The z \gtrsim 2 Ly \alpha forest traces the underlying dark-matter distribution on large scales and , given sufficient sightlines , can be used to create 3D maps of large-scale structure .
We examine the observational requirements to construct such maps and estimate the signal-to-noise as a function of exposure time and sightline density .
Sightline densities at z = 2.25 are n _ { \mathrm { los } } \approx [ 360 , 1200 , 3300 ] \mathrm { deg } ^ { -2 } at limiting magnitudes of g = [ 24.0 , 24.5 , 25.0 ] , resulting in transverse sightline separations of \langle d _ { \perp } \rangle \approx [ 3.6 , 1.9 , 1.2 ] h ^ { -1 } \mathrm { Mpc } , which roughly sets the reconstruction scale .
We simulate these reconstructions using mock spectra with realistic noise properties , and find that spectra with \mathrm { S / N } \approx 4 per angstrom can be used to generate maps that clearly trace the underlying dark-matter at overdensities of \rho / \langle \rho \rangle \sim 1 .
For the VLT/VIMOS spectrograph , exposure times t _ { \mathrm { exp } } = [ 4 , 6 , 10 ] \mathrm { hrs } are sufficient for maps with spatial resolution \epsilon _ { 3 D } = [ 5.0 , 3.2 , 2.3 ] h ^ { -1 } \mathrm { Mpc } .
Assuming \sim 250 h ^ { -1 } \mathrm { Mpc } is probed along the line-of-sight , 1 \mathrm { deg } ^ { 2 } of survey area would cover a comoving volume of \approx 10 ^ { 6 } h ^ { -3 } \mathrm { Mpc } ^ { 3 } at \langle z \rangle \sim 2.3 , enabling efficient mapping of large volumes with 8-10m telescopes .
These maps could be used to study galaxy environments , detect proto-clusters , and study the topology of large-scale structure at high-z .