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 \sim 2.0 ) { keV } ( M _ { vir } / 10 ^ { 14 } h _ { 70 } ^ { -1 } M _ { \odot } ) ^ % { 0.5 \sim 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 .