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A large narrow band H$α$ 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$α$ 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$α$ 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$α$ luminosity functions, which are well described by a Schechter function with $ϕ^* = 10^{-2.85\pm0.03}$ Mpc$^{-3}$ and $L^*_{Hα} = 10^{41.71\pm0.02}$ erg s$^{-1}$ (with a fixed faint end slope $α=-1.35$). 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$α$ luminosity function. We derive a star formation rate density of $ρ_\mathrm{SFRD} = 0.0094\pm0.0008$ $M_\odot$ yr$^{-1}$, in agreement with the redshift-dependent H$α$ parametrisation from Sobral et al. (2013). The two-point correlation function is described by a single power law $ω(θ) = (0.159\pm0.012) θ^{(-0.75\pm0.05)}$, corresponding to a clustering length of $r_0 = 3.3\pm0.8$ Mpc/h. We find that the most luminous H$α$ emitters at $z\sim0.2$ are more strongly clustered than the relatively fainter ones. The $L^*_{Hα}$ H$α$ 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 $L_\mathrm{Hα}/L^*_{Hα}(z)$, as proposed by Sobral et al. (2010).