The axis-ratio distribution of galaxy clusters in the SDSS-C4 catalog as a new cosmological probe

We analyze the C4 catalog of galaxy clusters from the Sloan Digital Sky Survey (SDSS) to investigate the axis-ratio distribution of the projected two-dimensional cluster profiles. We consider only those objects in the catalog whose virial mass is close to 10(14) h(-1) M-., with member galaxies within the scale radius 1000 kpc. The total number of such objects turns out to be 336. We also derive a theoretical distribution by incorporating the effect of projection onto the sky into the analytic formalism proposed recently by Lee, Jing,& Suto. The theoretical distribution of the cluster axis ratios is shown to depend on the amplitude of the linear power spectrum (sigma(8)) as well as the density parameter (Omega(m)). Finally, fitting the observational data to the analytic distribution with Omega(m) and sigma(8) as two adjustable free parameters, 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 new sigma(8)-Omega(m) relation, different from the previous one derived from the local abundance of X-ray clusters. We expect that the axis-ratio distribution of galaxy clusters, if combined with the local abundance of clusters, may put simultaneous constraints on sigma(8) and Omega(m).