High Redshift Galaxies in the Hubble Deep Field. Color Selection and Star Formation History to z=4

The Lyman decrement associated with the cumulative effect of HI in QSO absorption systems along the line of sight provides a distinctive feature for identifying galaxies at z>2.5. The Hubble Deep Field (HDF) observations offer the opportunity to exploit the ubiquitous effect of intergalactic absorption and obtain useful statistical constraints on the redshift distribution of galaxies considerably fainter than current spectroscopic limits. We model the HI cosmic opacity as a function of redshift, including scattering in resonant lines of the Lyman series and Lyman-continuum absorption, and use stellar population synthesis models with a wide variety of ages, metallicities, dust contents, and redshifts, to derive color selection criteria that provide a robust separation between high redshift and low redshift galaxies. From the HDF images we construct a sample of star-forming galaxies at 2<z<4.5. While none of the more than 60 objects in the HDF having known Keck/LRIS spectroscopic redshifts in the range 0<z<1.4 is found to contaminate our high-redshift sample, our color criteria are able to efficiently select the 2.6<z<3.2 galaxies identified by Steidel et al. (1996b). The ultraviolet (and blue) dropout technique opens up the possibility of investigating cosmic star and element formation in the early universe.