Context. A significant fraction of the predicted baryons remain undetected in the local Universe. We adopted the common assumption that a large fraction of the missing baryons correspond to the hot (log T(K) = 5.5–7) phase of the warm-hot intergalactic medium (WHIM). We base our missing baryons search on the scenario whereby the WHIM has been heated up via accretion shocks and galactic outflows, and it is concentrated towards the filaments of the cosmic web. Aims. Our aim is to improve the observational search for the poorly detected hot WHIM. Methods. We detected the filamentary structure within the EAGLE hydrodynamical simulation by applying the Bisous formalism to the galaxy distribution. To test the reliability of our results, we used the MMF/NEXUS+ classification of the large-scale environment of the dark matter component in EAGLE. We then studied the spatio-thermal distribution of the hot baryons within the extracted filaments. Results. While the filaments occupy only ≈5% of the full simulation volume, the diffuse hot intergalactic medium in filaments amounts to ≈23%−25% of the total baryon budget, or ≈79%−87% of all the hot WHIM. The optimal filament sample, with a missing baryon mass fraction of ≈82%, is obtained by selecting Bisous filaments with a high galaxy luminosity density. For these filaments, we derived analytic formulae for the radial gas density and temperature profiles, consistent with recent Planck Sunyaev-Zeldovich and cosmic microwave background lensing observations within the central r ≈ 1 Mpc. Conclusions. Results from the EAGLE simulation suggest that the missing baryons are strongly concentrated towards the filament axes. Since the filament finding methods used here are applicable to galaxy surveys, a large fraction of the missing baryons can be localised by focusing the observational efforts on the central ∼1 Mpc regions of the filaments. To optimise the observational signal, it is beneficial to focus on the filaments with the highest galaxy luminosity densities detected in the optical data.

We investigate the alignment of haloes with the filaments of the cosmic web using an unprecedently large sample of dark matter haloes taken from the P-Millennium ΛCDM cosmological N-body simulation. We use the state-of-the-art NEXUS morphological formalism which, due to its multiscale nature, simultaneously identifies structures at all scales. We find strong and highly significant alignments, with both the major axis of haloes and their peculiar velocity tending to orient along the filament. However, the spin -filament alignment displays a more complex trend changing from preferentially parallel at low masses to preferentially perpendicular at high masses. This "spin flip" occurs at an average mass of 5 × 10 11 h −1 M . This mass increases with increasing filament diameter, varying by more than an order of magnitude between the thinnest and thickest filament samples. We also find that the inner parts of haloes have a spin flip mass that is several times smaller than that of the halo as a whole. These results confirm that recent accretion is responsible for the complex behaviour of the halo spin -filament alignment. Low-mass haloes mainly accrete mass along directions perpendicular to their host filament and thus their spins tend to be oriented along the filaments. In contrast, high-mass haloes mainly accrete along their host filaments and have their spins preferentially perpendicular to them. Furthermore, haloes located in thinner filaments are more likely to accrete along their host filaments than haloes of the same mass located in thicker filaments.