The temperature of the intergalactic medium and the Compton y parameter

Abstract

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 T̄g 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 T̄ 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 Tg and ȳ. We find that the simulated temperature probability distribution function and T̄g shows good convergence. For the WMAP cosmology, our highest-resolution simulation (10243 cells, 100 Mpc h-1 box size) reliably simulates T̄g with better than 10 per cent 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 per cent underestimated). Since y is mainly contributed by the IGM at z ≳ 0.5, this simulation effect on y is no larger than ∼10 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 T̄g and ȳ to several per cent accuracy. For a low matter density ΛCDM cosmology, the present T̄g is 0.32 (σ8/0.84)3.05-0.15Ωm(Ω m/0.268)1.28-0.2σ8 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 2.6 × 10-6 (σ8/0.84)4.1-2Ωm(Ω m/0.268)1.28-0.2σ8. The current upper limit of y < 1.5 × 10-5 measured by FIRAS has already ruled out combinations of high σ8 ≳ 1.1 and high Ω m ≳ 0.5.