Studying the WHIM Content of the Galaxy Large-Scale Structures along the Line of Sight to H 2356-309

We make use of a 500ks Chandra HRC-S/LETG spectrum of the blazar H2356-309, combined with a lower S/N spectrum of the same target, to search for the presence of warm-hot absorbing gas associated with two Large-Scale Structures (LSSs) crossed by this sightline at z=0.062 (the Pisces-Cetus Supercluster, PCS) and at z=0.128 ("Farther Sculptor Wall", FSW). No statistically significant (>=3sigma) individual absorption is detected from any of the strong He- or H-like transitions of C, O and Ne at the redshifts of the structures. However we are still able to constrain the physical and geometrical parameters of the associated putative absorbing gas, by performing joint spectral fit of marginal detections and upper limits of the strongest expected lines with our self-consistent hybrid ionization WHIM spectral model. At the redshift of the PCS we identify a warm phase with logT=5.35_-0.13^+0.07 K and log N_H =19.1+/-0.2 cm^-2 possibly coexisting with a hotter and less significant phase with logT=6.9^+0.1_-0.8 K and log N_H=20.1^+0.3_-1.7 cm^-2 (1sigma errors). For the FSW we estimate logT=6.6_-0.2^+0.1 K and log N_H=19.8_-0.8^+0.4 cm^-2. Our constraints allow us to estimate the cumulative number density per unit redshifts of OVII WHIM absorbers. We also estimate the cosmological mass density obtaining Omega_b(WHIM)=(0.021^+0.031_-0.018) (Z/Z_sun)^-1, consistent with the mass density of the intergalactic 'missing baryons' for high metallicities.