MAMMOTH-Subaru. V. Effects of Cosmic Variance on Ly 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 sigma(g) of galaxy numbers in observational astronomy, which significantly affects the luminosity function (LF) measurement of Ly alpha emitters (LAEs). For most previous Ly alpha LF studies, sigma(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 approximate to 2.2 Ly alpha 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 similar or equal to 11.62 deg(2) and a comoving volume of similar or equal to 8.71 x 10(6) Mpc(3). We report a best-fit Schechter function with parameters alpha = -1.75 (fixed), L-Ly alpha(* )=5.95(-0.96)(+1.22 )x 10(42 )erg s(-1), and phi(* )(Ly alpha)= 5.26(-1.27)(+1.65 )x 10(-4) Mpc(-3) for the overall Ly alpha LFs. After clipping out the regions that may bias the cosmic variance measurements, we calculate sigma(g) by sampling LAEs within multiple pointings on the field image. We investigate the relation between sigma(g) and survey volume V, and fit a simple power-law sigma(g )= k x (V/10(5)Mpc(3))(beta). We find best-fit values of -1.399(-0.156)(+0.160) for beta 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.