2022MNRAS.513.5034L

Existing ubiquitously in the Universe with the highest luminosity, the Lyman-α (Lyα) emission line encodes abundant physical information about the gaseous medium it interacts with. Nevertheless, the resonant nature of the Lyα line complicates the radiative transfer (RT) modelling of the line profile. We revisit the problem of deciphering the Lyα emission line with RT modelling. We reveal intrinsic parameter degeneracies in the widely used shell model in the optically thick regime for both static and outflowing cases, which suggest the limitations of the model. We also explore the connection between the more physically realistic multiphase, clumpy model, and the shell model. We find that the parameters of a 'very clumpy' slab model and the shell model have the following correspondences: (1) the total column density, the effective temperature, and the average radial clump outflow velocity of the clumpy slab model are equal to the H I column density, effective temperature, and expansion velocity of the shell model, respectively; (2) large intrinsic linewidths are required in the shell model to reproduce the wings of the clumpy slab models; (3) adding another phase of hot interclump medium increases peak separation, and the fitted shell expansion velocity lies between the outflow velocities of two phases of gas. Our results provide a viable solution to the major discrepancies associated with Lyα fitting reported in previous literature, and emphasize the importance of utilizing information from additional observations to break the intrinsic degeneracies and interpreting the model parameters in a more physically realistic context.