As well known, theoretical predictions of cluster colours make use of suitable libraries of evolutionary tracks to produce synthetic stellar clusters, i.e., to simulate the CM distribution of stars for each given assumption about the cluster age and original chemical composition. In such a procedure, one is usually neglecting faint evolutionary phases which cannot sensitively contribute to the total cluster luminosity. However, since synthetic stellar clusters are of relevance in a much more general context than in predicting colours, the evolutionary library adopted in Paper I has been implemented to cover with suitable theoretical predictions all the evolutionary phases of cluster stars, from the Very Low Mass MS stars, at the lower mass limit for H burning ignition, to the final sequence of cooling White Dwarfs. As a result, with the present libraries the program can produce "complete" synthetic clusters in the range of ages 50 Myr to 20 Gyr and for metallicity from Z=0.0001 to Z=0.02. Figure 1 gives an example of these predictions, as given for a synthetic cluster with the given values of age and chemical composition.
In the present form, the bulk of the code relies on the set of
homogeneous evolutionary computations presented by Straniero &
Chieffi (1991), Castellani et al. (1991),
Castellani et al. (1992a),
Cassisi et al. (1994),
covering both the H and the He burning phase for stars with original
masses in the range
and where the He burning
phase is followed till the Carbon ignition or, alternatively, the
onset of the thermal pulse phase. In the last case, the relevant one
for old globulars, the tracks have been prolonged through the thermal
pulse phase according to the semianalitical procedure envisaged by
Groenewegen & De Jong (1993, see also Marigo et al. 1996). The above
evolutionary computations have been implemented with theoretical
predictions about VLM structures from Cassisi et al. (2000) whereas
cooling White Dwarf sequences have been finally evaluated according to
the Brocato et al. (1999b) procedure, as based on
evolutionary data by Wood (1992).
A detailed description of the program can be found in Poli (1997) and Paper I.
Here we notice that mass loss has been taken into account by
adopting Reimers formula
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(1) |
To orientate the reader in such a scenario, Fig. 2 gives the
predicted mass and effective temperature of new born HB stars as a
function of
for selected assumption about the cluster age or
metallicity.
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Figure 2:
Predicted masses and temperatures of HB stars as a function of ![]() |
For each given age and chemical composition and for each given
assumption on ,
we make use of the above procedure to evaluate
the original mass of the star at the tip of the red giant branch and
the amount of mass lost, deriving from these values, the mass of the
HB star, its CM diagram location and the lifetime in the HB
phase. This lifetime is used to derive the number of expected HB stars
(
)
through a suitable proportion with the proper RGB
lifetime and the already known number of RGB stars.
As well known, the HB colour distribution observed in the galactic globulars
has to be interpreted as an evidence for a dispersion in HB
masses, as due to a dispersion in the amount of mass loss. To simulate
this occurrence, we follow the prescriptions early given by Rood (1973) by assuming the computed HB mass as
the mean value of a stochastic distribution of masses with a given standard deviation,
normally in the range
.
For each given HB
mass, the star is put on its evolutionary track with a random fraction
of its He burning lifetime, still evaluating the amount of mass
loss (Reimers) during the rising along the AGB phase.
As derived by Fig. 4 of
Castellani et al. (1992b),
if and when the mass of the H-rich envelope decreases
below a critical value
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(2) | |
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-4.1 | 12 | 0.005 | 0.01 |
-5.9 | 74 | 0.03 | 0.08 |
-6.7 | 146 | 0.07 | 0.15 |
-7.5 | 288 | 0.13 | 0.30 |
-7.9 | 436 | 0.20 | 0.46 |
-8.5 | 730 | 0.33 | 0.77 |
-9.0 | 1166 | 0.53 | 1.22 |
-10.0 | 2904 | 1.32 | 3.08 |
-11.0 | 7304 | 3.32 | 7.74 |
-12.0 | 18326 | 8.33 | 19.45 |
Assuming cluster ages in the range 10-15 Gyr, from preliminary
computations we find that the assumption
appears able
to nicely reproduce the observed dependence of the HB type on
metallicity, when the occurrence of a second parameter is not taken
into account. This is shown in Fig. 3, where we report the predicted
CM diagram for cluster with an age of 15 Gyr and for the various
labelled assumptions about the metallicity, adopting Yale
(http://shemesh.gsfc.nasa.gov/iso/color.tblextg)
colour temperature relations and bolometric corrections.
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Figure 3: Predicted CM diagrams for clusters with age t=15 Gyr and for the labelled assumptions on the metallicity Z |
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