The H alpha luminosity function and global star formation rate from redshifts of 1-2

We present a luminosity function for H alpha emission from galaxies at reds hifts between 0.7 and 1.9 based on slitless spectroscopy with the near-infr ared camera and multiobject spectrometer on the Hubble Space Telescope. The luminosity function is well fit by a Schechter function over the range 6 x 10(41) < L (H alpha) < 2 x 10(43) ergs s(-1) with L* = 7 x 10(42) ergs s(- 1) and phi* = 1.7 x 10(-3) Mpc(-3) for H-0 = 50 km s(-1) Mpc(-1) and q(0) = 0.5. We derive a volume-averaged star formation rate at z = 1.3 +/- 0.5 of 0.13 M. yr(-1) Mpc(-3) without correction for extinction. The star formati on rate that we derive at similar to 6500 Angstrom is a factor of 3 higher than that deduced from 2800 Angstrom continua. If this difference is caused entirely by reddening, the extinction correction at 2800 Angstrom is quite significant. The precise magnitude of the total extinction correction at r est-frame UV wavelengths (e.g., 2800 and 1500 Angstrom) is sensitive to the relative spatial distribution of the stars, gas, and dust, as well as to t he extinction law. In the extreme case of a homogeneous foreground dust scr een and a Milky Way or LMC extinction law, we derive a total extinction at 2800 Angstrom of 2.1 mag, or a factor of 7 correction to the UV luminosity density. If we use the Calzetti reddening curve, which was derived for the model in which stars, gas, and dust are well mixed and nebular gas suffers more extinction than stars, our estimate of A(2800) is increased by more th an 1 mag.