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