be identified approximatively with the galaxies: NGC 4934 and 4840, 4889, 4898 and 4864, 4874 and 4839, 4927, 4875.