Expected properties of the Two-Point Autocorrelation Function of the IGM

Recent analyses of the fluctuations of the soft Diffuse X-ray Background (DXB) have provided indirect detection of a component consistent with the elusive Warm Hot Intergalactic Medium (WHIM). In this work we use theoretical predictions obtained from hydrodynamical simulations to investigate the angular correlation properties of the WHIM in emission and assess the possibility of indirect detection with next-generation X-ray missions. Our results indicate that the angular correlation signal of the WHIM is generally weak but dominates the angular correlation function of the DXB outside virialized regions. Its indirect detection is possible but requires rather long exposure times [0.1-1] Ms, large (~1{\deg} x1{\deg}) fields of view and accurate subtraction of isotropic fore/background contributions, mostly contributed by Galactic emission. The angular correlation function of the WHIM is positive for {\theta} < 5' and provides limited information on its spatial distribution. A satisfactory characterization of the WHIM in 3D can be obtained through spatially resolved spectroscopy. 1 Ms long exposures with next generation detectors will allow to detect ~400 O VII+O VIII X-ray emission systems that we use to trace the spatial distribution of the WHIM. We predict that these observations will allow to estimate the WHIM correlation function with high statistical significance out to ~10 Mpc h^-1 and characterize its dynamical state through the analysis of redshift-space distortions. The detectable WHIM, which is typically associated with the outskirts of virialized regions rather than the filaments has a non-zero correlation function with slope {\gamma} = -1.7 \pm 0.1 and correlation length r0 = 4.0 \pm 0.1 Mpc h^-1 in the range r = [4.5, 12] Mpc h^-1. Redshift space distances can be measured to assess the dynamical properties of the gas, typically infalling onto large virialized structures.