Prospects for Observing the low-density Cosmic Web in Lyman-alpha
  Emission
  Mapping the intergalactic medium (IGM) in Lyman-$\alpha$ emission would yield
unprecedented tomographic information on the large-scale distribution of
baryons and potentially provide new constraints on the UV background and
various feedback processes relevant to galaxy formation. Here, we use a
cosmological hydrodynamical simulation to examine the Lyman-$\alpha$ emission
of the IGM due to collisional excitations and recombinations in the presence of
a UV background. We focus on gas in large-scale-structure filaments in which
Lyman-$\alpha$ radiative transfer effects are expected to be moderate. At low
density the emission is primarily due to fluorescent re-emission of the
ionising UV background due to recombinations, while collisional excitations
dominate at higher densities. We discuss prospects of current and future
observational facilities to detect this emission and find that the emission of
filaments of the cosmic web will typically be dominated by the halos and
galaxies embedded in them, rather than by the lower density filament gas
outside halos. Detecting filament gas directly would require a very long
exposure with a MUSE-like instrument on the ELT. Our most robust predictions
that act as lower limits indicate this would be slightly less challenging at
lower redshifts ($z \lesssim 4$). We also find that there is a large amount of
variance between fields in our mock observations. High-redshift protoclusters
appear to be the most promising environment to observe the filamentary IGM in
Lyman-$\alpha$ emission.
