We examine the sensitivity of the spatial morphologies of galaxy clusters to \Omega _ { 0 } and P ( k ) using high-resolution N-body simulations with large dynamic range .
Variants of the standard CDM model are considered having different spatial curvatures , SCDM ( \Omega _ { 0 } = 1 ) , OCDM ( \Omega _ { 0 } = 0.35 ) , LCDM ( \Omega _ { 0 } = 0.35 , \lambda _ { 0 } = 0.65 ) , and different normalizations , \sigma _ { 8 } .
We also explore critical density models with different spectral indices , n , of the scale-free power spectrum , P ( k ) \propto k ^ { n } .
Cluster X-ray morphologies are quantified with power ratios ( PRs ) , where we take for the X-ray emissivity j _ { gas } \propto \rho ^ { 2 } _ { DM } , which we argue is a suitable approximation for analysis of PRs .
We find that \Omega _ { 0 } primarily influences the means of the PR distributions whereas the power spectrum ( n and \sigma _ { 8 } ) primarily affects their variances : \log _ { 10 } ( P _ { 3 } / P _ { 0 } ) is the cleanest probe of \Omega _ { 0 } since its mean is very sensitive to \Omega _ { 0 } but very insensitive to P ( k ) .
The PR means easily distinguish the SCDM and OCDM models , while the SCDM and LCDM means show a more modest , but significant , difference ( \sim 3 \sigma ) .
The OCDM and LCDM models are largely indistinguishable in terms of the PRs .
Finally , we compared these models to a sample of ROSAT clusters and find that the PR means of the SCDM clusters exceed the ROSAT means with a high formal level of significance ( \sim 4 \sigma ) .
Though the formal significance level of this \rho ^ { 2 } _ { DM } / X-ray comparison should be considered only approximate , we argue that taking into account the hydrodynamics and cooling will not reconcile a discrepancy this large .
The PR means of the OCDM clusters are consistent , and the means of the LCDM clusters are marginally consistent , with those of the ROSAT clusters .
Thus , we conclude that cluster morphologies strongly disfavor \Omega _ { 0 } = 1 , CDM while favoring low density , CDM models with or without a cosmological constant .