THE ASTROPHYSICAL JOURNAL, 485:447-459, 1997 August 20 EVIDENCE OF SUBSTRUCTURE IN THE CLUSTER OF GALAXIES A3558 CHRISTINE C. DANTAS[1], REINALDO R. DE CARVALHO[2,3], HUGO V. CAPELATO[1], AND ALAIN MAZURE[4] ABSTRACT We investigate the dynamical properties of the cluster of galaxies A3558 (Shapley 8). Studying a region of 1 deg^2 (~3 Mpc^2) centered on the cluster cD galaxy, we have obtained a statistically complete photometric catalog with positions and magnitudes of 1421 galaxies (down to a limiting magnitude of B ~ 21). This catalog has been matched to the recent velocity data obtained by Mazure et al. and from the literature, yielding a radial velocity catalog containing 322 galaxies. We analyze the resulting catalog in search of substructure, using different statistical techniques. This analysis shows that the position/velocity space distribution of galaxies shows significant substructure. A central bimodal core, detected previously in a preliminary study by Dantas, de Carvalho, & Capelato and by an analysis of the X-ray emission map by Slezak, Durret, & Gerbal, is confirmed using the adaptive kernel technique and wavelet analysis. We show that this central bimodal substructure is nevertheless composed of a projected feature, kinematically unrelated to the cluster, plus a group of galaxies probably in its initial merging phase into a relaxed core. The cD galaxy's velocity offset with respect to the average cluster redshift, reported earlier by several authors, is completely eliminated as a result of our dynamical analysis. The untangling of the relaxed core component also allows a better, more reliable determination of the central velocity dispersion, which in turn eliminates the "Beta problem" for A3558. The cluster also shows a "preferential" distribution of subclumps coinciding with the direction of the major-axis position angle of the cD galaxy and of the central X-ray emission ellipsoidal distribution, in agreement with the anisotropic merger scenario described by West. Subject headings: catalogs -- galaxies: clusters: individual (A3558) -- galaxies: distances and redshifts -- galaxies: elliptical and lenticular, cD -- galaxies: photometry 1 Divisao de Astrofisica, Insitutio Nacional de Pesquisas Espacias/MCT, C.P. 515, 12201-970 Sao Jose dos Campos, SP, Brazil. 2 Present address: Department of Astronomy, California Institute of Technology, Pasadena, CA 91125. 3 On leave of absence from Departamento de Astrofisica, Observatorio Nacional, CNPq, Brazil. 4 Laboratoire d'Astronomie Spatiale, IGRAP, Traverse du Siphon, F-13012 Marseille, France.