MAMMOTH-Subaru. V. Effects of Cosmic Variance on Lyα Luminosity Functions at z = 2.2-2.3

Cosmic variance introduces significant uncertainties into galaxy number density properties when surveying the high-redshift Universe with a small volume. Such uncertainties produce the field-to-field variance σ _g of galaxy numbers in observational astronomy, which significantly affects the luminosity function (LF) measurement of Lyα emitters (LAEs). For most previous Lyα LF studies, σ _g is often adopted from predictions by cosmological simulations, but barely confirmed by observations. Measuring cosmic variance requires a huge sample over a large volume, exceeding the capabilities of most astronomical instruments. In this study, we demonstrate an observational approach for measuring the cosmic variance contribution for z ≈ 2.2 Lyα LFs. The LAE candidates are observed using the narrow band and broad band of the Subaru/Hyper Suprime-Cam in eight independent fields, making the total survey area ≃11.62 deg² and a comoving volume of ≃8.71 × 10⁶ Mpc³. We report a best-fit Schechter function with parameters α = -1.75 (fixed), ${L}_{\mathrm{Ly}\alpha }^{* }={5.95}_{-0.96}^{+1.22}\times {10}^{42}$ erg s^-1, and ${\phi }_{\mathrm{Ly}\alpha }^{* }={5.26}_{-1.27}^{+1.65}$ × 10^-4 Mpc^-3 for the overall Lyα LFs. After clipping out the regions that may bias the cosmic variance measurements, we calculate σ _g by sampling LAEs within multiple pointings on the field image. We investigate the relation between σ _g and survey volume V, and fit a simple power-law ${\sigma }_{g}=k\times {\left(\tfrac{V}{{10}^{5}\,{\mathrm{Mpc}}^{3}}\right)}^{\beta }$ . We find best-fit values of $-{1.399}_{-0.156}^{+0.160}$ for β and ${1.249}_{-0.193}^{+0.213}$ for k. We compare our measurements with predictions from simulations and find that the cosmic variance of LAEs is likely larger than that of general star-forming galaxies.