In this section we address the long debated question whether the colour
evolution of galaxies exhibits signatures that can be used as
age indicators. Renzini & Buzzoni (1986) first suggested that the
variation in
broad-band colours such as V-K
expected to occur
in a SSP at the
onset of the first AGB and RGB stars at the ages
Gyr and
Gyr,
could be used as an age indicator for those galaxies
closely
resembling SSP, i.e. elliptical galaxies, if trace of this
variation named Phase Transitions can be detected at
suitable values of the red-shift. The analysis of this problem by
Bressan et al. (1994) and Tantalo et al. (1996),
first clarified that in a
SSP only the variation caused by AGB
stars at the age of about 0.1 Gyr can be detected whereas that
of the RGB stars is masked by the presence of the former.
Figure 19: UV colours of Model A (top panel), Model B (central panel)
and Model C (lower panel)
as a function of the red-shift. For purpose of comparison the classical colour
(V-I), 
, is also shown.
The two models differ in the mean and maximum metallicity. See the text for
more details
The explanation of this resides in the Fuel Consumption
Theorem of Renzini & Buzzoni (1986). Applied to an elliptical galaxy
conceived as an assembly of stars undergoing passive evolution since
the initial prominent phase of star formation, the extremely young
age of the epoch at which the AGB colour variation occurs, implies
large values of the red-shift. The analysis of this problem by
Bressan et al. (1994) and Tantalo et al. (1996)
has shown that this signature in the rest-frame
(V-K) cannot be traced back in the colour corresponding to the red-shift
implied by the age of 0.1 Gyr, at least for any reasonable combination
of the three parameters defining a cosmological model of the Universe, i.e.
the Hubble constant 
, the
deceleration parameter 
, and finally the red-shift of galaxy formation
. Indeed the cosmological distortion
of the spectrum wipes out the colour signature.
The quest is to look for a feature occurring in a recent past so that small
values of the red-shift and little cosmological distortions are involved.
Standard broad-band colours such as (B-V), (V-R), ... (V-K) are not useful
to this purpose because going back in time
either they vary smoothly or even
remain constant over several Gyr.
Bressan et al. (1994) and Tantalo et al. (1996)
have suggested that the uprise in the UV flux
at the onset of the H-HB and AGB manqué stars can be used as
a probe of galaxy ages.
Since these stars are expected to appear at the rest-frame age of about
5.6 Gyr for 
,
a sudden change in the colour (1550-V) should be observable at
relatively low red-shifts, perhaps reachable with the
present day space instrumentation.
The precise value of the red-shift
corresponding to the above age depends on the particular model of the
Universe in usage.
Aim of this section is to quantify the Bressan et al. (1994) and Tantalo et al. (1996) predictions on the ability of UV colours to probe the age of galaxies. For the sake of clarity first we summarize the key properties of the UV emission detected in elliptical galaxies and the type of stars currently indicated as responsible of this phenomenon, and then make detailed predictions for the colour-red-shift evolution of these stellar systems.
The basic information on UV emission in elliptical galaxies (Burstein et al. 1988) can be summarized as follows:
(1) All studied elliptical galaxies have detectable UV flux short-ward of about 2000 Å.
(2) There are large galaxy to galaxy differences in the level of the UV flux. The intensity of the UV emission is measured by the colour (1550-V).
(3) The colour (1550-V) correlates with the index Mg2, the velocity
dispersion 
, and the luminosity (mass) of the galaxy. The few
galaxies (e.g. NGC 205) in which active star formation is seen do not obey
these relations.
(4) Another important constraint is posed by the HUT
observations by Ferguson et al. (1991) and Ferguson & Davidsen (1993)
of the UV excess in the bulge of M 31. In this galaxy the UV emission
shows a drop-off short-ward of about
1000 Å whose interpretation requires that
the temperature of the emitting source must be about
25 000 K. Only a small percentage of the 
Å flux can be
coming from stars hotter than 30 000 K and cooler than 20 000 K.
See also Brown et al. (1995) for more recent data.
Excluding ongoing star formation, the UV excess owes
its origin to an old component that gets hot enough to power the integrated
spectral energy distribution (ISED) of a galaxy in the far UV regions.
Four possible candidates are envisaged
(cf. Greggio & Renzini 1990; Bressan et al. 1994; and Tantalo et al. 1996).
The appearance of the various
types of UV sources is governed by several important physical factors, each
of which is affected by a certain degree of uncertainty still far from being
fully assessed. These are the efficiency of mass loss during the RGB and
AGB phases,
the enrichment law 
, and finally for the
specific case of the P-AGB stars the detailed relation between the initial and
final mass of the stars at the end of the AGB phase.
Figure 20: UV colours of Models A (top panel) and B (bottom panel)
as a function of the red-shift. The cosmological parameters are
,
. For purpose of comparison the classical colour
(V-I), 
, is also shown.
The two models differ in the kind of star formation. See the text for
more details
(1) The classical
post asymptotic giant branch (P-AGB) stars
(see Bruzual 1992; Bruzual & Charlot 1993;
Charlot & Bruzual
1991), which are always present in the stellar mix of a galaxy.
However, they cannot be the sole source of UV flux
because of their high 
(about 100 000 K) and lack
of sufficient fuel (cf. Greggio & Renzini 1990).
Another point of uncertainty is
the precise relation between the P-AGB mass and the
turn-off mass (and hence age), which is far from being established.
The Weidemann
(1987) relation provides the most favorable case
for being P-AGB stars an important source of UV flux.
However, the response of the UV flux to
details of this relation (for instance its dependence on the
metallicity) is so strong that firm conclusions cannot yet be reached
(Bressan 1996).
We remind the reader that
for ages older than about 10 Gyr, the whole problem is
driven by the initial-final mass relation in the mass range 0.8 to
1.0 
.
Finally, it is worth mentioning that P-AGB stars have perhaps been
detected
with HST observations in the nucleus of M 31 (Bertola et al. 1995)
where they seem to contribute by as much
as 50% to the UV light.
(2) Very blue HB (VB-HB) stars of extremely low
metallicity (Lee 1994). These stars have 
hotter than
about 15 000 K but much cooler than those of the P-AGB stars. Therefore,
depending on their actual 
, they can generate ISEDs
in agreement with the observational data.
In addition to a marginal difficulty with the age,
which turns out to be older than commonly assigned to globular clusters
(
Gyr, Fusi-Pecci & Cacciari 1991), there is
the question whether their luminosity and
relative frequency are compatible with the observed ISED
of elliptical galaxies in the range 
Å.
Indeed, Bressan et al. (1994) and Tantalo et al. (1996)
pointed out that the observed
ISEDs hint that only very few stars with metallicity
lower than about Z=0.008
ought to exist in a typical elliptical galaxy
(the analog of the G-Dwarf Problem in the solar vicinity).
(3) The H-HB and AGB-manqué stars of high metallicity
(say Z > 0.07) which are
expected to be present albeit in small percentages in the stellar content of
bulges and elliptical galaxies in general (cf. Bressan et al. 1994;
Tantalo et al. 1996). Indeed, these stars
have 
in the right interval and generate
ISEDs whose intensity drops short-ward of about 1000 Å by the amount
indicated by the observational data.
With normal mass loss and 
, the first
H-HB and AGB manqué stars
occur at the age of about 5.6 Gyr. This age is lowered if
is higher than 2.5 and mass loss during the RGB phase
is enhanced with respect to the value given by the classical Reimers (1975)
law (cf. Dorman et al. 1993, 1995).
(4) Finally, the analog of the above H-HB and AGB-manqué stars, but generated by enhancing the mass loss rate during the RGB phase at increasing metallicity. These types of stars have been named by Dorman et al. (1993, 1995) extremely hot HB objects (E-HB). They share nearly the same properties of the H-HB and AGB-manqué stars. The main difficulty with this option is the uncertainty concerning the metallicity dependence of the mass loss rate during the RGB phase (cf. Carraro et al. 1996).
Bressan et al. (1994, 1996) and Tantalo et al. (1996)
elaborated
new chemo - spectro - photometric models of
elliptical galaxies particularly designed to match the colour-magnitude
relation (CMR), cf. Bower et al. (1992), and to provide a robust
explanation for the UV flux and its dependence on the galactic luminosity
(and hence mass), the index 
, and the velocity dispersion
.
No details of these models are given here for the sake of brevity.
Suffice it to recall that Bressan et al. (1994) made use of the
closed-box approximation, whereas Tantalo et al. (1996)
adopted the infall description.
In both cases the enrichment law is
and the mass-loss rates for the RGB phase, are the Reimers (1975) law
with 
in Bressan et al.
(1994) and 
in Tantalo et al. (1996).
Finally, the models allow for galactic winds halting
star formation. Galactic winds are at the base of the current interpretation
of the CMR for elliptical galaxies (Bower et al.
1992). The models used in the analysis below are from Tantalo et al.
(1996)
with gas
accretion time scale 
Gyr and rate of star formation 
proportional
to the current value of the gas mass: 
with k=1 and
an efficiency parameter.
Figure 21: The ISED of Models A and B for three different values of the age,
i.e. 5 (long dashed), 10 (dotted) and 15 Gyr (solid)
Figure 22: UV colours of Models A (top panel) and B (bottom panel)
as a function of the red-shift.
The cosmological parameters are 
,
For purpose of comparison the classical colour
(V-I), 
, is also shown.
The two models differ in the kind of star formation. See the text for
more details
Figure 23: UV colours of Models A (top panel) and B (bottom panel)
as a function of the red-shift.
The cosmological parameters are 
,
For purpose of comparison the classical colour
(V-I), 
, is also shown.
The two models differ in the kind of star formation. See the text for
more details
Given these premises, we consider three galactic models characterized by
the parameters 
, and 
. The main properties of these models are
summarized in Table 2, which contains the galaxy mass, the mass accretion time
scale, the star formation efficiency, the adopted cosmological parameters
and 
, the age at the onset of galactic winds 
,
the total age of the galaxy,
the mean and maximum metallicity in stars, and the
present age
colours (B-V) and (V-K)
of the Johnson-Cousins system and the standard (1550-V).
The various groups of models have the same physical properties but differ in
the age because of the different choice for 
and 
.
For all the models, the red-shift of galaxy formation is assumed to be
.
The models under consideration are meant to represent three
extreme cases: Model A
with 
Gyr and 
undergoes the wind phase halting any
further star
formation activity in a very early past. The metallicity cannot grow to
the threshold
value required to activate the UV emission by H-HB and AGB-manqué
stars and only P-AGB stars are present.
Model B suffers from
galactic wind at later ages. The maximum metallicity goes above the
threshold value to activate the H-HB and AGB-manqué channels (the fraction
of stars in these metallicity bins is however very small). Now P-AGB,
H-HB and AGB-manqué stars all concur
to generate the UV flux. Finally, Model C has very long mass
accretion time scale (
Gyr) and very low efficiency of star formation
(
). This model never undergoes the galactic wind phase
and thus has ever
continuing star formation. It corresponds to a sort of spiral galaxy.
In order to assess the ability of UV colours in determining the age of galaxies
we examine the variation as a function of the red-shift of the colours
,
, similar to the standard (1550-V), and 
,
equivalent to the Johnson-Cousins (V-I).
Preliminary to any other consideration is to check whether the
age dependence of the integrated colours
and (1550-V) is somewhat affected by the particular
choice for the
cosmological parameters 
and 
.
This is shown in the two panels
of Fig. 18 (click here), where only ages older than 3 Gyr are considered.
As expected, but for the maximum age of the
galaxies indicated by the vertical arrows,
the colour relations are the same
at varying 
and 
.
Examining the color-age relations in more detail, we notice:
has a minimum at the age of 11.5 Gyr.
How these signatures in the rest-frame evolution of the colours for the three models will be affected by the cosmological distorsion of the ISED ?
The topic is addressed showing
in the series of Figs. 19 (click here), 20 (click here), 22 (click here), and
23 (click here)
the colour red-shift evolution for different choices of 
and 
.
We begin by assuming 
and 
and in Fig. 19 (click here)
we compare Model A (top panel)
with Model B (central panel),
i.e. the effect of different sources of UV radiation (P-AGB stars
alone versus
P-AGB plus H-HB and AGB-manqué stars), and Models B (central panel) with
model C (bottom panel), i.e.
the extreme avenues of star formation: an early burst and ever
continuing activity.
Looking at the three panels of Fig. 19 (click here), we notice that the colours
and 
of Model B are somehow anti-correlated. While 
gets redder at
increasing red-shift, 
gets bluer. At
corresponding to the age of 5.6 Gyr
at which the H-HB and AGB manqué stars start shining in the UV, both colors suffer
from a sharp change reversing their trend, and run smooth afterward.
In contrast
the UV colours of Model A (only P-AGB stars present) have a different behaviour:
the colour 
, equivalent to (1550-V),
runs smooth as expected from
the gradual appearance of the P-AGB stars, whereas the colour 
shows a marked dip at 
, which does not find immediate
correspondence in any particular stage of the rest-frame evolution
(
means an age of 10.8 Gyr). Since this value is close to age
at which the rest-frame colour 
has the bluest value one
could argue that this reversal of the trend
causes the dip in the colour-red-shift relation.
The discussion below will clarify that this is not the explanation.
Even more noticeable is the different
behaviour of the colours of Model C with continuing star formation. At z=0 all
the UV colours are extremely blue as expected due to the
combined effect of
star formation and occurrence of P-AGB, H-HB and AGB-manqué stars
(the latter two are present
because of the high mean and maximum metallicity of the model). Going back
in time, the colour 
gets first bluer and then redder (the
bluest value is at 
, whereas the colour 
has its
reddest value at 
. This trends cannot be straightforwardly
related to any particular feature in the rest-frame evolution of the colours
because ongoing star formation wipes out the signature of the old components
(cf. Fig. 18 (click here)).
Passing from 
to 
and keeping
(Fig. 20 (click here)),
the discontinuity in the colour
occurs at z=0.5, whereas the dip in the colour
remains at the same red-shift as in the previous case.
Since for 
, a red-shift 
translates into an age
of about 7 Gyr, at which no signature is found in the rest-frame colour
evolution is found (cf. Fig. 18 (click here)), the constancy of the red-shift
at which the dip is found strongly argues against any possible evolutionary
interpretation of this latter.
In order to prove this statement, we examine
how the ISED of Models A and B vary with age.
This is shown in Fig. 21 (click here), which displays for three selected values of
the age the rest-frame ISED of Model A and B in the wavelength region
. In Model A (only P-AGB dominating the
UV flux), the shape of the ISED does not vary with time at any significant
level over a large range of ages. The only effect to be noticed is that
the level of the flux in the 
region increases with the age. In contrast in Model B both the shape and the
flux level significantly vary with the age passing from 5 Gyr to older
galaxies. The reason of it is easy to understand.
In Model A, over the age range under consideration the source of UV flux are
P-AGB of nearly identical 
with nearly identical ISED. In
contrast, in Model B both P-AGB and H-HB stars intervene, whose 
and
resulting ISED greatly vary with time. Therefore, in the case of Model A
the minimum in the colour 
simply reflects the gradual effect
of the red-shift transferring radiation from one pass-band to the other. Since
there is no age effect, the red-shift at which the reversal of the colour
trend occurs does not depend on the 
and 
. In the case of
Model B the onset of the H-HB and AGB-manqué stars changes both the shape
and intensity of the ISED. Therefore a real age term is present whose
effect is to make the colour-red-shift relation vary
with 
and 
.
As a result of this analysis, only the colour 
might be
a promising age indicator.
Changing the Hubble constant 
from 50 to
80 
(Figs. 22 (click here) and 23 (click here)) we get
similar results for 
, but very different ones for 
.
In this latter case, the maximum galaxy ages are so young that the
contribution from the above stellar sources to the UV radiation are almost lost.
Although the red-shift dependence of the colours 
and
does no longer allow us to discriminate between H-HB and
P-AGB dominated UV emission, its remarkable difference with respect
to those for the other values of 
and 
might turn out to
be useful to set constraints on the cosmological parameters rather than
on the age.
Although promising, the results of the above analysis could be somewhat
weakened by two remarks. First,
the HST UV filters suffer from a strong/visible
red leak. It is very plausible that they might be
sensitive to other kind of emissions such as that caused by
residual bursts of star
formation still emitting in the visible, nebular emissions... which
could make the age dependence of the colour 
less significant.
Second, the intensity of the UV emission is known to vary
with the distance from the galactic centre, being more
intense in the nuclear than in the external regions. To this aim
see for instance the
change of UV colour (1500-2200) in NGC 1399, M 31, and M 81 with the radial
distance (O'Connell 1992). Disentangling whether this is an age or a metallicity
effect is a cumbersome affair. Certainly it reflects different types
of stars generating the UV flux. Bressan et al. (1996) studying the narrow band
indices 
and 
of the Gonzales (1993) sample of galaxies
(ellipticals) suggest that the vast
majory of these have the nuclear region younger and more metal-rich than the
peripheral regions.
Unless the central
regions of these galaxies
have sufferend from a very recent episode of star formation,
they are the natural site
to look at in which H-HB and AGB-manqué stars can be found, whose UV
emission should vary with time as shown in Fig. 18 (click here). In the remaining
part of the galaxy the UV emission should be generated by the ever present
P-AGB
stars. Going to higher and higher red-shifts, with a given aperture of the
detecting instument, a larger volume of the galaxy is sampled so that
the different sources of UV radiation are more and
more mixed together, thus diluting
the signatures of each component.
Despite the above remarks, what we learn from these examples is that using
observations in the UV at different red-shifts, we can perhaps pin down
the dominant
source of UV radiation, constrain the relation between 
, 
and
and in principle determine the age of galaxies.
However, it
is beyond the aims of this paper to further
investigate the problem, which is left to future studies.