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 approximate to 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 beta (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)/F(1600) versus beta relation in terms of A(1600) (the dust absorption at 1600 Angstrom) and the transformation from broadband photometric color to beta. 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 A(1600). 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 beta: 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 approximate to 3. The absorptioncorrected UV luminosity function of U dropouts extends up to M(1600,0) approximate to -24 AB mag, corresponding to a star formation rate similar to 200 M. yr(-1) (H(0) = 50 km s(-1) Mpc(-3) and q(0) = 0.5 are assumed throughout). The absorption-corrected UV luminosity density at z approximate to 3 is rho 1600,0 greater than or equal to 1.4 x 10(27) ergs(-1) Hz(-1) Mpc(-1). It is still a lower limit since completeness corrections have not been done and because only galaxies with A(1600) less than or similar to 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 Angstrom.