Starting with the well-known NFW dark matter halo distribution , we construct a simple polytropic model for the intracluster medium which is in good agreement with high resolution numerical hydrodynamical simulations , apply this model to a very large scale concordance dark matter simulation , and compare the resulting global properties with recent observations of X-ray clusters , including the mass-temperature and luminosity-temperature relations .
We make allowances for a non-negligible surface pressure , removal of low entropy ( short cooling time ) gas , energy injection due to feedback , and for a relativistic ( non-thermal ) pressure component .
A polytropic index n = 5 ( \Gamma = 1.2 ) provides a good approximation to the internal gas structure of massive clusters ( except in the very central regions where cooling becomes important ) , and allows one to recover the observed M _ { 500 } - T , L _ { x } - T and T / n _ { e } ^ { 2 / 3 } \propto T ^ { 0.65 } relations .
Using these concepts and generalizing this method so that it can be applied to fully three-dimensional N-body simulations , one can predict the global X-ray and SZE trends for any specified cosmological model .
We find a good fit to observations when assuming that twelve percent of the initial baryonic mass condenses into stars , the fraction of rest mass of this condensed component transferred back to the remaining gas ( feedback ) is 3.9 \times 10 ^ { -5 } , and the fraction of total pressure from a nonthermal component is near ten percent .