A large narrow band H$\alpha$ survey at $z\sim 0.2$: the bright end of the luminosity function, cosmic variance and clustering across cosmic time

Abstract

We carried out the largest ($>3.5\times 10^5$ Mpc${}^3$, 26 deg${}^2$) H$\alpha$ narrow band survey to date at $z\sim 0.2$ 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 $\sim 10^{42.4}$ erg s${}^{-1}$, equivalent to $\sim 11M_{\odot }$ yr${}^{-1}$. Using our sample of $220$ sources brighter than $>10^{41.4}$ erg s${}^{-1}$ ($>1M_{\odot }$ yr${}^{-1}$), we derive H$\alpha$ luminosity functions, which are well described by a Schechter function with ${\varphi }^{\ast }=10^{-2.85\pm 0.03}$ Mpc${}^{-3}$ and $L_{H\alpha }^{\ast }=10^{41.71\pm 0.02}$ erg s${}^{-1}$ (with a fixed faint end slope $\alpha =-1.35$). We find that surveys probing smaller volumes ($\sim 3\times 10^4$ 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 ${\rho }_{\mathrm{SFRD}}=0.0094\pm 0.0008$ $M_{\odot }$ 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 $\omega (\theta )=(0.159\pm 0.012){\theta }^{(-0.75\pm 0.05)}$, corresponding to a clustering length of $r_0=3.3\pm 0.8$ Mpc/h. We find that the most luminous H$\alpha$ emitters at $z\sim 0.2$ are more strongly clustered than the relatively fainter ones. The $L_{H\alpha }^{\ast }$ H$\alpha$ emitters at $z\sim 0.2$ in our sample reside in $\sim 10^{12.5-13.5}$ $M_{\odot }$ 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 $L_{\mathrm{H}\alpha }/L_{H\alpha }^{\ast }(z)$, as proposed by Sobral et al. (2010).

Accepted for publication in MNRAS; 18 pages, 19 figures, 6 tables

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