Cluster Ellipticities as a Cosmological Probe

We investigate the dependence of ellipticities of clusters of galaxies oncosmological parameters using large-scale cosmological simulations. Wedetermine cluster ellipticities out to redshift unity for LCDM models withdifferent mean densities $\Omega_m$ and amplitudes of mass fluctuation$\sigma_{8,0}$. The mean ellipticity increases monotonically with redshift forall models. Larger values of $\sigma_{8,0}$, i.e., earlier cluster formationtime, produce lower ellipticities. The dependence of ellipticity on $\Omega_m$is relatively weak in the range $0.2 \leq \Omega_m \leq 0.5$ for high massclusters. The mean ellipticity $\bar{e}(z)$ decreases linearly with theamplitude of fluctuations at the cluster redshift $z$, nearly independent of$\Omega_m$; on average, older clusters are more relaxed and are thus lesselliptical. The distribution of ellipticities about the mean is approximated bya Gaussian, allowing a simple characterization of the evolution of ellipticitywith redshift as a function of cosmological parameters. At $z=0$, the meanellipticity of high mass clusters is approximated by $\bar{e}(z=0) =0.248-0.069 \sigma_{8,0} + 0.013 \Omega_{m,0}$. This relation opens up thepossibility that, when compared with future observations of large clustersamples, the mean cluster ellipticity and its evolution could be used as a new,independent tool to constrain cosmological parameters, especially the amplitudeof mass fluctuations, $\sigma_{8,0}$.Comment: 16 pages, 4 figure