The L_X-T and L_X-σ 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 velocity dispersion, σ, of the cluster galaxies are updated for galaxy clusters using the largest sample of 256 clusters drawn from literature. The newly established relationships, based on the doubly weighted orthogonal distance regression (ODR) method, are justified by both their self-consistency and 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-σ relationships, L_X ∝ T^2.72±0.05 ∝ σ^5.24±0.29, are marginally consistent with those predicted by the scenario in which both intracluster gas and galaxies are in isothermal and hydrostatic equilibrium with the underlying gravitational potential of clusters. A comparison between these observed and predicted L_X-T relationships also suggests that the mean cluster baryon fraction, f_b, remains approximately constant among different clusters, f_b ≈ 0.17, which gives rise to a low mass density universe of Ω_m ≈ 0.3.