Dust Absorption and the Ultraviolet Luminosity Density at<i>z</i> ≈ 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 FFIR/F1600 versus β relation in terms of A1600 (the dust absorption at 1600˚A), and the transformation from broad band photometric color to β. Both calibrations are almost completely independent of theoretical stellar population models. We show that the recent marginal and non-detections of HDF U-dropouts at radio and sub-mm 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