The Impact of Scatter in the Galaxy UV Luminosity to Halo Mass Relation
  on Ly$\alpha$ Visibility During the Epoch of Reionization
  The reionization of hydrogen is closely linked to the first structures in the
universe, so understanding the timeline of reionization promises to shed light
on the nature of these early objects. In particular, transmission of Lyman
alpha (Ly$\alpha$) from galaxies through the intergalactic medium (IGM) is
sensitive to neutral hydrogen in the IGM, so can be used to probe the
reionization timeline. In this work, we implement an improved model of the
galaxy UV luminosity to dark matter halo mass relation to infer the
volume-averaged fraction of neutral hydrogen in the IGM from Ly$\alpha$
observations. Many models assume that UV-bright galaxies are hosted by massive
dark matter haloes in overdense regions of the IGM, so reside in relatively
large ionized regions. However, observations and N-body simulations indicate
that scatter in the UV luminosity-halo mass relation is expected. Here, we
model the scatter (though we assume the IGM topology is unaffected) and assess
the impact on Ly$\alpha$ visibility during reionization. We show that UV
luminosity-halo mass scatter reduces Ly$\alpha$ visibility compared to models
without scatter, and that this is most significant for UV-bright galaxies. We
then use our model with scatter to infer the neutral fraction,
$\overline{x}_{\mathrm{HI}}$, at $z \sim 7$ using a sample of Lyman-break
galaxies in legacy fields. We infer $\overline{x}_{\mathrm{HI}} =
0.55_{-0.13}^{+0.11}$ with scatter, compared to $\overline{x}_{\mathrm{HI}} =
0.59_{-0.14}^{+0.12}$ without scatter, a very slight decrease and consistent
within the uncertainties. Finally, we place our results in the context of other
constraints on the reionization timeline and discuss implications for future
high-redshift galaxy studies.
