The $z \sim 2$ $\rm{[O\ III]}$ Luminosity Function of Grism-selected Emission-line Galaxies

Upcoming missions such as Euclid and the Nancy Grace Roman Space Telescope (Roman) will use emission-line selected galaxies to address a variety of questions in cosmology and galaxy evolution in the $z>1$ universe. The optimal observing strategy for these programs relies upon knowing the number of galaxies that will be found and the bias of the galaxy population. Here we measure the $\rm{[O\ III]}\ \lambda 5007$ luminosity function for a vetted sample of 1951 $m_{\rm J+JH+H} < 26$ galaxies with unambiguous redshifts between $1.90 < z < 2.35$, which were selected using HST/WFC3 G141 grism frames made available by the 3D-HST program. These systems are directly analogous to the galaxies that will be identified by the Euclid and Roman missions, which will utilize grism spectroscopy to find $\rm{[O\ III]}\ \lambda 5007$-emitting galaxies at $0.8 \lesssim z \lesssim 2.7$ and $1.7 \lesssim z \lesssim 2.8$, respectively. We interpret our results in the context of the expected number counts for these upcoming missions. Finally, we combine our dust-corrected $\rm{[O\ III]}$ luminosities with rest-frame ultraviolet star formation rates to present the first estimate of the SFR density associated with $1.90 < z < 2.35$ $\rm{[O\ III]}$-emitting galaxies. We find that these grism-selected galaxies contain roughly half of the total star formation activity at $z\sim2$.