Abstract Resonance lines encode rich information about astrophysical sources and their environments, yet fully analytic treatments of multi-line radiative transfer remain almost entirely unexplored. We present exact, closed-form solutions for steady-state resonant-line radiative transfer in “V-shaped” atomic networks, where a single ground state couples to multiple transitions. Starting from the full angle-dependent transfer equation, we generalise absorption and emission coefficients to an arbitrary number of lines, derive a modified Fokker–Planck expansion of the frequency-redistribution integral, and use a judicious change of variables to reduce the problem to a Helmholtz equation with pointlike sources in frequency space. This transformation admits analytic solutions for arbitrary sets of lines with fixed frequency offsets and strengths in both slab and spherical geometries. We implement V-shaped line networks in the colt Monte Carlo radiative transfer code and find excellent agreement with the analytic predictions across a wide range of line separations, optical depths, and damping parameters, establishing our solutions as stringent validation benchmarks. For concrete applications related to the Lyman-alpha (Ly α ) transition of neutral hydrogen, we examine how fine-structure splitting and deuterium injection modify the emergent spectra, internal radiation field, and radiative force multiplier. We show that these effects leave previous conclusions about Ly α feedback in the early universe essentially unchanged. Even when direct observational diagnostics are subtle, our framework provides novel analytic and numerical insights into coupled resonance-line transport and facilitates progress in general modelling of multi-line radiative transfer in diverse astrophysical settings.
Stace et al. (Thu,) studied this question.