Measuring alignments between galaxies and the cosmic web at $z \sim 2-3$
  using IGM tomography
  Many galaxy formation models predict alignments between galaxy spin and the
cosmic web (i.e. the directions of filaments and sheets), leading to intrinsic
alignment between galaxies that creates a systematic error in weak lensing
measurements. These effects are often predicted to be stronger at
high-redshifts ($z\gtrsim1$) that are inaccessible to massive galaxy surveys on
foreseeable instrumentation, but IGM tomography of the Ly$\alpha$ forest from
closely-spaced quasars and galaxies is starting to measure the $z\sim2-3$
cosmic web with the requisite fidelity. Using mock surveys from hydrodynamical
simulations, we examine the utility of this technique, in conjunction with
coeval galaxy samples, to measure alignment between galaxies and the cosmic web
at $z\sim2.5$. We show that IGM tomography surveys with $\lesssim5$ $h^{-1}$
Mpc sightline spacing can accurately recover the eigenvectors of the tidal
tensor, which we use to define the directions of the cosmic web. For galaxy
spins and shapes, we use a model parametrized by the alignment strength,
$\Delta\langle\cos\theta\rangle$, with respect to the tidal tensor eigenvectors
from the underlying density field, and also consider observational effects such
as errors in the galaxy position angle, inclination, and redshift. Measurements
using the upcoming $\sim1\,\mathrm{deg}^2$ CLAMATO tomographic survey and 600
coeval zCOSMOS-Deep galaxies should place $3\sigma$ limits on extreme alignment
models with $\Delta\langle\cos\theta\rangle\sim0.1$, but much larger surveys
encompassing $>10,000$ galaxies, such as Subaru PFS, will be required to
constrain models with $\Delta\langle\cos\theta\rangle\sim0.03$. These
measurements will constrain models of galaxy-cosmic web alignment and test
tidal torque theory at $z\sim2$, improving our understanding of the redshift
dependence of galaxy-cosmic web alignment and the physics of intrinsic
alignments.
