Giant Lyman-Alpha Nebulae in the Illustris Simulation
  Several `giant' Lyman-$\alpha$ (Ly$\alpha$) nebulae with extent $\gtrsim
300\,$kpc and observed Ly$\alpha$ luminosity of $\gtrsim 10^{44}\,{\rm
erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}\,{\rm arcsec}^{-2}$ have recently been
detected, and it has been speculated that their presence hints at a substantial
cold gas reservoir in small cool clumps not resolved in modern hydro-dynamical
simulations. We use the Illustris simulation to predict the Ly$\alpha$ emission
emerging from large halos ($M > 10^{11.5}M_{\odot}$) at $z\sim 2$ and thus test
this model. We consider both AGN and star driven ionization, and compare the
simulated surface brightness maps, profiles and Ly$\alpha$ spectra to a model
where most gas is clumped below the simulation resolution scale. We find that
with Illustris no additional clumping is necessary to explain the extents,
luminosities and surface brightness profiles of the `giant Ly$\alpha$ nebulae'
observed. Furthermore, the maximal extents of the objects show a wide spread
for a given luminosity and do not correlate significantly with any halo
properties. We also show how the detected size depends strongly on the employed
surface brightness cutoff, and predict that further such objects will be found
in the near future.
