Revealing the z~2.5 Cosmic Web With 3D Lyman-Alpha Forest Tomography: A
  Deformation Tensor Approach
  Studies of cosmological objects should take into account their positions
within the cosmic web of large-scale structure. Unfortunately, the cosmic web
has only been extensively mapped at low-redshifts ($z<1$), using galaxy
redshifts as tracers of the underlying density field. At $z>1$, the required
galaxy densities are inaccessible for the foreseeable future, but 3D
reconstructions of Lyman-$\alpha$ forest absorption in closely-separated
background QSOs and star-forming galaxies already offer a detailed window into
$z\sim2-3$ large-scale structure. We quantify the utility of such maps for
studying the cosmic web by using realistic $z=2.5$ Ly$\alpha$ forest
simulations matched to observational properties of upcoming surveys. A
deformation tensor-based analysis is used to classify voids, sheets, filaments
and nodes in the flux, which is compared to those determined from the
underlying dark matter field. We find an extremely good correspondence, with
$70\%$ of the volume in the flux maps correctly classified relative to the dark
matter web, and $99\%$ classified to within 1 eigenvalue. This compares
favorably to the performance of galaxy-based classifiers with even the highest
galaxy densities at low-redshift. We find that narrow survey geometries can
degrade the cosmic web recovery unless the survey is $\gtrsim
60\,h^{-1}\,\mathrm{Mpc}$ or $\gtrsim 1\,\mathrm{deg}$ on the sky. We also
examine halo abundances as a function of the cosmic web, and find a clear
dependence as a function of flux overdensity, but little explicit dependence on
the cosmic web. These methods will provide a new window on cosmological
environments of galaxies at this very special time in galaxy formation, "high
noon", and on overall properties of cosmological structures at this epoch.
