X-RAY-CLUSTERS IN A COLD DARK-MATTER-PLUS-LAMBDA UNIVERSE - A DIRECT,LARGE-SCALE, HIGH-RESOLUTION, HYDRODYNAMIC SIMULATION

A new, three-dimensional, shock-capturing, hydrodynamic code is utiliz ed to determine the distribution of hot gas in a CDM + A model univers e. Periodic boundary conditions are assumed: a box with size 85 h-1 Mp c, having cell size 0.31 h-1 Mpc, is followed in a simulation with 270 (3) = 10(7.3) cells. We adopt OMEGA = 0.45, Lambda = 0.55, h = H/100 k m s-1 Mpc-1 = 0.6, and then, from COBE and light element nucleosynthes is, sigma8 = 0.77, OMEGA(b) = 0.043. We identify the X-ray emitting cl usters in the simulation box, compute the luminosity function at sever al wavelength bands, the temperature function and estimated sizes, as well as the evolution of these quantities with redshift. This open mod el succeeds in matching local observations of clusters in contrast to the standard OMEGA = 1, CDM model, which fails. It predicts an order o f magnitude decline in the number density of bright (hnu = 2-10 keV) c lusters from z = 0 to z = 2 in contrast to a slight increase in the nu mber density for standard OMEGA = 1, CDM model. This COBE-normalized C DM + A model produces approximately the same number of X-ray clusters having L(x) > 10(43) ergs s-1 as observed. The background radiation fi eld at 1 keV due to clusters is approximately 10% of the observed back ground which, after correction for numerical effects, again indicates that the model is consistent with observations. The number density of bright clusters increases to z approximately 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 s hows a broad peak near z = 0.5, and then a rapid decline as z --> 3. T he most interesting point which we find is that the temperatures of cl usters in this model freeze out at later times (z less-than-or-equal-t o 0.3), while previously we found in the CDM model that there was a st eep increase during the same interval of redshift. Equivalently, we fi nd 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 monotonica lly decreasing function of redshift. Both trends should be detectable even with a relatively ''soft'' X-ray instrument such as ROSAT, provid ing a powerful discriminant between OMEGA = 1 and OMEGA < 1 models. De taILed 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 cl uster cores (r less-than-or-equal-to 0.5 h-1 Mpc) and total luminositi es (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 evo lution. We find little dependence of core radius on cluster luminosity and the dependence of temperature on luminosity long kT(x) = A + B lo g L(x), which is slightly steeper (B = 0.32 +/- 0.01) than indicated b y observation (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 i n the OMEGA = 1 model, and the evolution far slower (-30% vs. -50%) th an in the OMEGA = 1 model to redshift z = 0.5. A modest average temper ature 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 f ind a slight antibias [b = 0.9 or (OMEGA(gas)/OMEGA(tot)cl = 0.083 +/- 0.007], which is consistent with observations [OMEGA(gas)/OMEGA(tot)) obs = 0.097 +/- 0.019 for the Coma cluster for the given value of h, c f., White 1991].