A large narrow band H$\alpha$ survey at $z\sim0.2$: the bright end of
  the luminosity function, cosmic variance and clustering across cosmic time
  We carried out the largest ($>3.5\times10^5$ Mpc$^3$, 26 deg$^2$) H$\alpha$
narrow band survey to date at $z\sim0.2$ in the SA22, W2 and XMMLSS
extragalactic fields. Our survey covers a large enough volume to overcome
cosmic variance and to sample bright and rare H$\alpha$ emitters up to an
observed luminosity of $\sim10^{42.4}$ erg s$^{-1}$, equivalent to $\sim11
M_\odot$ yr$^{-1}$. Using our sample of $220$ sources brighter than
$>10^{41.4}$ erg s$^{-1}$ ($>1 M_\odot$ yr$^{-1}$), we derive H$\alpha$
luminosity functions, which are well described by a Schechter function with
$\phi^* = 10^{-2.85\pm0.03}$ Mpc$^{-3}$ and $L^*_{H\alpha} = 10^{41.71\pm0.02}$
erg s$^{-1}$ (with a fixed faint end slope $\alpha=-1.35$). We find that
surveys probing smaller volumes ($\sim3\times10^4$ Mpc$^3$) are heavily
affected by cosmic variance, which can lead to errors of over $100$ per cent in
the characteristic density and luminosity of the H$\alpha$ luminosity function.
We derive a star formation rate density of $\rho_\mathrm{SFRD} =
0.0094\pm0.0008$ $M_\odot$ yr$^{-1}$, in agreement with the redshift-dependent
H$\alpha$ parametrisation from Sobral et al. (2013). The two-point correlation
function is described by a single power law $\omega(\theta) = (0.159\pm0.012)
\theta^{(-0.75\pm0.05)}$, corresponding to a clustering length of $r_0 =
3.3\pm0.8$ Mpc/h. We find that the most luminous H$\alpha$ emitters at
$z\sim0.2$ are more strongly clustered than the relatively fainter ones. The
$L^*_{H\alpha}$ H$\alpha$ emitters at $z\sim0.2$ in our sample reside in
$\sim10^{12.5-13.5}$ $M_\odot$ dark matter haloes. This implies that the most
star forming galaxies always reside in relatively massive haloes or group-like
environments and that the typical host halo mass of star-forming galaxies is
independent of redshift if scaled by $L_\mathrm{H\alpha}/L^*_{H\alpha}(z)$, as
proposed by Sobral et al. (2010).
