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 ( \sim 1 ^ { \circ } \times 1 ^ { \circ } ) 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 ^ { \prime } 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 \sim 400 O VII +O VIII X-ray emission systems that could be used 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 \sim 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 r _ { 0 } = 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 , that we predict to be typically infalling onto large virialized structures .