Cross Correlation of Pencil-beam Galaxy Surveys and Line-intensity Maps: An Application of the James Webb Space Telescope

Line-intensity mapping (IM) experiments seek to perform statistical measurements of large-scale structure with spectral lines such as 21 cm, CO, and Ly alpha. A challenge in these observations is to ensure that astrophysical foregrounds, such as galactic synchrotron emission in 21 cm measurements, are properly removed. One method that has the potential to reduce foreground contamination is to cross correlate with a galaxy survey that overlaps with the IM volume. However, telescopes sensitive to high-redshift galaxies typically have small field of views compared to IM surveys. Thus, a galaxy survey for cross correlation would necessarily consist of pencil beams that sparsely fill the IM volume. In this paper, we develop the formalism to forecast the sensitivity of cross correlations between IM experiments and pencil-beam galaxy surveys. We find that a random distribution of pencil beams leads to very similar overall sensitivity as a lattice spaced across the IM survey and derive a simple formula for random configurations that agrees with the Fisher matrix formalism. We explore examples of combining high-redshift James Webb Space Telescope (JWST) observations with both an SPHEREx-like Ly alpha IM survey and a 21 cm experiment based on the Hydrogen Epoch of Reionization Array (HERA). We find that the JWST-SPHEREx case is promising, leading to a total signal-to-noise ratio of similar to 5 after 100 total hours of JWST (at z = 7). We find that HERA is not well-suited for this approach owing to its drift-scan strategy, but that a similar experiment that can integrate down on one field could be.