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The reionization of hydrogen is closely linked to the first structures in theuniverse, so understanding the timeline of reionization promises to shed lighton the nature of these early objects. In particular, transmission of Lymanalpha (Ly$\alpha$) from galaxies through the intergalactic medium (IGM) issensitive to neutral hydrogen in the IGM, so can be used to probe thereionization timeline. In this work, we implement an improved model of thegalaxy UV luminosity to dark matter halo mass relation to infer thevolume-averaged fraction of neutral hydrogen in the IGM from Ly$\alpha$observations. Many models assume that UV-bright galaxies are hosted by massivedark matter haloes in overdense regions of the IGM, so reside in relativelylarge ionized regions. However, observations and N-body simulations indicatethat scatter in the UV luminosity-halo mass relation is expected. Here, wemodel the scatter (though we assume the IGM topology is unaffected) and assessthe impact on Ly$\alpha$ visibility during reionization. We show that UVluminosity-halo mass scatter reduces Ly$\alpha$ visibility compared to modelswithout scatter, and that this is most significant for UV-bright galaxies. Wethen use our model with scatter to infer the neutral fraction,$\overline{x}_{\mathrm{HI}}$, at $z \sim 7$ using a sample of Lyman-breakgalaxies 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 consistentwithin the uncertainties. Finally, we place our results in the context of otherconstraints on the reionization timeline and discuss implications for futurehigh-redshift galaxy studies.

The Impact of Scatter in the Galaxy UV Luminosity to Halo Mass Relation on Ly$\alpha$ Visibility During the Epoch of Reionization