Constraints on the Epoch of Reionization with Roman Space Telescope and the Void Probability Function of Ly Emitters

We use large simulations of Ly alpha emitters with different fractions of ionized intergalactic medium to quantify the clustering of Ly alpha emitters as measured by the void probability function (VPF), and how it evolves under different ionization scenarios. We quantify how well we might be able to distinguish between these scenarios with a deep spectroscopic survey using the future Nancy Grace Roman Space Telescope. Because Roman will be able to carry out blind spectroscopic surveys of Ly alpha emitters continuously between 7 < z < 12 to sensitivities of at least 10(-17) erg s(-1) over a wide field of view, it can measure the epoch of reionization as well as the pace of ionization of the intergalactic medium (IGM). We compare deep Roman surveys covering roughly 1, 4, and 16 deg(2), and quantify what constraints on reionization the VPF may find for these surveys. A survey of 1 deg(2) would distinguish between very late reionization and early reionization to 3 sigma near z = 7.7 with the VPF. The VPF of a 4 deg(2) survey can distinguish between slow versus fast, as well as early versus late, reionization at >3 sigma-4 sigma at several redshifts between 7 < z < 9. However, a survey of 13-16 deg(2) would allow the VPF to give several robust constraints (>5-8 sigma) across the epoch of reionization, and would yield a detailed history of the reionization of the IGM and its effect on Ly alpha emitter clustering.