Abstract
Line intensity mapping (LIM) is a rapidly emerging technique for constraining cosmology and galaxy formation using multi-frequency, low angular resolution maps. Many LIM applications crucially rely on cross-correlations of two line intensity maps, or of intensity maps with galaxy surveys or galaxy/CMB lensing. We present a consistent halo model to predict all these cross-correlations and enable joint analyses, in 3D redshift-space and for 2D projected maps. We extend the conditional luminosity function formalism to the multi-line case, to consistently account for correlated scatter between multiple galaxy line luminosities. This allows us to model the scale-dependent decorrelation between two line intensity maps, a key input for foreground rejection and for approaches that estimate auto-spectra from cross-spectra. This also enables LIM cross-correlations to reveal astrophysical properties of the interstellar medium inacessible with LIM auto-spectra. We expose the different sources of luminosity scatter or "line noise" in LIM, and clarify their effects on the 1-halo and galaxy shot noise terms. In particular, we show that the effective number density of halos can in some cases exceed that of galaxies, counterintuitively. Using observational and simulation input, we implement this halo model for the Hα, [Oiii], Lyman-α, CO and [Cii] lines. We encourage observers and simulators to measure galaxy luminosity correlation coefficients for pairs of lines whenever possible. Our code is publicly available at https://github.com/EmmanuelSchaan/HaloGen/tree/LIM. In a companion paper, we use this halo model formalism and code to highlight the degeneracies between cosmology and astrophysics in LIM, and to compare the LIM observables to galaxy detection for a number of surveys.