Forecasts and Statistical Insights for Line Intensity Mapping Cross-Correlations: A Case Study with 21cm x [CII]

Intensity mapping -- the large-scale mapping of selected spectral lines without resolving individual sources -- is quickly emerging as an efficient way to conduct large cosmological surveys. Multiple surveys covering a variety of lines (such as the hydrogen 21cm hyperfine line, CO rotational lines, and [CII] fine structure lines, among others) are either observing or will soon be online, promising a panchromatic view of our Universe over a broad redshift range. With multiple lines potentially covering the same volume, cross-correlations have become an attractive prospect, both for probing the underlying astrophysics and for mitigating observational systematics. For example, cross correlating 21cm and [CII] intensity maps during reionization could reveal the characteristic scale of ionized bubbles around the first galaxies, while simultaneously providing a convenient way to reduce independent foreground contaminants between the two surveys. However, many of the desirable properties of cross-correlations in principle emerge only under ideal conditions, such as infinite ensemble averages. In this paper, we construct an end-to-end pipeline for analyzing intensity mapping cross-correlations, enabling instrumental effects, foreground residuals, and analysis choices to be propagated through Monte Carlo simulations to a set of rigorous error properties, including error covariances, window functions, and full probability distributions for power spectrum estimates. We use this framework to critically examine the applicability of simplifying assumptions such as the independence and Gaussianity of power spectrum errors. As worked examples, we forecast the sensitivity of near-term and futuristic 21cm-[CII] cross-correlation measurements, providing recommendations for survey design.