Mass-temperature relation of galaxy clusters: Implications from the observed luminosity-temperature relation and X-ray temperature function

We derive constraints on the mass-temperature relation of galaxy clusters from their observed luminosity-temperature relation and X-ray temperature function. Adopting the isothermal gas in hydrostatic equilibrium embedded in the universal density profile of dark matter halos, we compute the X-ray luminosity for clusters as a function of their hosting halo mass. We find that in order to reproduce the two observational statistics, the mass-temperature relation is fairly well constrained as T-gas = (1.5 similar to 2.0) keV (M-vir/10(14) h(70)(-1) M.)(0.5similar to0.55), and a simple self-similar evolution model (T-gas proportional to M-vir(2/3)) is strongly disfavored. In the cosmological model that we assume (a LambdaCDM universe with Omega(0) = 0.3, lambda(0) = 0.7, and h(70) = 1), the derived mass-temperature relation suggests that the mass fluctuation amplitude sigma(8) is 0.7-0.8.