and Cosmology

3. The World of Galaxies
136
3.9.4 Star Formation History and Galaxy Colors
Up to now, we have considered the evolution of a stellar
population of a common age (called an instantaneous
burst of star formation). However, star formation in
a galaxy takes place over a finite period of time.
We expect that the star-formation rate decreases over
time because more and more matter is bound in stars
and thus no longer available to form new stars. Since
the star-formation history of a galaxy is a priori unknown,
it needs to be parametrized in a suitable manner.
A “standard model” of an exponentially decreasing
star-formation rate was established for this,
ψ(t) = τ −1 exp [−(t − t f )/τ] H(t − t f ) , (3.69)
where τ is the characteristic duration and t f the onset
of star formation. The last factor in (3.69) is the Heaviside
step function, H(x) = 1forx ≥ 0, H(x) = 0for
x < 0. This Heaviside step function accounts for the fact
that ψ(t) = 0fort < t f . We may hope that this simple
model describes the basic aspects of a stellar population.
Results of this model are plotted in Fig. 3.49(a) in
a color–color diagram.
From the diagram we find that the colors of the population
depend strongly on τ. Specifically, galaxies do
not become very red if τ is large because their starformation
rate, and thus the fraction of massive blue
stars, does not decrease sufficiently. The colors of Sc
spirals, for example, are not compatible with a constant
star-formation rate – except if the total light of spirals is
strongly reddened by dust absorption (but there are good
reasons why this is not the case). To explain the colors
of early-type galaxies we need τ 4 × 10 9 yr. In general,
one deduces from these models that a substantial
evolution to redder colors occurs for t τ. Since the
luminosity of a stellar population in the blue spectral
range decreases quickly with the age of the population,
whereas increasing age affects the red luminosity much
less, we conclude:
The spectral distribution of galaxies is mainly determined
by the ratio of the star-formation rate
today to the mean star-formation rate in the past,
ψ(today)/ 〈ψ〉.
One of the achievements of this standard model is
that it explains the colors of present day galaxies, which
have an age of 10 billion years. However, this model
is not unambiguous because other star-formation histories
ψ(t) can be constructed with which the colors of
galaxies can be modeled as well.
3.9.5 Metallicity, Dust, and HII Regions
Predictions of the model depend on the metallicity Z –
see Fig. 3.49(b). A small value of Z results in a bluer
color and a smaller M/L ratio. The age and metallicity
of a stellar population are degenerate in the sense that
an increase in the age by a factor X is nearly equivalent
to an increase of the metallicity by a factor 0.65X with
respect to the color of a population. The age estimate of
a population from color will therefore strongly depend
on the assumed value for Z. However, this degeneracy
can be broken by taking several colors, or information
from spectroscopy, into account.
Intrinsic dust absorption will also change the colors
of a population. This effect cannot be easily accounted
for in the models because it depends not only on the
properties of the dust but also on the geometric distribution
of dust and stars. For example, it makes a difference
whether the dust in a galaxy is homogeneously distributed
or concentrated in a thin disk. Empirically, it is
found that galaxies show strong extinction during their
active phase of star formation, whereas normal galaxies
are presumably not much affected by extinction, with
early-type galaxies (E/S0) affected the least.
Besides stellar light, the emission by HII regions also
contributes to the light of galaxies. It is found, though,
that after ∼ 10 7 yr the emission from gas nebulae only
marginally contributes to the broad-band colors of galaxies.
However, this nebular radiation is the origin of
emission lines in the spectra of galaxies. Therefore,
emission lines are used as diagnostics for the starformation
rate and the metallicity in a stellar population.
3.9.6 Summary
After this somewhat lengthy section, we shall summarize
the most important results of population synthesis
here: