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 very tightly constrained as T_{ gas} = (1.5~2.0)keV (M_{ vir}/10^{ 14}h_{ 70}^{ -1}M_\odot)^{ 0.5~0.55}, and a simple self-similar evolution model (T_{ gas} \propto M_{ vir}^{ 2/3}) is strongly disfavored. In the cosmological model that we assume (a \Lambda CDM 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.
Categories: astro-ph