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Line-intensity mapping (IM) experiments seek to perform statisticalmeasurements of large-scale structure with spectral lines such as 21cm, CO, andLyman-$\alpha$ (Ly$\alpha$). A challenge in these observations is to ensurethat astrophysical foregrounds, such as galactic synchrotron emission in 21cmmeasurements, are properly removed. One method that has the potential to reduceforeground contamination is to cross correlate with a galaxy survey thatoverlaps with the IM volume. However, telescopes sensitive to high-redshiftgalaxies typically have small field of views (FOVs) compared to IM surveys.Thus, a galaxy survey for cross correlation would necessarily consist of pencilbeams which sparsely fill the IM volume. In this paper, we develop theformalism to forecast the sensitivity of cross correlations between IMexperiments and pencil-beam galaxy surveys. We find that a random distributionof pencil beams leads to very similar overall sensitivity as a lattice spacedacross the IM survey and derive a simple formula for random configurations thatagrees with the Fisher matrix formalism. We explore examples of combininghigh-redshift James Webb Space Telescope (JWST) observations with both aSPHEREx-like Ly$\alpha$ IM survey and a 21cm experiment based on the HydrogenEpoch of Reionization Array (HERA). We find that the JWST-SPHEREx case ispromising, leading to a total signal-to-noise of ${\sim}5$ after 100 totalhours of JWST (at $z=7$). We find that HERA is not well-suited for thisapproach owing to its drift-scan strategy, but that a similar experiment thatcan integrate down on one field could be.

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