HOT GAS IN THE COLD DARK-MATTER SCENARIO - X-RAY-CLUSTERS FROM A HIGH-RESOLUTION NUMERICAL-SIMULATION

A new, three-dimensional, shock-capturing hydrodynamic code is utilize d to determine the distribution of hot gas in a standard cold dark mat ter (CDM) model of the universe. Periodic boundary conditions are assu med: a box with size 85 h-1 Mpc having cell size 0.31 h-1 Mpc is follo wed in a simulation with 270(3) = 10(7.3) cells. Adopting standard par ameters determined from COBE and light-element nucleosynthesis, sigma8 = 1.05, OMEGA(b), = 0.06, and assuming h = 0.5, we find the X-ray-emi tting clusters and compute the luminosity function at several waveleng ths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. We find that most (great er-than-or-equal-to 3/4) of the total X-ray (hv > 0.3 keV) emissivity in our box originates in a relatively small number of identifiable clu sters which occupy approximately 10(-3) of the box volume. This standa rd CDM model, normalized to COBE, produces approximately 5 times too m uch emission from clusters having L(x) > 10(43) ergs s-1, a not-unexpe cted result. If all other parameters were unchanged, we would expect a dequate agreement for sigma8 = 0.6. This provides a new and independen t argument for lower small-scale power than standard CDM at the 8 h-1 Mpc scale. The background radiation field at 1 keV due to clusters in this model is approximately one-third of the observed background, whic h, after correction for numerical effects, again indicates approximate ly 5 times too much emission and the appropriateness of sigma8 = 0.6. If we have used the observed ratio of gas to total mass in clusters, r ather than basing the mean density on light-element nucleosynthesis, t hen the computed luminosity of each cluster would have increased still further, by a factor of approximately 10. The number density of clust ers increases to z approximately 1, but the luminosity per typical clu ster decreases, with the result that evolution in the number density o f bright clusters is moderate in this redshift range, showing a broad peak near z = 0.7, and then a rapid decline above redshift z = 3. Deta iled computations of the luminosity functions in the range L(x) = 10(4 0)-10(44) ergs s-1 in various energy bands are presented for both clus ter central regions (r < 0.5 h-1 Mpc) and total luminosities (r < 1 h- 1 Mpc) to be used in comparison with ROSAT and other observational dat a sets. The quantitative results found disagree significantly with tho se found by other investigators using semianalytic techniques. For exa mple, the total volume emission from hot cluster gas is found to incre ase by about a factor of 1.5 between z = 0 and z = 1, but for the same CDM model Kaiser (1986) predicted an increase of a factor of 5.7, for self-similar evolution of clusters. We find little dependence of core radius on cluster luminosity and a dependencc of temperature on lumin osity given by log kT(x) = A + B log L(x), which is slightly steeper ( B = 0.38) than is indicated by observations. Computed temperatures are somewhat higher than observed, as expected, in that COBE-normalized C DM has too much power on the relevant scales. A modest average tempera ture gradient is found, with temperatures dropping to 90% of central v alues at 0.4 h-1 Mpc and 70% of central values at 0.9 h-1 Mpc. In thes e models the decrease of the core radius and temperature with redshift is significant (in rough accord with the analytic calculations). We d o not expect to see the same result in open-universe models, so this p roperty should provide an important discriminant among cosmological mo dels. Examining the ratio of gas to total mass in the clusters (which we find to be antibiased by a factor of approximately 0.6), normalized to OMEGA(b) h2 = 0.015, and comparing with observations, we conclude, in agreement with White (1991), that the cluster observations argue f or an open universe.