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 Tgas = (1.5 ∼ 2.0) keV(Mvir/10h 70 M⊙), and a simple self-similar evolution model (Tgas ∝ M vir ) is strongly disfavored. In the cosmological model that we assume (a ΛCDM universe with Ω0 = 0.3, λ0 = 0.7 and h70 = 1), the derived mass-temperature relation suggests that the mass fluctuation amplitude σ8 is 0.7–0.8. Subject headings: cosmology: theory — dark matter — galaxies: clusters: general — X-rays: galaxies