  We use the EAGLE (Evolution and Assembly of GaLaxies and their Environments)
cosmological simulation to study the distribution of baryons, and
far-ultraviolet (O VI), extreme-ultraviolet (Ne VIII) and X-ray (O VII, O VIII,
Ne IX, and Fe XVII) line absorbers, around galaxies and haloes of mass
$\mathrm{M}_{200c}=10^{11}$-$10^{14.5}\,\mathrm{M}_{\odot}$ at redshift 0.1.
EAGLE predicts that the circumgalactic medium (CGM) contains more metals than
the interstellar medium across halo masses. The ions we study here trace the
warm-hot, volume-filling phase of the CGM, but are biased towards temperatures
corresponding to the collisional ionization peak for each ion, and towards high
metallicities. Gas well within the virial radius is mostly collisionally
ionized, but around and beyond this radius, and for O VI, photoionization
becomes significant. When presenting observables we work with column densities,
but quantify their relation with equivalent widths by analysing virtual
spectra. Virial-temperature collisional ionization equilibrium ion fractions
are good predictors of column density trends with halo mass, but underestimate
the diversity of ions in haloes. Halo gas dominates the highest column density
absorption for X-ray lines, but lower density gas contributes to strong UV
absorption lines from O VI and Ne VIII. Of the O VII (O VIII) absorbers
detectable in an Athena X-IFU blind survey, we find that 41 (56) per cent arise
from haloes with $\mathrm{M}_{200c}=10^{12.0}$-$10^{13.5}\,\mathrm{M}_{\odot}$.
We predict that the X-IFU will detect O VII (O VIII) in 77 (46) per cent of the
sightlines passing
$\mathrm{M}_{\star}=10^{10.5}$-$10^{11.0}\,\mathrm{M}_{\odot}$ galaxies within
100 pkpc (59 (82) per cent for
$\mathrm{M}_{\star}>10^{11.0}\,\mathrm{M}_{\odot}$). Hence, the X-IFU will
probe covering fractions comparable to those detected with the Cosmic Origins
Spectrograph for O VI.
