We examine the observational relation between the X-ray temperatures and the robust galaxy velocity dispersions, T vs. sigma, in a sample of 55 galaxy clusters. In this sample the T vs. sigma relation is only marginally consistent (at s.l. = 95 %), with the theoretical isothermal relation where T ~ sigma^2. In particular, richer clusters have larger galaxy-energy to gas-energy ratios than poorer clusters. We are analyzing many possible bias sources for sigma estimate, such as the presence of substructures and velocity anisotropy in galaxy orbits. According to preliminary results, the slight discrepancy between the observed and theoretical relation is not easily solved. Different processes occurring in the ICM (cooling flows, galactic winds, turbulence, magnetic fields) could be responsible for a noticeable masking of the true T vs. sigma relation since the observed X-ray temperatures do not always coincide with the virial temperatures. We point out that each possible deviation of the observed T vs. sigma relation from the isothermal model reveals the existence of problems in determination of virial temperature and/or velocity dispersion, and consequenctly in cluster mass and mass function estimates.
