  The visibility of high-redshift Lyman-alpha emitting galaxies (LAEs) provides
important constraints on galaxy formation processes and the Epoch of
Reionization (EoR). However, predicting realistic and representative statistics
for comparison with observations represents a significant challenge in the
context of large-volume cosmological simulations. The THESAN project offers a
unique framework for addressing such limitations by combining state-of-the-art
galaxy formation (IllustrisTNG) and dust models with the Arepo-RT
radiation-magneto-hydrodynamics solver. In this initial study we present
Lyman-alpha centric analysis for the flagship simulation that resolves atomic
cooling haloes throughout a (95.5 cMpc)^3 region of the Universe. To avoid
numerical artifacts we devise a novel method for accurate frequency-dependent
line radiative transfer in the presence of continuous Hubble flow, transferable
to broader astrophysical applications as well. Our scalable approach highlights
the utility of LAEs and red damping-wing transmission as probes of
reionization, which reveal nontrivial trends across different galaxies,
sightlines, and frequency bands that can be modelled in the framework of
covering fractions. In fact, after accounting for environmental factors
influencing large-scale ionized bubble formation such as redshift and UV
magnitude, the variation across galaxies and sightlines mainly depends on
random processes including peculiar velocities and self-shielded systems that
strongly impact unfortunate rays more than others. Throughout the EoR local and
cosmological optical depths are often greater than or less than unity such that
the exp(-tau) behavior leads to anisotropic and bimodal transmissivity. Future
surveys will benefit by targeting both rare bright objects and Goldilocks zone
LAEs to infer the presence of these (un)predictable (dis)advantages.
