MAMMOTH-Subaru V. Effects of Cosmic Variance on Ly$\hat{I}\pm$ Luminosity Functions at $z=2.2-2.3$

Abstract

Cosmic variance introduces significant uncertainties into galaxy number density properties when surveying the high-z Universe with a small volume, such uncertainties produce the field-to-field variance of galaxy number $\ddot{I}{ƒ}_g$ in observational astronomy. This uncertainty significantly affects the Luminosity Functions (LF) measurement of Lya Emitters (LAEs). For most previous Lya LF studies, $\ddot{I}{ƒ}_g$ 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 $z\approx 2.2$ Lya LFs. The LAE candidates are observed using narrowband and broadband of the Subaru/Hyper Suprime-Cam (HSC), with 8 independent fields, making the total survey area $\simeq 11.62$deg${}^2$ and a comoving volume of $\simeq 8.71\times 10^6$Mpc${}^3$. These eight fields are selected using the project of MAMMOTH. We report a best-fit Schechter function with parameters $\hat{I}\pm =-1.75$ (fixed), $L_{Ly\hat{I}\pm }^{\ast }=5.18_{-0.40}^{+0.43}\times 10^{42}$erg s${}^{-1}$ and $\ddot{I}{•}_{Lya}^{\ast }=4.87_{-0.55}^{+0.54}\times 10^{-4}$Mpc${}^{-3}$ for the overall Lya LFs. After clipping out the regions that can bias the cosmic variance measurements, we calculate $\ddot{I}{ƒ}_g$, by sampling LAEs within multiple pointings assigned on the field image. We investigate the relation between $\ddot{I}{ƒ}_g$ and survey volume $V$, and fit a simple power law: $\ddot{I}{ƒ}_g=k\times (\frac{V_{\mathrm{eff}}}{10^5{\mathrm{Mpc}}^3}{)}^2$. We find best-fit values of $-1.209_{-0.106}^{+0.106}$ for ${\hat{I}}^2$ and $0.986_{-0.100}^{+0.108}$ for k. We compare our measurements with predictions from simulations and find that the cosmic variance of LAEs might be larger than that of general star-forming galaxies.

14 pages, 7 figures