Theoretical Hertzsprung-Russell diagrams (HRD) for the ensemble of our models are shown in Fig. 1 (click here), from the early PMS phase up to the beginning of the first thermal pulse (or He-shell flash) along the AGB phase.
Figure 1:
Theoretical HRD, from the beginning of the PMS phase up to the beginning
of the first thermal pulse along the AGB phase, for Z = 0.02 (left) and
Z = 0.005 (right)
The lifetimes are given in Table 1 (click here) for the PMS, the H-burning phase (from the zero-age-main sequence to central H-exhaustion), the RGB phase (from central H-exhaustion to central He-ignition), the He-burning phase (up to central He-exhaustion), the early (E) AGB phase (up to the first thermal pulse) and the thermally pulsing (TP) AGB phase. This last duration includes our extrapolation procedure up to the convective envelope exhaustion (see Sect. 6.3).
Table 1:
Lifetimes in all the evolutionary phases for the modeled stars which
undergo thermal pulses
The occurrence of the first thermal pulse marks the end of the E-AGB phase
and the beginning of the TP-AGB phase. This precise time, marked by the
maximum surface luminosity just preceding the first major thermal
instability, will be called 
in the following. Table 2 (click here) presents
some characteristics of our models at 
.
Table 2:
Main features concerning the internal and surface structure of our
models at the end of the E-AGB phase. [He] ([H]) specifies values
taken at the maximum energy production rate in the helium (hydrogen)
burning shell. [H-He] refers to the inter-shell region (i.e. between
the HeBS top and the HBS base) and [env] to the convective envelope
bottom. 
is the mass thickness of a region
For the main sequence duration, our results for Z = 0.02 are in better agreement with Bressan et al. (1993) predictions than with the slightly higher values given by Schaller et al. (1992). The central helium burning lifetime crucially depends on the amount of overshooting. As our stellar models are computed without overshooting, we can only compare our predictions at this phase with those of the Padova group calculated in the same conditions; we obtain very similar results.
The other important quantity for the AGB phase is the core mass (i.e.
the mass contained up to the HBS) at the end of the central He-burning
phase. Indeed, its value determines the surface luminosity (through the
core mass-luminosity relation; see e.g. Boothroyd & Sackmann 1988a), the
mass loss rate, and consequently the AGB phase duration. Last but not
least, along the TP-AGB phase, the thermal pulses are stronger and the
third dredge-up deeper when the core mass is higher. Our 
star
with Z = 0.02 enter the AGB phase with a core mass of 
(see
Table 2 (click here)), a value very close to that of the comparable model of
Boothroyd & Sackmann (1988a) or Lattanzio (1986), also computed without
overshooting. Always for a reference 
star, the TP-AGB phase
of the Straniero et al. (1995) models begins with a core mass of
(2 % lower). At a comparable evolution stage however,
the 
TP-AGB star of Vassiliadis & Wood (1993), also computed
without any kind of extra-mixing, has a core mass 
% higher than
ours. This could be due to the somewhat lower metallicity of their models
(Z = 0.016). In conclusion, the core mass at the beginning of the
TP-AGB phase, although very important for this phase, still depends on
various uncertainties related to the treatment of convection during the
previous evolutionary phases.