We present new synthetic models of the TP-AGB evolution .
They are computed for 7 values of initial metal content ( Z from 0.0001 to 0.03 ) and for initial masses between 0.5 and 5.0 M _ { \odot } , thus extending the low- and intermediate-mass tracks of Girardi et al .
( 2000 ) until the beginning of the post-AGB phase .
The calculations are performed by means of a synthetic code that incorporates many recent improvements , among which we mention : ( 1 ) the use of detailed and revised analytical relations to describe the evolution of quiescent luminosity , inter-pulse period , third dredge-up , hot bottom burning , pulse cycle luminosity variations , etc .
; ( 2 ) the use of variable molecular opacities – i.e .
opacities consistent with the changing photospheric chemical composition – in the integration of a complete envelope model , instead of the standard choice of scaled-solar opacities ; ( 3 ) the use of formalisms for the mass-loss rates derived from pulsating dust-driven wind models of C- and O-rich AGB stars ; and ( 4 ) the switching of pulsation modes between the first overtone and the fundamental one along the evolution , which has consequences in terms of the history of mass loss .
It follows that , in addition to the time evolution on the HR diagram , the new models predict in a consistent fashion also variations in surface chemical compositions , pulsation modes and periods , and mass-loss rates .
The onset and efficiency of the third dredge-up process are calibrated in order to reproduce basic observables like the carbon star luminosity functions in the Magellanic Clouds , and TP-AGB lifetimes ( star counts ) in Magellanic Cloud clusters .
In this paper , we describe in detail the model ingredients , basic properties , and calibration .
Particular emphasis is put in illustrating the effects of using variable molecular opacities .
Forthcoming papers will present the theoretical isochrones and chemical yields derived from these tracks , and additional tests performed with the aid of a complete population synthesis code .