Expected properties of the two-point autocorrelation function of the intergalactic medium

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 (similar to 1 degrees x 1 degrees) fields of view and accurate subtraction of isotropic fore/background contributions, mostly contributed by Galactic emission. The angular correlation function of the WHIM, which turns out to be positive for theta < 5 arcmin, provides limited information on its spatial distribution. A satisfactory characterization of the WHIM in 3D can be obtained through spatially resolved spectroscopy. 1Ms long exposures with next generation detectors will allow to detect similar to 400 OVII+OVIII X-ray emission systems that could be used to trace the spatial distribution of the WHIM. We predict that these observations will allow us to estimate the WHIM correlation function with high statistical significance out to similar 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 +/- 0.1 and correlation length r(0) = 4.0 +/- 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 that we predict to be typically infalling on to large virialized structures.