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 
<
25.5 is ~ 1.2 arcmin-2, or
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
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
M
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
= 24.5 would
be forming stars at a rate of ~ 60 (145)
h-250
M yr-1
after dereddening
by a factor of 5, while the brightest galaxies
(
23)
would have sfr ~ 400 (1000) h-250
M 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
M) 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 
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
H
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
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.