For the purpose of illustration we present here the CMD
of a composite stellar
system containing both very old and young stars, such as for instance
an old galaxy with some recent star formation.
This example is meant
to mimic the stellar content of NGC 205 in which in addition to the
old component young stars are observed. Since the early studies
by Baade (1951), this
galaxy has long been considered to show evidence of ongoing star formation
because of the UV-bright stars as well as large number of regions of
absorption and dust (Hodge 1973).
Mould et al.
(1983, 1984) determined a metallicity 
from the CMD in the
outer regions. Peletier (1993) studied the color profile of the galaxy and
found a very blue center and colors that get redder slowly going outward.
Because of the presence of blue luminous stars in the center, the color
gradient is interpreted as a gradient in age. The existence of luminous blue
stars sets a limit to the age of the recent episode of star formation at
a few 
yr. Furthermore, the galaxy contains a number of bright red stars,
which are so bright that they either are red supergiants or evolved AGB
stars (Gallagher & Mould 1981). Following Peletier (1992),
NGC 205 can
be modeled as an old galaxy with some young stars in the center. The age of
the underlying old component is more difficult to assess. The study of
Mould et al. (1983, 1984) perhaps implies an age not younger than a few
Gyr. Using the static population synthesis
technique, Bica et al. (1990) inferred from the observed spectral energy
the existence of an old component whose metallicity lies the range
, and whose age is older than 5 Gyr
with
typical value of 12-13 Gyr. They also confirmed the existence of
a young component with age in the range
0.01 Gyr to a few 0.1 Gyr, which contributes to about 80% of the visible
light.
With the aid of the Bertelli et al. (1994)
isochrones and luminosity functions, we estimate that
the young component though
dominating the visible light yet contains only about 2% of the total mass
of stars in the galaxy.
On the basis of these observational hints, we model the star formation history in NGC 205 as a burst-like episode at constant rate whose duration is from 0.5 Gyr ago to the present time, say a few 0.001 Gyr, superposed to an exponential law that was maximum in the past, say 13 Gyr ago, and then quickly declined toward the present. The rate of decline of the exponential component and the amplitude of star formation in the burst with respect to that in the previous phase, are chosen in such a way that the above percentages in the relative total mass of stars born in the two episodes are matched. We find that an e-folding of 1 Gyr and relative amplitude of the burst of about 0.1 are good choices.
Figure 17 (click here) shows four synthetic CMDs:
the theoretical plane, the classical
(B-V) versus 
plane, the
versus 
plane, and finally
the 
versus 
plane.
The distortion of the CMD induced by the non monotonic behaviour of the
colour 
is evident. Indeed the RGB, HB and AGB
sequences are folded
onto the main sequence so that disentangling the various components is very
difficult if not impossible. Similar behaviours are expected with other
UV pass-bands such as the 17W, 21W, 22F and 34F.
This is a remarkable
feature to be kept in mind when analyzing the data acquired with the
UV pass-bands of HST. The CMDs in the other pass-bands look normal.
Figure 18: The colour evolution of Models A, B and C as a function of the
rest-frame age. The three models have different histories of star formation
and chemical enrichment. See the text for more details.
Upper panel:
the colour 
The vertical arrows show the maximum age of the galaxy for different choices
of the cosmological parameters 
and 
and
(see also the entries of
Table 2).
Lower panel; the same but for the colour (1550-V)