Studying the WHIM Content of Large-scale Structures Along the Line of Sight to H 2356-309

We make use of a 500 ks Chandra HRC-S/LETG spectrum of the blazar H 2356-309, combined with a lower signal-to-noise ratio (S/N; 100 ks) pilot LETG 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 sight line and to constrain its physical state and geometry. Strong (log N{sub O{sub VII}} {>=} 10{sup 16} cm{sup -2}) O VII K{alpha} absorption associated with a third LSS crossed by this line of sight (the Sculptor Wall (SW)), at z = 0.03, has already been detected in a previous work. Here, we focus on two additional prominent filamentary LSSs along the same line of sight, one at z = 0.062 (the Pisces-Cetus Supercluster (PCS)) and another at z = 0.128 (the 'Farther Sculptor Wall' (FSW)). The combined LETG spectrum has an S/N of {approx}11.6-12.6 per resolution element in the 20-25 A and an average 3{sigma} sensitivity to intervening O VII K{alpha} absorption line equivalent widths (EWs) of EW{sub O{sub VII}} {approx_gt} 14 mA in the available redshift range (z < 0.165). No statistically significant (i.e., {>=}3{sigma}) individual absorption is detected from any of the strong He- or H-like transitions of C, O, and Ne (the most abundant metals in gas with solar-like composition) at the redshifts of the PCS and FSW structures and down to the EW thresholds mentioned above. However, we are still able to constrain the physical and geometrical parameters of the putative absorbing gas associated with these structures, by performing a joint spectral fit of various 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 log T = 5.35{sup +0.07}{sub -0.13} K and log N{sub H} = (19.1 {+-} 0.2) cm{sup -2} possibly co-existing with a much hotter and statistically less significant phase with log T = 6.9{sup +0.1}{sub -0.8} K and log N{sub H} = 20.1{sup +0.3}{sub -1.7} cm{sup -2} (1{sigma} errors). These two separate physical phases are identified through, and mainly constrained by, C V K{alpha} (warm phase) and O VIII K{alpha} (hot phase) absorption, with single line significances of 1.5{sigma} each. For the second LSS, at z {approx_equal} 0.128, only one hot component is hinted in the data, through O VIII K{alpha} (1.6{sigma}) and Ne IX K{alpha} (1.2{sigma}). For this system, we estimate log T = 6.6{sup +0.1}{sub -0.2} K and log N{sub H} = 19.8{su