Hα Observations of a Large Sample of Galaxies at z ~ 2: Implications for Star Formation in High-Redshift Galaxies^*

Using Hα spectra of 114 rest-frame UV-selected galaxies at z ~ 2, we compare inferred star formation rates (SFRs) with those determined from the UV continuum luminosity. After correcting for extinction using standard techniques based on the UV continuum slope, we find excellent agreement between the indicators, with ⟨SFR_Hα⟩ = 31 M_☉ yr^-1 and ⟨SFR_UV⟩ = 29 M_☉ yr^-1. The agreement between the indicators suggests that the UV luminosity is attenuated by a typical factor of ~4.5 (ranging from no attenuation to a factor of ~100 for the most obscured object in the sample), in good agreement with estimates of obscuration from X-ray, radio, and mid-IR data. The Hα luminosity is attenuated by a factor of ~1.7 on average, and the maximum Hα attenuation is a factor of ~5. In agreement with X-ray and mid-IR studies, we find that the SFR increases with increasing stellar mass and at brighter K magnitudes to ⟨SFR_Hα⟩ ~ 60 M_☉ yr^-1 for galaxies with K_s < 20; the correlation between K magnitude and SFR is much stronger than the correlation between stellar mass and SFR. All galaxies in the sample have SFRs per unit area Σ_SFR in the range observed in local starbursts. We compare the instantaneous SFRs and the past average SFRs as inferred from the ages and stellar masses, finding that for most of the sample, the current SFR is an adequate representation of the past average. There is some evidence that the most massive galaxies (M_⋆ > 10¹¹ M_☉) have had higher SFRs in the past.