The L-X-T and L-X-sigma relationships for galaxy clusters revisited

The relationships between the X-ray-determined bolometric luminosity, L-x, the temperature, T, of the intracluster gas, and the optical measured veloc ity dispersion, sigma, of the cluster galaxies are updated for galaxy clust ers using the largest sample of 256 clusters drawn from literature. The new ly established relationships, based on the doubly weighted orthogonal dista nce regression (ODR) method, are justified by both their self-consistency a nd co-consistency, which can then be used to test the theoretical models of cluster formation and evolution. The observationally determined L-x-T and L-x-sigma relationships, L(x)proportional to T2.72+/-0.05 proportional to s igma(5.24+/-0.29), are marginally consistent with those predicted by the sc enario in which both intracluster gas and galaxies are in isothermal and hy drostatic equilibrium with the underlying gravitational potential of cluste rs. A comparison between these observed and predicted L-x-T relationships a lso suggests that the mean cluster baryon fraction, fbr remains approximate ly constant among different clusters,f(b) approximate to 0.17, which gives rise to a low mass density universe of Omega(m) approximate to 0.3.