Quantifying the Effect of Field Variance on the Hα Luminosity Function with the New Numerical Galaxy Catalog (ν2GC)

We construct a model of Hα emitters (HAEs) based on a semianalytic galaxy formation model, the New Numerical Galaxy Catalog (ν²GC). In this paper, we report our estimate for the field variance of the HAE distribution. By calculating the Hα luminosity from the star formation rate of galaxies, our model well reproduces the observed Hα luminosity function (LF) at z = 0.4. The large volume of the ν²GC 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 ${L}_{{\rm{H}}\alpha }\geqslant {10}^{40}$ 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 (>5σ) at clusters and the filamentary structures. The Hα LFs within a survey area of ∼2 deg² (typical for previous observational studies) show a significant field variance up to ∼1 dex. Based on our model, one can estimate the variance on the Hα LFs within given survey areas.