Quantifying the effect of field variance on the H$\alpha$ luminosity
  function with the New Numerical Galaxy Catalogue ($\nu^2$GC)
  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 $L_{\rm
H\alpha} \geq 10^{40}$ 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.
