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 (Ω = 1) and low-density flat (Ω = 0.45 and λ = 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 a ∼ 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 h₅₀^-1.5 for clusters, while Ω = 1 CDM yields a gas mass that is 3 times lower (M_gas = 0.045 ± 0.004M h₅₀^-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, Ω_b/Ω, with a slight antibias. Therefore, because of the low baryon density given by nucleosynthesis, Ω ≃ 0.06 h₅₀^-2, Ω = 1 models produce too few baryons in clusters compared with observations. Scaling our results as a function of Ω, we find that a low-density CDM model, with Ω ∼ 0.3-0.4, best reproduces the observed mean baryon fraction in clusters. The observed β parameter of clusters, β = σ²/(kT/μm_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 Ω = 1 (0.70 ± 0.14).