TheLX‐TandLX‐σ Relationships for Galaxy Clusters Revisited

The relationships between the X-ray determined bolometric luminosity Lx, thetemperature T of the intracluster gas, and the optical measured velocitydispersion sigma of the cluster galaxies are updated for galaxy clusters usingthe largest sample of 256 clusters drawn from literature. The newly establishedrelationships, 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 andevolution. The observationally determined Lx-T and Lx-sigma relationships,$L_x\propto T^{2.72\pm0.05}\propto \sigma^{5.24\pm0.29}$, are marginallyconsistent with those predicted in the scenario that both intracluster gas andgalaxies are in isothermal and hydrostatic equilibrium with the underlyinggravitational potential of clusters. A comparison between these observed andpredicted Lx-T relationships also suggests that the mean cluster baryonfraction fb remains approximately constant among different clusters,$f_b\approx0.17$, which gives rise to a low-mass density universe of$\Omega_m\approx0.3$.Comment: 34 pages, 7 figures, 2 tables, accepted for publication in Ap