The baryon fraction and velocity-temperature relation in galaxy clusters: Models versus observations

The observed baryon fraction and velocity-temperature relation in clusters of galaxies are compared with hydrodynamic simulations in two cosmological models: standard (Omega = 1) and low-density flat (Omega = 0.45 and lambda = 0.55) cold dark matter (CDM) models, normalized to the COBE background fluctuations. The observed properties of clusters include the velocity dispersion versus temperature relation, the gas mass versus total mass relation, and the gas mass fraction versus velocity dispersion relation. We find that, while both cosmological models reproduce well the shape of these observed functions, only low-density CDM can reproduce the observed amplitudes. We find that sigma similar to T-0.5+/-0.1, as expected for approximate hydrostatic equilibrium with the cluster potential, and the ratio of gas to total mass in clusters is approximately constant for both models. The amplitude of the relations, however, differs significantly between the two models. The low-density CDM model reproduces well the average observed relation of M(gas) = (0.13 +/- 0.02)M h(50)(-1.5) for clusters, while Omega = 1 CDM yields a gas mass that is 3 times lower (M(gas) = 0.045 +/- 0.004M h(50)(-1.5)) with both gas and total mass measured within a fiducial radius of 1.5 h(-1) Mpc. The cluster gas mass fraction reflects approximately the baryon fraction in the models, Omega(b)/Omega, with a slight antibias. Therefore, because of the low baryon density given by nucleosynthesis, Omega(b) similar or equal to 0.06 h(50)(-2), Omega = 1 mdoels produce too few baryons in clusters compared with observations. Scaling our results as a function of Omega, we find that a low-density CDM model, with Omega similar to 0.3-0.4, best reproduces the observed mean baryon fraction in clusters. The observed beta parameter of clusters, beta = sigma(2)/(kT/mu m(p)) = 0.94 +/- 0.08, discriminates less well between the models; it is consistent with that produced by low-density CDM (1.10 +/- 0.22), while it is slightly larger than expected but still consistent with Omega = 1 (0.70 +/- 0.14).