Analytic formulae are presented to construct detailed secular lightcurves of both early asymptotic giant branch ( AGB ) and thermally pulsing AGB stars .
They are based on an extensive grid of evolutionary calculations , performed with an updated stellar evolution code .
Basic input parameters are the initial mass M _ { \mathrm { i } } , 0.8 \leq M _ { \mathrm { i } } / M _ { \odot } \leq 7 , metallicity Z _ { \mathrm { i } } = 0.0001 , 0.008 , 0.02 , and the mixing length theory ( MLT ) parameter .
The formulae allow for two important effects , namely that the first 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 relations of the usual type .

Furthermore , the dependence of the effective temperature and a few other quantities characterizing the conditions at the base of the convective envelope , which are relevant for HBB , are investigated as functions of luminosity , total and core mass for different formulations of the convection theory applied , MLT or Canuto & Mazzitelli ’ s ( [ 1991 ] ) theory .