Several ‘ giant ’ Lyman- \alpha ( Ly \alpha ) nebulae with extent \gtrsim 300 kpc and observed Ly \alpha luminosity of \gtrsim 10 ^ { 44 } { erg } { s } ^ { -1 } { cm } ^ { -2 } { 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 .