Updating the σ-T relationship for galaxy clusters

The relationship between the X-ray determined temperature T of the intracluster gas and the optical measured velocity dispersion σ of the cluster galaxies is often believed to be not only a straightforward but also robust test for the dynamical properties of galaxy clusters. Here, we present the σT relationship using the 94 clusters drawn from the largest sample of 149 clusters in literature, for which both σ and T are observationally determined. Employment of the doubly weighted orthogonal distance regression to our sample yields σ = 102.47±0.06T 0.67±0.09, indicating an apparent deviation of dynamical state from that predicted by the isothermal and hydrostatic equilibrium model for galaxy clusters, though the average ratio βspec of specific energy in galaxies to that in gas is found to be in excellent agreement with unity. It shows that a nonisothermal gas distribution with a mean polytropic index of γ = 1.3 can account for the reported σ-T relationship, while overall clusters can still be regarded as dynamically-relaxed systems.