We present the first measurements of the shape of the far-ultraviolet (far-UV; lambda=950-1500 A) dust attenuation curve at high redshift (z~3). Our analysis employs rest-frame UV spectra of 933 galaxies at z~3, 121 of which have very deep spectroscopic observations (>7 hrs) at lambda=850-1300 A, with the Low Resolution Imaging Spectrograph on the Keck Telescope. By using an iterative approach in which we calculate the ratios of composite spectra in different bins of continuum color excess, E(B-V), we derive a dust curve that implies a lower attenuation in the far-UV for a given E(B-V) than those obtained with standard attenuation curves. We demonstrate that the UV composite spectra of z~3 galaxies can be modeled well by assuming our new attenuation curve, a high covering fraction of HI, and absorption from the Lyman-Werner bands of H2 with a small (<20%) covering fraction. The low covering fraction of H2 relative to that of the HI and dust suggests that most of the dust in the ISM of typical galaxies at z~3 is unrelated to the catalysis of H2, and is associated with other phases of the ISM (i.e., the ionized and neutral gas). The far-UV dust curve implies a factor of ~2 lower dust attenuation of Lyman continuum (ionizing) photons relative to those inferred from the most commonly assumed attenuation curves for L* galaxies at z~3. Our results may be utilized to assess the degree to which ionizing photons are attenuated in HII regions or, more generally, in the ionized or low column density (N(HI)<10^17.2 cm^-2) neutral ISM of high-redshift galaxies.
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