The temperature of the intergalactic medium and the Compton y parameter

The thermal Sunyaev-Zeldovich (SZ) effect directly probes the thermal energy of the Universe. Its precision modelling 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 modelling of the gas density weighted temperature (T) over bar (g) and the mean SZ Compton y parameter. We run high-resolution adiabatic hydrodynamic simulations adopting the WMAP cosmology to study the temperature and density distribution of the intergalactic medium (IGM). To quantify possible simulation limitations, we run n=-1, -2 self-similar simulations. Our analytical model on (T) over bar (g) is based on energy conservation and matter clustering and has no free parameter. Combining both simulations and analytical models thus provides the precision modelling of (T) over bar (g) and (y) over bar. We find that the simulated temperature probability distribution function and (T) over bar (g) shows good convergence. For the WMAP cosmology, our highest-resolution simulation (1024(3) cells, 100 Mpc h(-1) box size) reliably simulates (T) over bar (g) with better than 10 per cent accuracy for zgreater than or similar to0.5. Toward z=0, the simulation mass-resolution effect becomes stronger and causes the simulated (T) over bar (g) to be slightly underestimated (at z=0, similar to20 per cent underestimated). Since (y) over bar is mainly contributed by the IGM at zgreater than or similar to0.5, this simulation effect on (y) over bar is no larger than similar to10 per cent. Furthermore, our analytical model is capable of correcting this artefact. It passes all tests of self-similar simulations and WMAP simulations and is able to predict (T) over bar (g) and (y) over bar to several per cent accuracy. For a low matter density LambdaCDM cosmology, the present (T) over bar (g) is 0.32 (sigma(8)/0.84)(3.05-0.15Omega m) (Omega(m)/0.268)(1.28-0.2sigma 8) keV, which accounts for 10(-8) of the critical cosmological density and 0.024 per cent of the cosmic microwave background (CMB) energy. The mean y parameter is 2.6x10(-6) (sigma(8)/0.84)(4.1-2Omega m)(Omega(m)/0.268)(1.28-0.2sigma 8). The current upper limit of y<1.5x10(-5) measured by FIRAS has already ruled out combinations of high sigma(8)greater than or similar to 1.1 and high Omega(m)greater than or similar to 0.5.