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 utilized to determine the distribution of hot gas in a standard cold dark matter (CDM) model of the 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 270^3^ = 10^7.3^ cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, σ_8_ = 1.05, {OMEGA}_b_ = 0.06, and assuming h = 0.5, we find the X-ray-emitting clusters and compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. We find that most (>= 3/4) of the total X-ray (hv > 0.3 keV) emissivity in our box originates in a relatively small number of identifiable clusters which occupy approximately 10^-3^ of the box volume. This standard CDM model, normalized to COBE, produces approximately 5 times too much emission from clusters having L_x_ > 10^43^ ergs s^-1^, a not-unexpected result. If all other parameters were unchanged, we would expect adequate agreement for σ_8_ = 0.6. This provides a new and independent 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, which, after correction for numerical effects, again indicates approximately 5 times too much emission and the appropriateness of σ_8_ = 0.6. If we have used the observed ratio of gas to total mass in clusters, rather than basing the mean density on light-element nucleosynthesis, then the computed luminosity of each cluster would have increased still further, by a factor of approximately 10. The number density of clusters increases to z ~ 1, but the luminosity per typical cluster decreases, with the result that evolution in the number density of 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. Detailed computations of the luminosity functions in the range L_x_ = 10^40^-10^44^ ergs s^-1^ in various energy bands are presented for both cluster 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 data sets. The quantitative results found disagree significantly with those found by other investigators using semianalytic techniques. For example, the total volume emission from hot cluster gas is found to increase 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 dependence of temperature on luminosity 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 CDM has too much power on the relevant scales. A modest average temperature gradient is found, with temperatures dropping to 90% of central values at 0.4 h^-1^ Mpc and 70% of central values at 0.9 h^-1^ Mpc. In these models the decrease of the core radius and temperature with redshift is significant (in rough accord with the analytic calculations). We do not expect to see the same result in open- universe models, so this property should provide an important discriminant among cosmological models. 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_h^2^ = 0.015, and comparing with observations, we conclude, in agreement with White (1991), that the cluster observations argue for an open universe.