  Quasar absorption-line studies in the ultraviolet (UV) can uniquely probe the
nature of the multiphase cool-warm (10^4 < T < 10^6 K) gas in and around galaxy
clusters, promising to provide unprecedented insights into 1) interactions
between the circumgalactic medium (CGM) associated with infalling galaxies and
the hot (T > 10^6 K) X-ray emitting intracluster medium (ICM), 2) the stripping
of metal-rich gas from the CGM, and 3) a multiphase structure of the ICM with a
wide range of temperatures and metallicities. In this work, we present results
from a high-resolution simulation of a ~10^14 solar mass galaxy cluster to
study the physical properties and observable signatures of this cool-warm gas
in galaxy clusters. We show that the ICM becomes increasingly multiphased at
large radii, with the cool-warm gas becoming dominant in cluster outskirts. The
diffuse cool-warm gas also exhibits a wider range of metallicity than the hot
X-ray emitting gas. We make predictions for the covering fractions of key
absorption-line tracers, both in the ICM and in the CGM of cluster galaxies,
typically observed with the Cosmic Origins Spectrograph aboard the Hubble Space
Telescope (HST). We further extract synthetic spectra to demonstrate the
feasibility of detecting and characterizing the thermal, kinematic, and
chemical composition of the cool-warm gas using H I, O VI, and C IV lines, and
we predict an enhanced population of broad Ly-alpha absorbers tracing the warm
gas. Lastly, we discuss future prospects of probing the multiphase structure of
the ICM beyond HST.
