The H$\alpha$ Luminosity Function and Star Formation Rate at $z\approx 0.24$ in the Cosmos 2 Square-Degree Field

To derive a new H$\alpha$ 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$\alpha$ emitting galaxies in the HST COSMOS 2 square degree field. We used the narrow-band filter NB816 ($\lambda_c = 8150$\mathring{A},$\Delta \lambda = 120$\mathring{A})andsampledH$\alpha$emitterswith$EW_{\rm obs}(\rm H\alpha + [N$\text{textsc}ii$]) > 12$ \AA in a redshift range between $z=0.233$ and $z=0.251$ corresponding to a depth of 70 Mpc. We obtained 980 H$\alpha$ emitting galaxies in a sky area of 5540 arcmin${}^2$, corresponding to a survey volume of $3.1\times {10}^4\mathrm{M}\mathrm{p}{\mathrm{c}}^3$. We derive a H$\alpha$ luminosity function with a best-fit Schechter function parameter set of $\alpha = -1.35^{+0.11}{-0.13}$,$\log\phi* = -2.65^{+0.27}{-0.38}$,and$\log L* ({\rm erg s^{-1}}) = 41.94^{+0.38}{-0.23}$\mathrm{.}TheH$\alpha$ luminosity density is $2.7_{-0.6}^{+0.7}\times {10}^{39}$ ergs s${}^{-1}$ Mpc${}^{-3}$. After subtracting the AGN contribution (15 %) to the H$\alpha$ luminosity density, the star formation rate density is evaluated as $1.8^{+0.7}{-0.4} \times 10^{-2}$ $M_{\text{sun}}$ yr${}^{-1}$ Mpc${}^{-3}$. The angular two-point correlation function of H$\alpha$ emitting galaxies of $\log L(\mathrm{H}\alpha )>39.8$ is well fit by a power law form of $w(\theta) = 0.013^{+0.002}_{-0.001} \theta^{-0.88 \pm 0.03}$,correspondingtothecorrelationfunctionof$\xi® = (r/1.9{\rm Mpc})^{-1.88}$\mathrm{.}WealsofindthattheH$\alpha$ emitters with higher H$\alpha$ luminosity are more strongly clustered than those with lower luminosity.