The Void Clustering of Ly-Alpha Emitters as a Probe of Reionization

The distribution of galaxies traces the structure of underlying dark matter, and carries signatures of both the cosmology that evolved the universe as well as details of how galaxies interact with their environment and each other. There are many ways to measure the clustering of galaxies, each with unique strengths, uses, theoretical background, and connection to other physical concepts. One uncommon clustering statistic is the Void Probability Function (VPF): it simply asks, how likely is a circle/sphere of a given size to be empty in your galaxy sample? Simple and efficient to calculate, the VPF is tied to all higher order volume-averaged correlation functions as the 0$^{\text{th}}$ moment of count-in-cells, and encodes information from higher order clustering that the robust two-point correlation function cannot always capture. Using simulations of Lyman-alpha emitting galaxies across either redshift history or the epoch of reionization, this work asks: how powerful is the VPF itself? When can and should it be used for galaxy clustering? What unique constraints or guidelines can it give for the pacing of reionization, in the Lyman-$\alpha$ Galaxies in the Epoch of Reionization (LAGER) narrowband survey or across the Roman Space Telescope grism? This work provides practical guidelines for creating and carrying out clustering studies using the the VPF, and motivates the use of the VPF for reionization. The VPF of LAEs can complement LAGER constraints for the end of reionization, and thoroughly inform the timing and pace of reionization with Roman.