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 ofsurveys.

线强度映射 (LIM) 是一种快速兴起的技术，用于使用多频率、低角分辨率映射来约束宇宙学和星系形成。许多 LIM 应用关键依赖于两条线强度图的互相关，或者强度图与星系调查或星系/CMB 透镜的互相关。我们提出了一个一致的光环模型来预测所有这些互相关并支持在 3D 红移空间和 2D 投影地图中进行联合分析。我们将条件光度函数形式主义扩展到多线情况，以一致地解释多个星系线光度之间的相关散射。这使我们能够对两个线强度图之间的尺度相关去相关进行建模，这是前景抑制和从交叉光谱估计自光谱的方法的关键输入。这也使 LIM 互相关能够揭示 LIM 自光谱无法到达的星际介质的天体物理特性。我们揭示了 LIM 中光度散射或“线噪声”的不同来源，并阐明了它们对 1 晕和星系散粒噪声项的影响。特别是，我们表明，在某些情况下，光晕的有效数密度可能超过星系，这与直觉相反。使用观察和模拟输入，我们为 Hα、[Oiii]、Lyman-α、CO 和 [Cii] 线实现了这个晕圈模型。我们鼓励观察者和模拟器尽可能测量成对线的星系光度相关系数。我们的代码在 https://github.com/EmmanuelSchaan/HaloGen/tree/LIM 上公开可用。在一篇配套论文中，