The contribution of the Warm-Hot Intergalactic Medium to the CMB anisotropies via the Sunyaev-Zeldovich effect

Abstract

Cosmological hydrodynamical simulations predict that a large fraction of all baryons reside within mildly non-linear structures with temperatures in the range $10^{5}-10^{7}$K. As the gas is highly ionized, it could be detected by the temperature anisotropies generated on the Cosmic Microwave Background radiation. We refine our previous estimates of the thermal Sunyaev-Zeldovich effect by introducing a non-polytropic equation of state to model the temperature distribution of the shock heated gas derived from temperature-density phase diagrams of different hydrodynamical simulations. Depending on the specific model, the Comptonization parameter varies in the range $10^{-7}\le y_c \le 2\times 10^{-6}$, compatible with the FIRAS upper limit. This amplitude is in agreement with a simple toy model constructed to estimate the average effect induced by filaments of ionized gas. Using the log-normal probability density function we calculate the correlation function and the power spectrum of the temperature anisotropies generated by the WHIM filaments. For a wide range of the parameter space, the maximum amplitude of the radiation power spectrum is $(\ell+1)\ell C_{\ell}/2\pi =0.7-70(\mu K)^2$ at $\ell \approx 200-500$. This amplitude scales with baryon density, Hubble constant and the amplitude of the matter power spectrum $\sigma_8$ as $[(\ell+1)\ell C_\ell]_{\mathrm{max}}/2\pi \propto \sigma_8^{2.6}(\Omega_b h)^2$. Since the thermal Sunyaev-Zeldovich effect has a specific frequency dependence, we analyze the possibility of detecting this component with the forthcoming Planck data.