New input data for synthetic AGB evolution

Analytic formulae are presented to construct detailed secular lightcurves o f both early asymptotic giant branch (AGB) and thermally pulsing AGE stars. They are based on an extensive grid of evolutionary calculations, performe d with an updated stellar evolution code. Basic input parameters are the in itial mass M-i, 0.8 less than or equal to M-i/M. less than or equal to 7, m etallicity Z(i) = 0.0001, 0.008, 0.02, and the mixing length theory (MLT) p arameter. The formulae allow for two important effects, namely that the fir st pulses do not reach the full amplitude, and hot bottom burning (HBB) in massive stars, which are both not accounted for by core mass luminosity rel ations of the usual type. Furthermore, the dependence of the effective temperature and a few other qu antities characterizing the conditions at the base of the convective envelo pe, which are relevant for HBB, are investigated as functions of luminosity , total and core mass for different formulations of the convection theory a pplied, MLT or Canuto & Mazzitelli's (1991) theory.