Synergies between the COMAP CO Line Intensity Mapping mission and a
  Ly{\alpha} galaxy survey: How to probe the early universe with voxel based
  analysis of observational data
  Line Intensity Mapping (LIM) offers a novel avenue to observe and
characterize our universe. LIM data of CO spectral lines are becoming
available, such as those obtained by the CO Mapping Array Project (COMAP).
COMAP data can be used to probe the molecular gas content of the universe from
the last stages of the Epoch of Reionization (EoR) ($z < 8.0$) to $z \sim 2.5$.
In this work, we examine the prospects for deriving voxel-level statistical
constraints on high-redshift galaxies from COMAP data by considering the
additional information available from observations of LAEs galaxies using the
Visible Integral-Field Replicable Unit Spectrograph (VIRUS) on the Hobby-Eberly
Telescope (HET). We post-process the IllustrisTNG300 galaxy-formation
simulation with a set of prescriptions to consistently determine CO and
Ly$\alpha$ line luminosities. The different line prescriptions span the
uncertainty in the CO line luminosity according to current observations by the
VLA high-z CO surveys and set the Ly$\alpha$ emission to be compatible with
observational LAE luminosity functions. We produce mock observations for the
two surveys over a $(300\, {\rm Mpc})^3$ volume. These are then used to
formulate and test methodologies for data analysis and to predict COMAP
constraints on CO emission. We use combinations of masking, stacking, voxel
intensity distribution (VID), and other statistics. We find that in combination
with VIRUS/HET, a voxel-level analysis of the COMAP Pathfinder survey can
detect and characterize the CO signal from $z\sim3$ and improve current
constraints on the $z\sim6$ signal, identify individual voxels with bright
CO(1-0) emission at $z\sim3$ and probe the redshift evolution of the CO
emission. This study illustrates the potential of synergies between LIM and
galaxy surveys both to improve the significance of a detection and to aid the
interpretation of noisy LIM data.
