Dust Absorption and the Ultraviolet Luminosity Density at z ≈ 3 as Calibrated by Local Starburst Galaxies^*

We refine a technique to measure the absorption-corrected ultraviolet (UV) luminosity of starburst galaxies using rest-frame UV quantities alone and apply it to Lyman-limit U dropouts at z ≈ 3 found in the Hubble Deep Field (HDF). The method is based on an observed correlation between the ratio of far-infrared (FIR) to UV fluxes with spectral slope β (a UV color). A simple fit to this relation allows the UV flux absorbed by dust and reprocessed to the FIR to be calculated, and hence the dust-free UV luminosity to be determined. International Ultraviolet Explorer spectra and Infrared Astronomical Satellite fluxes of local starbursts are used to calibrate the F_FIR/F₁₆₀₀ versus β relation in terms of A₁₆₀₀ (the dust absorption at 1600 Å) and the transformation from broadband photometric color to β. Both calibrations are almost completely independent of theoretical stellar-population models. We show that the recent marginal and nondetections of HDF U dropouts at radio and submillimeter wavelengths are consistent with their assumed starburst nature and our calculated A₁₆₀₀. This is also true of recent observations of the ratio of optical emission-line flux to UV flux density in the brightest U dropouts. This latter ratio turns out not to be a good indicator of dust extinction. In U dropouts, absolute magnitude M_1600,0 correlates with β: brighter galaxies are redder, as is observed to be the case for local starburst galaxies. This suggests that a mass-metallicity relationship is already in place at z ≈ 3. The absorption-corrected UV luminosity function of U dropouts extends up to M_1600,0 ≈ -24 AB mag, corresponding to a star formation rate ~200 _☉ yr^-1 (H₀ = 50 km s^-1 Mpc^-3 and q₀ = 0.5 are assumed throughout). The absorption-corrected UV luminosity density at z ≈ 3 is ρ_1600,0 ≥ 1.4 × 10²⁷ ergs^-1 Hz^-1 Mpc^-1. It is still a lower limit since completeness corrections have not been done and because only galaxies with A₁₆₀₀ ≲ 3.6 mag are blue enough in the UV to be selected as U dropouts. The luminosity-weighted mean dust-absorption factor of our sample is 5.4 ± 0.9 at 1600 Å.