Reading Between the Lines: Forward Modeling Dust, Continuum, and Spectral Cleaning for Multi-Line Intensity Mapping

Line intensity mapping (LIM) offers a tomographic view of galaxy evolution by measuring the aggregate emission from unresolved galaxies. In the optical and near-infrared, the line emission is accompanied by much brighter continuum emission that must be removed to recover line auto- and cross-power spectra. We develop a forward-modeling framework using a about2 deg squared lightcone drawn from a cosmological N-body simulation populated with galaxies using a physics-based semi-analytic model (SAM). We construct intensity maps for the stellar continuum and for the strongest optical lines, H alpha, H beta, [O III] lambda5007, and [O II] lambda3727, including nebular dust attenuation tied to galaxy properties. From these cubes, we measure cross-channel angular power spectra, C(lambda i, lambda j), and the normalized correlation matrix r ij. In line-only maps, the correlation matrices show same-redshift ridges between emission lines, demonstrating how multi-line intensity mapping (MLIM) can isolate large-scale structure and probe dust attenuation. We show that dust suppresses the line cross-power by an amount that depends on galaxy properties, wavelength, and line pair, so a single overall amplitude cannot capture its effect. In total maps, however, the continuum dominates the raw correlations and hides much of the line-ridge structure. We therefore apply principal component analysis (PCA)-based spectral cleaning and quantify the line-transfer function using the simulation truth. Removing 20 PCA modes gives the best trade-off between line recovery and continuum suppression in our mock maps. Our results demonstrate the promise and challenges of extracting dust-sensitive LIM observables from SPHEREx-like observations, and highlight the need to model continuum cleaning and its transfer function in quantitative inference pipelines.