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We estimate the detectability of X-ray metal-line emission from thecircumgalactic medium (CGM) of galaxies over a large halo mass range($\mathrm{M}_{\mathrm{200c}} = 10^{11.5}$-$10^{14.5}\,\mathrm{M}_{\odot}$)using the EAGLE simulations. With the XRISM Resolve instrument, a few bright(K-$\alpha$ or Fe L-shell) lines from $\mathrm{M}_{\mathrm{200c}} \gtrsim10^{13}\,\mathrm{M}_{\odot}$ haloes should be detectable. Using the AthenaX-IFU or the Lynx Main Array, emission lines (especially from O VIII and O VII)from the inner CGM of $\mathrm{M}_{\mathrm{200c}}\gtrsim10^{12.5}\,\mathrm{M}_{\odot}$ haloes become detectable, and intragroupand intracluster gas will be detectable out to the virial radius. With the LynxUltra-high Resolution Array, the inner CGM of haloes hosting $\mathrm{L}_{*}$galaxies is accessible. These estimates do assume long exposure times ($\sim 1\,$Ms) and large spatial bins ($\sim1$-$10\,\mathrm{arcmin}^{2}$). Thisemission is dominated by collisionally ionized (CI) gas, and tends to come fromhalo centres. The emission is biased towards temperatures close to the maximumemissivity temperature for CI gas ($\mathrm{T}_\mathrm{peak}$), and highdensities and metallicities. However, for the K-$\alpha$ lines, emission cancome from hotter gas in haloes where the virialized, volume-filling gas ishotter than $\mathrm{T}_\mathrm{peak}$. Trends of emission with halo mass canlargely be explained by differences in virial temperature. Differences in themass trends of K-$\alpha$, He-$\alpha$-like, and Fe L-shell lines mirrordifferences in their emissivities as a function of temperature. We concludethat upcoming X-ray missions will open up a new window onto the hot CGM.

The warm-hot circumgalactic medium around EAGLE-simulation galaxies and its detection prospects with X-ray line emission