  The current observational status of the hot (log T(K) > 5.5) warm-hot
intergalactic medium (WHIM) remains incomplete. While recent observations from
stacking large numbers of Cosmic Web filaments have yielded statistically
significant detections, direct measurements of single objects remain scarce.
The lack of such a sample currently prevents a robust analysis of the cosmic
baryon content composed of the hot WHIM, which could help solve the
cosmological missing baryons problem. To improve the search for the missing
baryons, we used the EAGLE simulation. Our aim is to understand the metal
enrichment and distribution of highly ionised metals in the Cosmic Web. We
detected the filaments by applying the Bisous formalism to the simulated
galaxies, and characterised the spatial distributions as well as mass and
volume fractions of the filamentary oxygen and OVII. We then constructed OVII
column density maps and determined their detectability with Athena X-IFU.
However, the oxygen and OVII number densities drop fast beyond the virial radii
of haloes, falling below detectable levels at 700 kpc. Thus, only ~1% of the
filament volumes are filled with OVII at detectable densities. This
non-homogeneous distribution of the OVII complicates its usage for tracing the
missing baryons. Instead, OVII forms narrow envelopes around haloes. This
localised nature results in a low chance (10-20% per sight line) of detecting
intergalactic OVII with Athena X-IFU within the SDSS catalogue of filaments.
With future filament samples from the 4MOST survey, the chances increase up to
a level of ~50%. Nonetheless, based on EAGLE results, this would not be enough
to conclusively solve the missing baryon problem, as it would be limited to a
few times the virial radii of haloes. Fortunately, the volumes around haloes
are dense in hot WHIM, and tracing it could reduce the content of baryons still
missing by ~25%.
