Towards Understanding Galaxy Clusters and Their Constituents:Projection Effects on Velocity Dispersion, X-Ray Emission, Mass Estimates, Gas Fraction and Substructure

We study the projection effects on various observables of clusters of galaxies at redshift near zero, including cluster richness, velocity dispersion, X-ray luminosity, three total mass estimates (velocity-based, temperature-based and gravitational lensing derived), gas fraction and substructure. Unlike previous studies focusing on the Abell clusters, we conservatively assume that both optical and X-ray observations can determine the source (galaxy or hot X-ray gas) positions along the line of sight as well as in the sky plane accurately; hence we only include sources inside the velocity space defined by the cluster galaxies (filtered through the pessimistic 3 sigma clipping algorithm) as possible contamination sources. Projection effects are found to be important for some quantities but insignificant for others. We show that, on average, the gas to total mass ratio in clusters appears to be 30-40% higher than its corresponding global ratio. Independent of its mean value, the broadness of the observed distribution of gas to total mass ratio is adequately accounted for by projection effects, alleviating the need to invoke (though not preventing) other non gravitational physical processes. While the moderate boost in the ratio narrows the gap, it is still not quite sufficient to reconcile the standard nucleosynthesis value of $\Omega_b=0.0125(H_0/100)^{-2}$ and $\Omega=1$ with the observed gas to mass ratio value in clusters of galaxies, $0.05(H_0/100)^{-3/2}$, for any plausible value of $H_0$. However, it is worth noting that real observations of X-ray clusters, especially X-ray imaging observations, may be subject to more projection contaminations than we allow for in our analysis. In contrast, the X-ray luminosity of a cluster within a radius $\leq 1.0h^{-1}$Mpc is hardly