This paper presents an analysis of XMM-Newton and Chandra X-ray spectra of the quasar 1ES 1553+113, in search for absorption lines from the intervening warm-hot intergalactic medium (WHIM). A search for O VII, O VIII, and Ne IX resonance absorption lines was performed at eight fixed redshifts that feature O VI or H I broad Lyman α absorption lines that were previously detected from Hubble Space Telescope (HST) data. The search yielded one possible detection of O VII at a redshift z ≃ 0.1877 with an O VI prior, with a statistical significance that is equivalent to a 2.6σ confidence level. The spectra were also stacked at the wavelengths of the expected redshifted O VII and O VIII lines, but the analysis did not reveal evidence for the presence of additional X-ray absorbing WHIM. Moreover, the spectra were used to investigate two putative O VII absorption lines that were detected serendipitously in an earlier analysis of the same data by F. Nicastro and collaborators. The paper also presents a comprehensive statistical framework for cosmological inferences from the analysis of absorption lines, which makes use of cosmological simulations for the joint probability distributions of far-ultraviolet (FUV) and X-ray ions. Accordingly, we conclude that the new possible O VII absorption at z ≃ 0.1877 is consistent with a contribution from the hot WHIM to the baryon density in an amount of ΩWHIM, X/Ωb = 44 ± 22 per cent. However, there are large systematic uncertainties associated with the temperature and abundances of the absorbers, and only a larger sample of X-ray sources can provide an accurate determination of the cosmological density of the WHIM.
