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A new, three-dimensional, shock-capturing, hydrodynamic code is utilized to determine the distribution of hot gas in a CDM + LAMBDA model universe. Periodic boundary conditions are assumed: a box with size 85 h^-1^ Mpc, having cell size 0. 31 h^-1^ Mpc, is followed in a simulation with 270³^ = 10⁷. 3^ cells. We adopt OMEGA = 0. 45, λ = 0. 55, h = H/100 km s^-1^ Mpc^-1^ = 0. 6, and then, from COBE and light element nucleosynthesis, σ₈_ = 0. 77, OMEGAb_= 0. 043. We identify the X-ray emitting clusters in the simulation box, compute the luminosity function at several wavelength bands, the temperature function and estimated sizes, as well as the evolution of these quantities with redshift. This open model succeeds in matching local observations of clusters in contrast to the standard OMEGA = 1, CDM model, which fails. It predicts an order of magnitude decline in the number density of bright (hv = 2-10 keV) clusters from z = 0 to z = 2 in contrast to a slight increase in the number density for standard OMEGA = 1, CDM model. This COBE-normalized CDM + LAMBDA model produces approximately the same number of X-ray clusters having Lₓ_ > 10⁴3^ ergs s^-1^ as observed. The background radiation field at 1 keV due to clusters is 10% of the observed background which, after correction for numerical effects, again indicates that the model is consistent with observations. The number density of bright clusters increases to z ~ 0. 2-0. 5 and then declines, but the luminosity per typical cluster decreases monotonically with redshift, with the result that the number density of bright clusters shows a broad peak near z = 0. 5, and then a rapid decline as z approaches 3. The most interesting point which we find is that the temperatures of clusters in this model freeze out at later times (z <= 0. 3), while previously we found in the CDM model that there was a steep increase during the same interval of redshift. Equivalently, we find that L^*^ of the Schechter fits of cluster luminosity functions peaks near z = 0. 3 in this model, while in the CDM model it is a monotonically decreasing function of redshift. Both trends should be detectable even with a relatively "soft" X-ray instrument such as ROSAT, providing a powerful discriminant between OMEGA = 1 and OMEGA < 1 models. Detailed computations of the luminosity functions in the range Lₓ_ = 10⁴0^-10⁴4^ ergs s^-1^ in various energy bands are presented for both cluster cores (r <= 0. 5 h^-1^ Mpc) and total luminosities (r < 1 h^- 1^ Mpc). These are to be used for comparison with ROSAT and other observational data sets. They show the above noted negative evolution. We find little dependence of core radius on cluster luminosity and the dependence of temperature on luminosity log kTₓ_ = A + B log Lₓ_, which is slightly steeper (B = 0. 32 +/- 0. 01) than indicated by observations (B = 0. 265 +/- 0. 035), but within observational errors. In contrast, the standard OMEGA = 1 model predicted temperatures which were significantly too high. The mean luminosity-weighted temperature is 1. 8 keV, dramatically lower (by a factor of 3. 5) than that found in the OMEGA = 1 model, and the evolution far slower (-30% vs. -50%) than in the OMEGA = 1 model to redshift z = 0. 5. A modest average temperature gradient in clusters is found with temperatures dropping to 90% of central values at 0. 4 h^-1^ Mpc and to 60% of central values at 0. 9 h^-1^ Mpc. Examining the ratio of gas-to-total mass in the clusters, we find a slight antibias b = 0. 9 or (OMEGAgas_/OMEGAₜot_) cl_ = 0. 083+/- 0. 007, which is consistent with observations (OMEGAgas_/OMEGAₜot_) ₒbs_ = 0. 097 +/- 0. 019 for the Coma cluster for the given value of h, cf. , White 1991.
Cen et al. (Fri,) studied this question.