COS Observations of the Cosmic Web: A Search for the Cooler Components
  of a Hot, X-ray Identified Filament
  In the local universe, a large fraction of the baryon content is believed to
exist as diffuse gas in filaments. While this gas is directly observable in
X-ray emission around clusters of galaxies, it is primarily studied through its
UV absorption. Recently, X-ray observations of large-scale filaments connecting
to the cosmic web around the nearby ($z=0.05584$) cluster Abell 133 were
reported. One of these filaments is intersected by the sightline to quasar
[VV98] J010250.2$-$220929, allowing for a first-ever census of cold, cool, and
warm gas in a filament of the cosmic web where hot gas has been seen in X-ray
emission. Here, we present UV observations with the Cosmic Origins Spectrograph
and optical observations with the Magellan Echellette spectrograph of [VV98]
J010250.2$-$220929. We find no evidence of cold, cool, or warm gas associated
with the filament. In particular, we set a $2\sigma$ upper limit on Ly$\alpha$
absorption of $\log(N_{HI} / \textrm{cm}^{-2}) < 13.7$, assuming a Doppler
parameter of $b=20\,\textrm{km}\,\textrm{s}^{-1}$. As this sightline is
${\sim}1100\,\textrm{pkpc}$ ($0.7R_\textrm{vir}$) from the center of Abell 133,
we suggest that all gas in the filament is hot at this location, or that any
warm, cool, or cold components are small and clumpy. A broader census of this
system -- combining more UV sightlines, deeper X-ray observations, and a larger
redshift catalog of cluster members -- is needed to better understand the roles
of filaments around clusters.
