The GLASS-JWST Early Release Science Program. V. H$\alpha$ luminosity functions at $z\sim1.3$ and $z\sim2.0$

We present H$\alpha$ luminosity function (LF) measurements at redshifts $z\sim1.3$ and $z\sim2.0$ using JWST NIRISS grism data from the GLASS-JWST survey. Based on emission lines spectroscopically identified in the F115W, F150W and F200W filters, we select 99 H$\alpha$ emitters. Through detailed effective volume and completeness analysis for each source, we construct the H$\alpha$ LF in two redshift bins. Thanks to the sensitivity of NIRISS WFSS and gravitational lensing magnification, our sample reaches intrinsic H$\alpha$ luminosities $\sim$10 times deeper than previous grism surveys, down to $L_{\rm H\alpha}\sim10^{40.5}~\rm erg~s^{-1}$ at $z\sim1.3$ and $L_{\rm H\alpha}\sim10^{40.9}~\rm erg~s^{-1}$ at $z\sim2.0$ with completeness larger than 0.8, corresponding to star formation rates of 0.4 and 1.0 $M_{\odot}~\rm yr^{-1}$, respectively. We robustly constrain the faint-end slope of the H$\alpha$ luminosity function to be $-1.50^{+0.14}_{-0.08}$ at $z\sim1.3$ and $-1.60^{+0.17}_{-0.09}$ at $z\sim2.0$ after considering the cosmic variance of $\sim 20\%$, consistent with previous estimations. The emission-line samples presented here will enable further detailed studies of galaxy properties including metallicities. We find a negligible contribution from bright active galactic nuclei in our sample. We estimate integrated cosmic star formation rate densities of $0.097^{+0.015}_{-0.016}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim1.3$ and $0.129^{+0.025}_{-0.030}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim2.0$. The methodology presented here can be readily applicable to other JWST slitless spectroscopic datasets and future wide-field slitless surveys, including those from Euclid, Roman, and the Chinese Space Station Telescope.