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 d ispersion, X-ray luminosity, three total mass estimates (velocity-base d, temperature-based, and gravitational lensing derived), gas fraction and substructure, utilizing a large simulation of st realistic cosmol ogical model (a cold dark matter model with the following parameters: H-0 = 65 km s(-1) Mpc(-1), Omega(0) = 0.4, Lambda(0) = 0.6, sigma(8) = 0.79). Unlike previous studies focusing on the Abell clusters, we con servatively assume that both optical and X-ray observations can determ ine the source (galaxy or hot X-ray gas) positions along the line of s ight as well as in the sky plane accurately; hence, we only include so urces inside the velocity space defined by the cluster galaxies (filte red through the pessimistic 3 sigma clipping algorithm) as possible co ntamination 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, t he broadness of the observed distribution of gas to total mass ratio i s adequately accounted for by projection effects, alleviating (though not preventing) the need to invoke other nongravitational physical pro cesses. While the moderate boost in the ratio narrows the gap, it is s till not quite sufficient to reconcile the standard nucleosynthesis va lue of Omega(b) = 0.0125(H-0/100)(-2) (Walker et al. 1991) and Omega(0 ) = 1 with the observed gas to mass ratio value in clusters of galaxie s, 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-r ay imaging observations, may be subject to more projection contaminati ons than we allow for in our analysis. In contrast, the X-ray luminosi ty of a duster within a radius less than or equal to 1.0 h(-1) Mpc is hardly altered by projection, rendering the cluster X-ray luminosity f unction a very useful and simple diagnostic for comparing observations with theoretical predictions. Rich cluster masses [M(<1.0 h(-1) Mpc) greater than or equal to 3 x 10(14) h(-1) M-circle dot] derived from X -ray temperatures or galaxy velocity dispersions underestimate, on ave rage, the true cluster masses by about 20%, with the former displaying a smaller scatter, thus providing a better means for cluster mass det ermination. 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 ve locity or temperature derived mass is about 1.2-1.3 for rich clusters, with a small fraction reaching about similar to 2.0. The dispersion i n that ratio increases rapidly for poor clusters, reaching about 1.0-2 .0 for clusters with masses of M similar to 1-3 x 10(14) M-circle dot. It appears that projection effects alone may be able to account for t he disparities in existing observational data for cluster masses, dete rmined by various methods. Projection inflates substructure measuremen ts in galaxy maps, but affects X-ray maps much less. Most clusters (gr eater than or equal to 90%) in this model universe do not contain sign ificant intrinsic substructure on scales greater than or equal to 50 h (-1) kpc at R-proj less than or equal to 1 h(-1) Mpc without projectio n effects, whereas more than similar to 50% of the same clusters would be ''observed'' to show statistically significant substructure as mea sured by the Dressler-Shectman Delta statistic. The fact that a compar able fraction (similar to 50%) of real observed clusters show substruc ture measured in the same way implies that most of the substructure ob served in real clusters of galaxies may be due to projection. Finally, we point out that it is often very difficult to correctly interpret c omplex structures seen in galaxy and X-ray maps of clusters, which fre quently display illusory configurations due to projection. Until we ca n determine real distances of X-ray sources and galaxies accurately, f or some observables, the only meaningful way to compare predictions of a cosmological model with the cluster observations is to subject clus ters in a simulated universe to exactly the same observational biases and uncertainties, including projection and other instrumental limitat ions, and to compare the ''observed'' simulated clusters with real one s.