Quantifying the effect of field variance on the H$\alpha$ luminosity function with the New Numerical Galaxy Catalogue (${\nu }^2$GC)

Abstract

We construct a model of H$\alpha$ emitters (HAEs) based on a semi-analytic galaxy formation model, the New Numerical Galaxy Catalog (${\nu }^2$GC). In this paper, we report our estimate for the field variance of the HAE distribution. By calculating the H$\alpha$ luminosity from the star-formation rate of galaxies, our model well reproduces the observed H$\alpha$ luminosity function (LF) at $z=0.4$. The large volume of the ${\nu }^2$GC makes it possible to examine the spatial distribution of HAEs over a region of (411.8 Mpc)${}^3$ in the comoving scale. The surface number density of $z=0.4$ HAEs with $L_{\mathrm{H}\alpha }\ge 10^{40}$ erg s${}^{-1}$ is 308.9 deg${}^{-2}$. We have confirmed that the HAE is a useful tracer for the large-scale structure of the Universe because of their significant overdensity ($>$ 5$\sigma$) at clusters and the filamentary structures. The H$\alpha$ LFs within a survey area of $\sim$2 deg${}^2$ (typical for previous observational studies) show a significant field variance up to $\sim$1 dex. Based on our model, one can estimate the variance on the H$\alpha$ LFs within given survey areas.

13 pages, 11 figures, accepted for publication in the ApJ