X-Ray Clusters in a CDM$+\Lambda$ Universe: A Direct, Large-Scale, High Resolution, Hydrodynamic Simulation

A new, three-dimensional, shock capturing, TVD hydrodynamic code is utilized to determine the distribution of hot gas in a CDM$+\Lambda$ model universe. 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 ($h\nu = 2-10$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 $L_x>10^{43}$erg/s as observed. The number density of bright clusters increases to $z\sim 0.2-0.5$ and 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 $z\rightarrow 3$. The most interesting point which we find is that the temperatures of clusters in this model freeze out at later times ($z\le 0.3$), while previously we found in the CDM model that there was a steep increase during the same interval of redshift. The trend 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. Examining the ratio of gas-to-total mass in the clusters, we find a slight antibias ($b=0.9$ or $({\Omega_{gas}\over\Omega_{tot}})_{cl} =0.083\pm 0.007$), which is consistent with observations [$({\Omega_{gas}\over\Omega_{tot}})_{obs}=0.097\pm 0.019$ for the Coma cluster for the given value of $h$, \cf, White 1991].