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**Session 12 - Cosmology, Large-Scale Structure and Distance Scales.**

*Display session, Monday, June 10*

*Great Hall, *

## [12.12] Constraints on the Linear Bias from Cluster Statistics

*J. M. Solanes, E. Salvador-Solé, A. Manrique (UB, Spain)*

The observed distributions of velocity dispersions and X-ray
temperatures in clusters of galaxies are related to the theoretical
mass function of these systems in the standard (Ømega_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\mathrel\hbox\rlap\hbox\lower4pt\hbox\sim\hbox<
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: 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 non-uniform 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 non-isothermal and
anisotropic cluster model. This latter gives b\sim 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 \sim 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.

**Program
listing for Monday**