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The Lyman-break galaxies represent a substantial population of star makers at a time when the age of the universe was about 15% of its current value. The ground-based survey is sensitive to systems at redshifts ~ 3 (see Figure 2a), whose surface density down to curlyR < 25.5 is ~ 1.2 arcmin-2, or approx 5% of the faint counts at the same magnitude. This corresponds to a comoving volume density of 8.5 x 10-4 h350 Mpc-3 (1.6 x 10-4h350) if q0 = 0.5 (0.05), or about the same density (1/5) of the present-day galaxies with L ~ L*.

The HDF Lyman-break galaxies are more numerous, with a surface density at the same magnitude limit that is larger than that of their ground-based counterparts by a factor approx 7x (see Mark Dickinson's contribution in this volume for a more complete discussion of this point). In part, this can be explained by the fact that the redshift distribution of the HDF galaxies extends to smaller values than the ground-based one, because the F300W filter is ~ 600 Å bluer than the Un. Therefore, for a given magnitude limit, the HDF probes a fainter portion of the absolute luminosity distribution and also a larger comoving volume per unit area. It is also likely that observational effects, such as the higher angular resolution and the deeper flux limit in the U band of the HDF respect to the ground-based survey, result in a higher number of candidates. However, we cannot exclude that the higher abundances of HDF galaxies can also be due to evolutionary effects. The HDF redshift distribution includes a larger fraction of galaxies around z ~ 2 and if at this epoch star-forming galaxies were more numerous than at z ~ 3 (particularly those with fainter UV absolute luminosities), this results in higher surface density of candidates.

With observed star-formation rates that reach ~ 50-70 h-250 Msun yr-1 (with q0 = 0.5) only for few very bright cases, at first sight it might seem that the Lyman-break population lacks the powerful star makers expected in the models of "monolithic collapse" for the formation of elliptical galaxies and spiral bulges. In these models, the galaxies assembled most of their stellar mass in powerful burst at high redshifts and subsequently evolved passively (e.g., Eggen, Lynden-Bell & Sandage 1962; Partridge & Peebles 1967). But as we have seen, dust obscuration is very likely directly responsible for a factor ~ 3-7 of attenuation, and the dereddened star-formation rates are actually in line with the expectations of models where the spheroids assembled most of their stars at high redshifts. For example, a galaxy with curlyR = 24.5 would be forming stars at a rate of ~ 60 (145) h-250 Msun yr-1 after dereddening by a factor of 5, while the brightest galaxies (curlyR ltapprox 23) would have sfr ~ 400 (1000) h-250 Msun yr-1 or more.

The age of the universe at redshift z ~ 3 is about 15% of its present value, so ~ 109 yr of sustained star formation with the above rates that started at z ~ 4 or so can easily accommodate an M* (i.e., 1011 Msun) worth of stars by z ~ 2 which will, from that epoch on, evolve mostly passively. In view of the fact that approximately half of the local stellar mass density is segregated in spheroidal systems (Schechter & Dressler 1987) and that these stars are among the oldest known, it is very interesting to ask which fraction of the cosmic stellar mass-density was produced in the Lyman-break galaxies at z gtapprox 2. Figure 2b shows a revision to the popular "Madau's plot" (Madau et al. 1996), namely the star-formation density as a function of redshift/cosmic time, once some dust corrections are taken into account. We have chosen to plot the data in linear scale and using the cosmic time in place of redshift to provide a more intuitive idea of the amount of evolution and the time scale of the cosmic star formation activity. The data relative to Lyman-break galaxies have been corrected by a factor of 5, while those from the CFRS a factor of 2, in general agreement with the recent comparison between Halpha and UV luminosities discussed by Tresse & Maddox (1998).

The conclusion that the cosmic star formations peaks somewhere between z = 1 and z = 3 is probably still valid. However, the relative proportions of stars that have been produced at different epochs change considerably. By integrating the curve relative to the unreddened data it is found that about 15% of the stars was formed at z > 2, while using the dereddened curve yields approx 35% of the stars. The exact fraction depends on the amount of correction of both the high- and moderate-redshift data points. The former is affected by the shape of the extinction law, the latter is uncertain because it depends on the star-formation history of the galaxies. However, despite these uncertainties its seems very likely that a significant fraction of the stellar content of the universe has been assembled at z > 2 in the Lyman-break population.

Even if the Lyman-break galaxies are responsible for the oldest stellar populations of the present-day universe (e.g., those segregated in the spheroids) we still do not know how these stars were collected together to form the stellar bodies of elliptical galaxies and spiral bulges. Are the LBGs sub-galactic fragments observed during an intense phase of star-formation that are destined to subsequently merge and form massive galaxies, as predicted by the hierarchical cosmological theory (e.g., Baugh et al. 1998)? Or are they already massive galaxies during an early evolutionary phase? Which fraction of them has passively evolved (i.e., did not undergo major merging events) until the present days? It is intriguing that these galaxies have overall morphologies and sizes that (as we are about to discuss) are similar to those of the present-day spheroids, and a volume density that can account for a significant fraction (depending on the choice of the cosmological parameters) of present-day galaxies with L ~ L*. However, their evolutionary history is presently unconstrained on an empirical basis. Important pieces of information will come from reliable estimates of the duration of the star-formation activity of the Lyman-break galaxies and their mass spectrum. These issues can be tackled observationally through deep multi-band spectro-photometry and high-resolution spectroscopy at optical and near-IR wavelengths with 10-m class telescopes.

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