The galaxy-IGM connection in THESAN: the physics connecting the IGM Lyman-$α$ opacity and galaxy density in the reionization epoch

Abstract: The relation between the Lyman-$\alpha$ effective optical depth of quasar sightlines ($\tau_\mathrm{los}$) and the distribution of galaxies around them is an emerging probe of the connection between the first collapsed structures and the IGM properties at the tail end of cosmic reionization. We employ the THESAN simulations to demonstrate that $\tau_\mathrm{los}$ is most sensitive to galaxies at a redshift-dependent distance, reflecting the growth of ionized regions around sources of photons and in agreement with studies of the galaxy--Lyman-$\alpha$ cross correlation. This is $d \sim 15 \, h^{-1} \, \mathrm{Mpc}$ at the tail end of reionization. The flagship THESAN run struggles to reproduce the most opaque sightlines as well as those with large galaxy densities, likely as a consequence of its limited volume. We identify a promising region of parameter space to probe with future observations in order to distinguish both the timing and sources of reionization. We present an investigation of the IGM physical conditions around opaque and transparent spectra, revealing that they probe regions that reionized inside-out and outside-in, respectively, and demonstrate that residual neutral islands at the end of reionization are not required to produce optical depths of $\tau_\mathrm{los} > 4$, although they facilitate the task. Finally, we investigate the sensitivity of the aforementioned results to the nature of ionizing sources and dark matter.