Analytic Model for Scattered Lyα Emission in the Post-reionization Intergalactic Medium

Lyα intensity mapping is emerging as a new probe of faint galaxies consisting the cosmic web that elude traditional surveys. However, the resonant nature of Lyα radiative transfer complicates the interpretation of observed data. In this study, we develop a fast and accurate analytic prescription for computing the Lyα intensity field on Mpc scales in the post-reionization Universe. Motivated by insights from Monte Carlo radiative transfer (MCRT) experiments, we exploit the fact that in a highly ionized intergalactic medium (IGM) with negligible damping-wing opacity, cosmological redshifting quickly drives Lyα photons out of resonance, terminating the scattering process and simplifying their large-scale behavior. Photons emitted blueward of the Lyα line center tend to scatter on a thin, nearly spherical surface of last scattering, with a radius determined by the redshifting distance to resonance. Based on this behavior, we derive closed-form expressions for the scattered emissivity and projected surface brightness that depend only on the source spectrum, the HI density, and the peculiar velocity field. When applied to a source in a realistically simulated IGM at z = 3, our model shows mild discrepancies with MCRT results within a physical Mpc of the host halo, where strong gravitational infall redistributes the scattered photons, but achieves better than 5% accuracy beyond that distance in both raw and cumulative surface brightness. Our prescription offers a computationally efficient alternative to MCRT for forward-modeling Lyα intensity maps from cosmological simulations, enabling the inference of underlying cosmological and astrophysical parameters from future observations.