The H$α$ Luminosity Function and Star Formation Rate at $z \approx 0.24$ in the Cosmos 2 Square-Degree Field
To derive a new H$α$ luminosity function and to understand the clustering properties of star-forming galaxies at $z \approx 0.24$, we have made a narrow-band imaging survey for H$α$ emitting galaxies in the HST COSMOS 2 square degree field. We used the narrow-band filter NB816 ($λ_c = 8150$ Å, $Δλ= 120$ Å) and sampled H$α$ emitters with $EW_{\rm obs}(\rm Hα+ [N\textsc{ii}]) > 12$ Åin a redshift range between $z=0.233$ and $z=0.251$ corresponding to a depth of 70 Mpc. We obtained 980 H$α$ emitting galaxies in a sky area of 5540 arcmin$^2$, corresponding to a survey volume of $3.1 \times 10^4 {\rm Mpc^3}$. We derive a H$α$ luminosity function with a best-fit Schechter function parameter set of $α= -1.35^{+0.11}_{-0.13}$, $\logϕ_* = -2.65^{+0.27}_{-0.38}$, and $\log L_* ({\rm erg s^{-1}}) = 41.94^{+0.38}_{-0.23}$. The H$α$ luminosity density is $2.7^{+0.7}_{-0.6} \times 10^{39}$ ergs s$^{-1}$ Mpc$^{-3}$. After subtracting the AGN contribution (15 %) to the H$α$ luminosity density, the star formation rate density is evaluated as $1.8^{+0.7}_{-0.4} \times 10^{-2}$ $M_{\sun}$ yr$^{-1}$ Mpc$^{-3}$. The angular two-point correlation function of H$α$ emitting galaxies of $\log L({\rm Hα}) > 39.8$ is well fit by a power law form of $w(θ) = 0.013^{+0.002}_{-0.001} θ^{-0.88 \pm 0.03}$, corresponding to the correlation function of $ξ(r) = (r/1.9{\rm Mpc})^{-1.88}$. We also find that the H$α$ emitters with higher H$α$ luminosity are more strongly clustered than those with lower luminosity.