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.
|Figure 1: The predicted CM diagram location of stars in a cluster with age t=15 Gyr and Y=0.23, Z=0.001, with a suitable simulation of photometric uncertainties. is the mass of Main Sequence star at the corresponding luminosity level; is the mass of the star at the Turn Off point; is the mass at the RGB tip; gives the actual mean value of HB stars after mass loss, whereas the two labelled values give the progenitor mass (i.e. the mass in MS) of the stars along the WD sequence|
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
To orientate the reader in such a scenario, Fig. 2 gives the
predicted mass and effective temperature of new born HB stars as a
for selected assumption about the cluster age or
|Figure 2: Predicted masses and temperatures of HB stars as a function of for the labelled assumptions about the cluster age or metallicity|
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
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.
|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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