Anatomy of Cosmic Tidal Reconstruction
  21-cm intensity surveys aim to map neutral hydrogen atoms in the universe
through hyper-fine emission. Unfortunately, long-wavelength (low-wavenumber)
radial modes are highly contaminated by smooth astrophysical foregrounds that
are six orders of magnitude brighter than the cosmological signal. This
contamination also leaks into higher radial and angular wavenumber modes and
forms a foreground wedge. Cosmic tidal reconstruction aims to extract the
large-scale signal from anisotropic features in the local small-scale power
spectrum through non-linear tidal interactions; losing small-scale modes to
foreground wedge will impair its performance. In this paper, we review tidal
interaction theory and estimator construction, and derive the theoretical
expressions for the reconstructed spectra. We show the reconstruction is robust
against peculiar velocities. Removing low line-of-sight $k$ modes, we
demonstrate cross-correlation coefficient $r$ is greater than 0.7 on large
scales ($k <0.1$ $h/$Mpc) even with a cutoff value $k^c_{\|}=0.1$ $h/$Mpc.
Discarding wedge modes yields $0.3< r < 0.5$ and completely removes the
dependency on $k^c_{\|}$. Our theoretical predictions agree with these
numerical simulations.
