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We use a representative sample of galaxy clusters to constrain the range of cluster X--ray morphologies. After developing and testing quantitative, objective, and reproducible measures of cluster X--ray morphology, we apply these measures to a sample of 65{\it\ Einstein} IPC cluster observations to constrain the intrinsic distributions of (i) emission weighted centroid variation $w_{\vec x}$, (ii) emission weighted axial ratio $\eta$, (iii) emission weighted orientation $\theta_o$, and (iv) measures of the radial fall--off, $\alpha$ and $\beta$. For each cluster we use a Monte--Carlo procedure to determine the effects of Poisson noise, detector imperfections, and foreground/background X--ray point sources.
We then use the range of cluster X--ray morphology to constrain three generic cosmological models ($\Omega$=1, $\Omega_o$=0.2, and $\Omega_o$=0.2 \& $\lambda_o$=0.8). We evolve eight sets of Gaussian random initial conditions consistent with an effective power spectrum $P(k)\propto k^{-1}$ on cluster scales. Using a sample of 24 numerical cluster simulations ($3\times8$) which include gravity and gas physics (but no cooling or ejection from galaxies), we compare observed cluster X--ray morphologies with the X--ray morphologies of clusters simulated with different underlying cosmological models. Specifically, we build artificial ensembles with the same distributions in the number of cluster photons, X--ray temperature, and cluster redshift as the{\it\ Einstein} ensemble; we then compare the observed and simulated distributions in $w_{\vec x}$, $\eta$, and $\alpha$.
The comparisons indicate that (i) these three morphological characteristics are sensitive to the underlying cosmological model, and (ii) galaxy clusters with the observed range of X--ray morphology are very unlikely in low $\Omega_o$ cosmologies. The analysis favors the $\Omega$=1 model, though some discrepancies remain. We discuss the effects of changing the initial conditions and of including additional physics in the simulations.
