The intergalactic medium temperature and Compton y parameter

The thermal Sunyaev Zeldovich (SZ) effect directly probes the thermal energy of the universe. Its precision modeling and future high accuracy measurements will provide a powerful way to constrain the thermal history of the universe. In this paper, we focus on the precision modeling of the gas density weighted temperature T̄g and the mean SZ Compton y parameter. We run high resolution adiabatic hydro simulations adopting the WMAP cosmology to study the intergalactic medium (IGM) temperature and density distribution. To quantify possible simulation limitations, we run n = −1,−2 self similar simulations. Our analytical model on T̄g is based on energy conservation and matter clustering and has no free parameter. Combining both simulations and analytical models thus provides the precision modeling of T̄g and ȳ. We find that the simulated temperature probability distribution function and T̄g shows good convergence. For the WMAP cosmology, our highest resolution simulation (1024 cells, 100 Mpc/h box size) reliably simulates T̄g with better than 10% accuracy for z & 0.5. Toward z = 0, the simulation mass resolution effect becomes stronger and causes the simulated T̄g to be slightly underestimated (At z = 0, ∼ 20% underestimated). Since ȳ is mainly contributed by IGM at z & 0.5, such simulation effect on ȳ is no larger than ∼ 10%. Furthermore, our analytical model is capable of correcting this artifact. It passes all tests of self similar simulations and WMAP simulations and is able to predict T̄g and ȳ to several percent accuracy. For low matter density ΛCDM cosmology, the present T̄g is 0.32(σ8/0.84) (Ωm/0.268) 1.28−0.2σ8 keV, which accounts for 10 of the critical cosmological density and 0.024% of the CMB energy. The mean y parameter is 2.6×10(σ8/0.84) (Ωm/0.268) 8. The current upper limit of y < 1.5×10 measured by FIRAS has already ruled out combinations of high σ8 & 1.1 and high Ωm & 0.5.