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 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, utilizing a large simulation of a realistic cosmological model (a cold dark matter model with the following parameters: H0 = 65 km s-1 Mpc-1, Ω0 = 0.4, Λ0 = 0.6, σ8 = 0.79). 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 3σ 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 (though not preventing) the need to invoke other nongravitational 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 Ωb = 0.0125(H0/100)-2 (Walker et al. 1991) and Ω0 = 1 with the observed gas to mass ratio value in clusters of galaxies, 0.05(H0/100)-3/2, for any plausible value of H0. 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 ≤1.0 h-1 Mpc is hardly altered by projection, rendering the cluster X-ray luminosity function a very useful and simple diagnostic for comparing observations with theoretical predictions. Rich cluster masses [M(<1.0 h-1 Mpc) ≥ 3 × 1014 h-1 M☉] derived from X-ray temperatures or galaxy velocity dispersions underestimate, on average, the true cluster masses by about 20%, with the former displaying a smaller scatter, thus providing a better means for cluster mass determination. The gravitational lensing reconstructed (assuming an ideal inversion) mass is, on average, overestimates the true mass by only 5%-10% but displays a dispersion significantly larger than that of the X-ray determined mass. The ratio of the lensing derived mass to the velocity or temperature derived mass is about 1.2-1.3 for rich clusters, with a small fraction reaching about ~2.0. The dispersion in that ratio increases rapidly for poor clusters, reaching about 1.0-2.0 for clusters with masses of M ~ 1 - 3 × 1014 M☉. It appears that projection effects alone may be able to account for the disparities in existing observational data for cluster masses, determined by various methods. Projection inflates substructure measurements in galaxy maps, but affects X-ray maps much less. Most clusters (≥90%) in this model universe do not contain significant intrinsic substructure on scales ≥50 h-1 kpc at Rproj ≤ 1 h-1 Mpc without projection effects, whereas more than ~50% of the same clusters would be "observed" to show statistically significant substructure as measured by the Dressler-Shectman Δ statistic. The fact that a comparable fraction (~50%) of real observed clusters show substructure measured in the same way implies that most of the substructure observed in real clusters of galaxies may be due to projection. Finally, we point out that it is often very difficult to correctly interpret complex structures seen in galaxy and X-ray maps of clusters, which frequently display illusory configurations due to projection. Until we can determine real distances of X-ray sources and galaxies accurately, for some observables, the only meaningful way to compare predictions of a cosmological model with the cluster observations is to subject clusters in a simulated universe to exactly the same observational biases and uncertainties, including projection and other instrumental limitations, and to compare the "observed" simulated clusters with real ones.