  We estimate the detectability of X-ray metal-line emission from the
circumgalactic 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 $\mathrm{M}_{\mathrm{200c}} \gtrsim
10^{13}\,\mathrm{M}_{\odot}$ haloes should be detectable. Using the Athena
X-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 intragroup
and intracluster gas will be detectable out to the virial radius. With the Lynx
Ultra-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 ($\sim1$-$10\,\mathrm{arcmin}^{2}$). This
emission is dominated by collisionally ionized (CI) gas, and tends to come from
halo centres. The emission is biased towards temperatures close to the maximum
emissivity temperature for CI gas ($\mathrm{T}_\mathrm{peak}$), and high
densities and metallicities. However, for the K-$\alpha$ lines, emission can
come from hotter gas in haloes where the virialized, volume-filling gas is
hotter than $\mathrm{T}_\mathrm{peak}$. Trends of emission with halo mass can
largely be explained by differences in virial temperature. Differences in the
mass trends of K-$\alpha$, He-$\alpha$-like, and Fe L-shell lines mirror
differences in their emissivities as a function of temperature. We conclude
that upcoming X-ray missions will open up a new window onto the hot CGM.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics