The secondary star-formation episode in some of the Local Group dE's could
have extended to redshifts as low as z 
0.3. This suggests
a possible link to the faint blue galaxy population that shows
up in deep surveys. Several authors have suggested that
dwarf galaxies form many (if not all) of their stars at
late epochs
(Silk et al. 1987;
Babul and Rees 1992;
Efstathiou 1992).
Because of the uncertainties in the physics of star formation, these
models do not make very detailed predictions. However, there are
a few reasonably model-independent requirements that must be met
if dwarf galaxies are to account for the majority of galaxies
fainter than B 21.
At high redshifts, the B band samples the rest-frame UV and depends
more on the star-formation rate than on the number of stars in the
galaxy. At a redshift of z 0.4, a B magnitude of 24 corresponds
to a star-formation rate of 5 M
yr-1, for a Salpeter IMF.
Even for a large dwarf galaxy, say 109 M, forming all
its stars at a rate of 5 M yr-1 would require a relatively
short burst of ~ 2 x 108 year duration.
Less massive galaxies would require even shorter bursts.
For comparison, the interval (0.3 < z < 1) incorporates a range of
4 Gyr in lookback time. This means that if dwarf galaxies are to
supply the excess blue counts, they must form their stars in
short bursts over a wide range of redshifts.
The widely varying star-formation histories of the Local Group dE's are
perhaps consistent with this requirement, although galaxies even as
bright as the Fornax dE are much lower in luminosity than those
detected in the deepest redshift surveys.
Cowie et
al. (1991) estimate
luminosities of 0.01 L* in the K band for the bulk of the galaxies
at B = 24. This is closer to SMC luminosities than Local Group dE
luminosities. However, the dE sequence in clusters continues up to
0.05 L*, so it may be
that the lower luminosity dE's are just
not showing up to the limits of the current redshift surveys. More
problematical is that for the local dE's, the data suggest the
star formation in the secondary episodes took place over a few Gyr
(Mighell and
Butcher 1992;
van den Bergh 1994),
star-formation rates lower than required by several orders of magnitude.