The Impact of Cosmic Variance on Inferences of Global Neutral Fraction Derived from Lyα Luminosity Functions during Reionization

We investigate the impact of field-to-field variation, deriving from cosmic variance, in measured Lyα emitter (LAE) luminosity functions (LFs) and this variation’s impact on inferences of the neutral fraction of the intergalactic medium (IGM) during reionization. We post-process a z = 7 IGM simulation to populate the dark matter halos with LAEs. These LAEs have realistic UV magnitudes, Lyα fluxes, and Lyα line profiles. We calculate the attenuation of Lyα emission in universes with varying IGM neutral fraction, x ¯ H I . In a x ¯ H I = 0.3 simulation, we perform 100 realizations of a mock 2 deg² survey with a redshift window Δz = 0.5 and flux limit f _Lyα > 1 × 10⁻¹⁷ erg s⁻¹ cm⁻²; such a survey is typical in depth and volume of the largest LAE surveys conducted today. For each realization, we compute the LAE LF and use it to recover the input x ¯ H I . Comparing the inferred values of x ¯ H I across the ensemble of the surveys, we find that cosmic variance, deriving from large-scale structure and variation in the neutral gas along the sightline, imposes a floor in the uncertainty of Δ x ¯ H I ∼ 0.2 when x ¯ H I = 0.3. We explore mitigation strategies to decrease this uncertainty, such as increasing the volume, decreasing the flux limit, or probing the volume with many independent fields. Increasing the area and/or depth of the survey does not mitigate the uncertainty, but composing a survey with many independent fields is effective. This finding highlights the best strategy for LAE surveys aiming at constraining the x ¯ H I of the universe during reionization.