The Hα Luminosity Function and Global Star Formation Rate From Redshifts of One to Two

We present a luminosity function for H$\alpha$ emission from galaxies at redshifts between 0.7 and 1.9 based on slitless spectroscopy with NICMOS on HST. The luminosity function is well fit by a Schechter function over the range $6 \times 10^{41} < L(H\alpha) < 2 \times 10^{43} erg/sec$ with $L^* = 7 \times 10^{42} erg/sec$ and $\phi^* = 1.7 \times 10^{-3} Mpc^{-3}$ for $H_0=50 km/s Mpc^{-1}$ and $q_0=0.5$. We derive a volume averaged star formation rate at $z = 1.3 \pm 0.5$ of 0.13 M_{\odot} yr^{-1} Mpc^{-3} without correction for extinction. The SFR that we derive at $\sim 6500 \AA is a factor of 3 higher than that deduced from 2800 \AA continua. If this difference is due entirely to reddening, the extinction correction at 2800 \AA is quite significant. The precise magnitude of the total extinction correction at rest-frame UV wavelengths (e.g. 2800 \AA and 1500 \AA) is sensitive to the relative spatial distribution of the stars, gas and dust, as well as on the extinction law. In the extreme case of a homogeneous foreground dust screen and a MW or LMC extinction law, we derive a total extinction at 2800 \AA of 2.1 magnitudes, or a factor of 7 correction to the UV luminosity density. If we use the Calzetti reddening curve, which was derived for the model where stars, gas and dust are well mixed and nebular gas suffers more extinction than stars, our estimate of A$_{2800}$ is increased by more than one magnitude.