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We analyze the C4 catalog of galaxy clusters from the Sloan Digital SkySurvey (SDSS) to investigate the axis-ratio distribution of the projected twodimensional cluster profiles. We consider only those objects in the catalogwhose virial mass is close to 10^{14}h^{-1}M_{sun}, with member galaxies withinthe scale radius 1000 kpc. The total number of such objects turns out to be336. We also derive a theoretical distribution by incorporating the effect ofprojection onto the sky into the analytic formalism proposed recently by Lee,Jing, & Suto. The theoretical distribution of the cluster axis-ratios is shownto depend on the amplitude of the linear power spectrum (sigma_8) as well asthe density parameter (Omega_{m}). Finally, fitting the observational data tothe analytic distribution with Omega_{m} and sigma_{8} as two adjustable freeparameters, we find the best-fitting value of sigma_{8}=(1.01 +/-0.09)(Omega_{m}/0.6)^{(0.07 +/- 0.02) +0.1 Omega_{m}}$. It is a newsigma_{8}-Omega_{m} relation, different from the previous one derived from thelocal abundance of X-ray clusters. We expect that the axis-ratio distributionof galaxy clusters, if combined with the local abundance of clusters, may putsimultaneous constraints on sigma_{8} and Omega_{m}.Comment: accepted for publication in ApJ, 17 pages, 3 figures, improved  analysis, more discussion on the validity and the caveats of the mode

The Axis‐Ratio Distribution of Galaxy Clusters in the SDSS‐C4 Catalog as a New Cosmological Probe