Constraints on the Linear Bias from Cluster Statistics
Abstract
The observed distributions of velocity dispersions and Xray temperatures in clusters of galaxies are related to the theoretical mass function of these systems in the standard (Omega_0 =1) CDM cosmogony. We obtain M(sigma_ {los}) and M(kT_X) relations as a function of the linear bias parameter b in spheres of 8\ h(1) Mpc. The inferred relations are unique inside any finite range of the variables. We find that, for b ~< 1.5, sigma_{los} and T_X vary very slowly with M, as observed in cosmological simulations. The comparison of these correlations with the ones predicted for different cluster models is used to further constrain the biasing. Two models are examined: (1) the classical beta model, which assumes that the intracluster medium and the galaxies are isotropic isothermal gases in hydrostatic equilibrium with the cluster potential; and (2) a less constrained model, with the same spatial distributions of the luminous components adopted for the former model, but with nonuniform velocity dispersions and temperatures, and a slight galaxy velocity anisotropy. For the beta model, the two values of b obtained from the galaxies and from the intracluster gas are higher than 2.0 and different from each other, reflecting the incompatibility of the kinematics adopted for these components with their observed spatial repartitions. Consistent values of b can only be obtained by means of the nonisothermal and anisotropic cluster model. This latter gives b ~ 1.5, in reasonable agreement with other independent estimates. Such a relatively low bias yields also total cluster masses similar to those inferred from gravitational lensing techniques and ~ 3 times larger than the ones derived in classical dynamical analysis. Accordingly, this second cluster model leads to a barion fraction three times smaller than conventionally found. This is just about the right amount needed to solve the problem of the barion fraction excess in flat universes.
 Publication:

American Astronomical Society Meeting Abstracts #188
 Pub Date:
 May 1996
 Bibcode:
 1996AAS...188.1212S