Crossing walls and windows: the curious escape of Lyman-α photons through ionised channels

The diverse Lyman-alpha (Ly α) line profiles are essential probes of gas in and around galaxies. While isotropic models can successfully reproduce a range of Ly α observables, the correspondence between the model and actual physical parameters remains uncertain. We investigate the effect of anisotropies on Ly α escape using a simplified setup: an empty hole (fractional size s̃) within a semi-infinite slab with constant column density. Due to the slab’s high line-centre optical depth (τ ₀ 10⁵⁻⁶), most photons should escape through the empty channel. However, our numerical findings indicate that only a fraction ~ s̃ of photons exit through this channel. To explain this puzzle, we developed an analytical model describing the scattering and transmission behaviour of Ly α photons in an externally illuminated slab. Our findings show that the number of scatterings per reflection follows a Lévy distribution (∝ N-3/2). This means that the mean number of scatterings is orders of magnitude greater than expectations, facilitating a shift in frequency and the subsequent photon escape. Our results imply that Ly α photons are more prone to traverse high-density gas and are surprisingly less biased to the ‘path of least resistance’. Hence, Ly α can trace an average hydrogen distribution rather than only low-column density channels.